Full Code of ytakano/blisp for AI

Repository: ytakano/blisp
Branch: master
Commit: b0ae5499141f
Files: 26
Total size: 603.8 KB

Directory structure:
gitextract_wiwtvaga/

├── .gitignore
├── Cargo.toml
├── LICENSE
├── README.md
├── docs/
│   ├── Makefile
│   ├── index.adoc
│   ├── index.html
│   ├── index.ja.adoc
│   └── index.ja.html
├── embed_macro/
│   ├── Cargo.toml
│   ├── LICENSE
│   ├── README.md
│   └── src/
│       └── lib.rs
├── history.md
├── specification/
│   ├── Makefile
│   ├── language.md
│   └── typing.tex
├── src/
│   ├── coq.rs
│   ├── lib.rs
│   ├── macro.rs
│   ├── parser.rs
│   ├── prelude.lisp
│   ├── runtime.rs
│   └── semantics.rs
└── tests/
    ├── embedded.rs
    └── transpile.rs

================================================
FILE CONTENTS
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================================================
FILE: .gitignore
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target/
Cargo.lock
.DS_Store


================================================
FILE: Cargo.toml
================================================
[package]
name = "blisp"
version = "0.4.7"
authors = ["Yuuki Takano <ytakanoster@gmail.com>", "Fumiya Saito"]
edition = "2021"
description = "A lisp like statically typed programing language for no_std."
repository = "https://github.com/ytakano/blisp"
keywords = [
    "no_std",
    "scripting",
    "scripting-engine",
    "scripting-language",
    "embedded",
]
categories = ["no-std", "embedded"]
license-file = "LICENSE"
readme = "README.md"
homepage = "https://ytakano.github.io/blisp/"

# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html

[dependencies]
blisp_embedded = "0.1"

[dependencies.num-bigint]
version = "0.4"
default-features = false

[dependencies.num-traits]
version = "0.2"
default-features = false
features = ["libm"]

[lib]
crate-type = ["rlib"]


================================================
FILE: LICENSE
================================================
MIT License

Copyright (c) 2020 Yuuki Takano <ytakano@wide.ad.jp>, Fumiya Saito

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


================================================
FILE: README.md
================================================
# BLisp

BLisp is a statically typed Lisp like programming language which adopts effect system for no_std environments.
BLisp supports higher order RPC like higher order functions of functional programming languages.

This repository provides only a library crate.
Please see [blisp-repl](https://github.com/ytakano/blisp-repl) to use BLisp,
and [baremetalisp](https://github.com/ytakano/baremetalisp) which is a toy OS.

**[Homepage](https://ytakano.github.io/blisp/) is here.**

## Features

- Algebraic data type
- Generics
- Hindley–Milner based type inference
- Effect system to separate side effects from pure functions
- Hygienic macro expansion for local binders introduced by macro templates
- Big integer
- Supporting no_std environments

## How to Use

```rust
use blisp;

fn main() {
    let code = "(export factorial (n) (Pure (-> (Int) Int))
    (if (<= n 0)
        1
        (* n (factorial (- n 1)))))";
    let exprs = blisp::init(code, vec![]).unwrap();
    let ctx = blisp::typing(exprs).unwrap();

    let e = "(factorial 10)";
    blisp::eval(e, &ctx).unwrap();
}
```

If Rust compiler or linker says warning of fmod,
please add fmod manually as follows.

```rust
#[no_mangle]
extern "C" fn fmod(x: f64, y: f64) -> f64 {
    libm::fmod(x, y)
}
```

Cargo.toml

```toml
[dependencies.blisp]
version = "0.4"
```

## Examples

```lisp
"Hello, World!" ; "Hello, World!"
(+ 0x10 0x20)   ; 48
(+ 0b111 0b101) ; 12
(+ 0o777 0o444) ; 803
(car '(1 2 3))  ; (Some 1)
(cdr '(1 2 3))  ; '(2 3)
(map (lambda (x) (* x 2)) '(8 9 10)) ; '(16 18 20)
(fold + 0 '(1 2 3 4 5 6 7 8 9))      ; 45
(reverse '(1 2 3 4 5 6 7 8 9))       ; '(9 8 7 6 5 4 3 2 1)
(filter (lambda (x) (= (% x 2) 0)) '(1 2 3 4 5 6 7 8 9)) ; '(2 4 6 8)
```


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FILE: docs/Makefile
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all: index.html index.ja.html

index.html: index.adoc
	asciidoctor index.adoc

index.ja.html: index.ja.adoc
	asciidoctor index.ja.adoc


================================================
FILE: docs/index.adoc
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= BLisp: A Statically Typed Lisp Like Language
Yuuki Takano <ytakano@wide.ad.jp>
v0.4.0, 2023-02
:doctype: article
:toc:
:sectnums:
:encoding: utf-8
:stem: latexmath
:source-highlighter: pygments


BLisp is a statically typed Lisp like programming language which adopts effect system for no_std environments.
BLisp supports higher order RPC like higher order functions of functional programming languages.

* https://github.com/ytakano/blisp[GitHub's Repository]
* https://crates.io/crates/blisp[BLisp's crates.io]

This repository provides only a library crate.
Please see https://github.com/ytakano/blisp-repl[blisp-repl] to use BLisp,
and https://github.com/ytakano/baremetalisp[baremetalisp] which is a toy OS.

https://ytakano.github.io/blisp/index.ja.html[日本語版はこちら]

.BLisp on no_std Environment
image:https://cdn-ak.f.st-hatena.com/images/fotolife/y/ytakano/20210221/20210221155657.gif[BLisp on no_std Environment]

== Features

* Algebraic data type
* Generics
* Hindley–Milner based type inference
* Effect system to separate side effects from pure functions
* Big integer
* Supporting no_std environments

== Values

.values
[source, lisp]
----
`A`       ; character literal
"Hello"   ; string literal
144       ; integer value
0xabcDEF  ; hexadecimal
0o777     ; octal
0b1001    ; binary
true      ; boolean value
false     ; boolean value
[true 10] ; tuple
[]        ; empty tuple
'(1 2 3)  ; list
'()       ; empty list, Nil
----

== Basic Types

.types
[source, lisp]
----
Char       ; character
String     ; string
Int        ; signed integer
Bool       ; boolean
'(Int)     ; list of Int
[Int Bool] ; tuple of Int and Bool
(Pure (-> (Int Int) Bool)) ; Pure function, which takes 2 integers and return boolean value
(IO (-> (Int) [])) ; IO function, which takes an integer and return []
----

Pure and IO are function effects.
In IO functions, both Pure and IO functions can be called.
However, in Pure functions, calling only Pure functions is permitted.

== Function Definition

Functions can be defined by defun or export.
"defun" defines a local function which cannot be called from Rust's eval function.

Suppose following 2 functions.

.defun
[source, lisp]
----
(defun double (x)         ; function name is "double" and "x" is an argument
    (Pure (-> (Int) Int)) ; function Type
    (* 2 x))              ; function body
----

.export
[source, lisp]
----
(export quad (x)          ; function name is "quad" and "x" is an argument
    (Pure (-> (Int) Int)) ; function Type
    (double (double x)))  ; function body
----

double cannot be called from Rust's eval, but can be called from internally defined functions.
quad can be called from Rust's eval, and it calls double internally.

This is the code what actually do in Rust.

.Rust's eval
[source, rust]
----
use blisp;

fn eval(e: &str, ctx: &blisp::semantics::Context) {
    // evaluate expressions
    let exprs = match blisp::eval(e, ctx) {
        Ok(es) => es,
        Err(err) => {
            println!("error:{}:{}: {}", err.pos.line, err.pos.column, err.msg);
            return;
        }
    };

    for r in exprs {
        match r {
            Ok(msg) => {
                println!("{}", msg);
            }
            Err(msg) => {
                println!("error: {}", msg);
            }
        }
    }
}

fn main() {
    // internal code
    let code = "
(defun double (x)         ; function name is double and x is an argument
    (Pure (-> (Int) Int)) ; function Type
    (* 2 x))              ; function body

(export quad (x)          ; function name is quad and x is an argument
    (Pure (-> (Int) Int)) ; function Type
    (double (double x)))  ; function body
";
    let exprs = blisp::init(code, vec![]).unwrap();
    let ctx = blisp::typing(&exprs).unwrap();

    let e = "(double 10) ; error";
    eval(e, &ctx);

    let e = "(quad 10) ; OK";
    eval(e, &ctx);
}
----

This code output as follows.

 error:0:1: Typing Error: double is not defined
 40

== Arithmetic Operations

.basic
[source, lisp]
----
; (Pure (-> (Int Int) Int))
(+ 10 20)
(- 30 40)
(* 6 100)
(/ 100 2)
(% 10 3)
----

== Boolean Operations

.logical
[source, lisp]
----
; (Pure (-> (Bool Bool) Bool))
(and true false)
(or true false)
(xor true false)
----

.negation
[source, lisp]
----
; (Pure (-> (Bool) Bool))
(not true)
----

== Comparison

=, !=, <, >, \<=, >= can be used for 2 values whose types are same.

.comparison between 2 values whose types are same
[source, lisp]
----
; (Pure (-> (t t) Bool))
(= 4 4)               ; true
(!= 4 4)              ; false
(= "Hello" "Hello")   ; true
(= (Some 1) (Some 2)) ; false
(< 6 7)
(> 6 7)
(<= 30 40)
(>= 30 40)
(< "Hello" "World")
(<= (Some 1) (Some 2))
----

_eq_, _neq_, _lt_, _gt_, _leq_, _geq_ can be used for any 2 values

.comparison between any 2 values
[source, lisp]
----
; (Pure (-> (t1 t1) Bool))
(geq (Some 1) "Hello") ; (Some 1) is greater than or qeual to "Hello"
(eq "Hello" 100)       ; Is "Hello" qeual to 100?
(neq "Hello" 100)      ; Is "Hello" not equal to 100?
(lt 100 (Some 20))     ; Is 100 less than (Some 20)?
(gt 200 "Hello")       ; Is 200 greater than "Hello"
----

== Bitwise Operations

[source, lisp]
----
(band 1 0) ; bitwise and
(band 1 1) ; bitwise and
(bor 1 0)  ; bitwise or
(bor 1 1)  ; bitwise or
(bxor 1 0) ; bitwise xor
----

.bit shift
[source, lisp]
----
; (Pure (-> (Int Int) (Option Int)))
(<< 8 4)   ; (Some 128)
(>> 128 4) ; (Some 8)
(>> -128 4) ; (Some -8)
----

If 2nd argument is greater or equal to 2^64^, then these function return None.

== Mathematical Operations

[source, lisp]
----
; (Pure (-> (Int Int) (Option Int)))
(pow 10 20) ; (Some 100000000000000000000)

; (Pure (-> (Int) (Option Int)))
(sqrt 16)   ; (Some 4)
----

If _pow_'s exponent portion is greater or equal to 2^32^, then _pow_ returns None.

If _sqrt_'s argument is less than 0. then _sqrt_ returns None.

== Algebraic Data Type

Algebraic data type can be defined as follows.

[source, lisp]
----
; in BLisp
(data Cardinal ; type name
    East       ; value
    North      ; value
    West       ; value
    South)     ; value
----

Type name's and its value's first character must be uppercase.
This is equivalent to Rust's following code.

[source, rust]
----
// in Rust
enum Cardinal {
    East,
    North,
    West,
    South
}
----

Each element can have values as follows.

[source, lisp]
----
; in BLisp
(data Dim2
    (Dim2 Int Int)) ; Dim2 has integers
----

Dim2 can be instantiated as follows.

[source, lisp]
----
(Dim2 10 20)
----

This type is equivalent to Rust's following type.

[source, rust]
----
// in Rust
use num_bigint::BigInt;
enum Dim2 {
    Dim2(BigInt, BigInt)
}
----

== Generics

Option and Result types are defined internally.

[source, lisp]
----
(data (Option t)
    (Some t)
    None)

(data (Result t e)
    (Ok t)
    (Err e))
----

_t_ and _e_ are type variables.
This code is equivalent to Rust's following code.

[source, rust]
----
// in Rust
enum Option<T> {
    Some(T),
    None,
}

enum Result<T, E> {
    Ok(T),
    Err(E),
}
----

List type is a built-in type as follows.

[source, lisp]
----
(data (List t)
    (Cons t (List t))
    Nil)
----

So, following 2 lists are equivalent.

[source, lisp]
----
(Cons 1 (Cons 2 (Cons 3 Nil)))
'(1 2 3)
----

== Generic Function

_car_ and _cdr_ are internally defined generic functions.
These definitions are as follows.

[source, lisp]
----
(export car (x) (Pure (-> ('(t)) (Option t)))
    (match x
        ((Cons n _) (Some n))
        (_ None)))

(export cdr (x) (Pure (-> ('(t)) '(t)))
    (match x
        ((Cons _ l) l)
        (_ '())))
----

_t_ is a type variable. These functions can be used as follows.

[source, lisp]
----
(car '(3 8 9))  ; returns (Some 3)
(cdr '(8 10 4)) ; returns '(10 4)
----

Normal and type variables' first character must be lowercase.

== If Expression

Straightforward.

[source, lisp]
----
(if (< 10 20)
    '(1 2 3)
    '())
----

== Match Expression

A list can be matched as follows.

[source, lisp]
----
(match '(1 2 3)
    ((Cons n _) n)
    ('() 0))
----

The expression

 (Cons n _)

is a pattern.
If the pattern is matched to '(1 2 3), 1 is assigned to a variable _n_. Then, _n_, namely 1, is returned.

This is an example of pattern matching of tuple.

[source, lisp]
----
(match [1 3]
    ([x y] [y x]))
----

This code swap 1st and 2nd elements of the tuple.

Integer values can be also used for pattern matching.

[source, lisp]
----
(match 20
    (20 true)
    (_ false))
----

More complex example is a as follows.

[source, lisp]
----
(match [(Some 10) true]
    ([(Some 10) false] 1)
    ([(Some 10) true] 2)
    (_ 0))
----

BLisp checks exhaustively of pattern.
So, following code will be rejected.

[source, lisp]
----
(match '(1 2)
    ('() 0))
----

== Let Expression

Let expression is used to bind variables as follows.

[source, lisp]
----
(let ((x 10) (y 20)) ; x is 10, y is 20
    (* x y))

(let ((x 10) (x (* x x)) (x (* x x))) ; x = 10, x = x * x, x = x * x
    x)
----

Destructuring can be also performed as follows.

[source, lisp]
----
(let (((Some x) (Some 10))) ; x is 10
    (* x 2))

(let (([x y] [10 20])) ; x is 10, y is 20
    (* x y))
----

== Lambda Expression

Lambda expression is defined as follows.

[source, lisp]
----
(lambda (x y) (* x y))
----

This lambda takes 2 integers and return the multiplication.
Applying arguments to this is simple as follows.

[source, lisp]
----
((lambda (x y) (* x y)) 10 20)
----

Every lambda expression is Pure.
IO functions cannot be called in any lambda expressions.

_map_ and _fold_ functions are internally defined as follows.

[source, lisp]
----
(export map (f x) (Pure (-> ((Pure (-> (a) b)) '(a)) '(b)))
    (match x
        ((Cons h l) (Cons (f h) (map f l)))
        (_ '())))

(export fold (f init x) (Pure (-> ((Pure (-> (a b) b)) b '(a)) b))
    (match x
        ((Cons h l) (fold f (f h init) l))
        (_ init)))
----

_map_ can be used to apply functions to elements of a list as follows.

[source, lisp]
----
; square each element
(let ((l '(1 2 3))
      (f (lambda (x) (* x x))))
        (map f l))
----

_fold_ can be used to calculate over elements of a list.
For example, summation can be computed as follows.

[source, lisp]
----
; summation
(let ((l '(20 50 60))
      (f (lambda (x y) (+ x y))))
        (fold f 0 l)) ; 0 is an initial value
----

Of course, this can be written as follows.

[source, lisp]
----
; summation
(fold + 0 '(20 50 60))
----

== Macro

Macros can be defined by `macro`.
Each rule consists of a pattern and a template, and the first matching rule is expanded.

[source, lisp]
----
(macro add
    ((add $e1 $e2) (+ $e1 $e2))
    ((add $e1 $e2 $e3 ...) (+ $e1 (add $e2 $e3 ...))))
----

Identifiers beginning with `$` are pattern variables.
They are substituted with the expressions matched at the call site.
`...` can be used after a pattern variable or a template fragment to match and expand the remaining arguments.

[source, lisp]
----
(add 1 2)         ; 3
(add 1 2 3 4 5)   ; 15
----

Macros can also generate expressions that introduce local bindings.
For example, a temporary variable can be introduced in a lambda expression.

[source, lisp]
----
(macro with_tmp
    ((_ $x) ((lambda (tmp) (+ tmp $x)) 1)))

(export test (tmp) (Pure (-> (Int) Int))
    (with_tmp tmp))
----

BLisp macros are hygienic for local binders introduced by macro templates.
Variables introduced by `lambda` arguments, `let` bindings, and `match` pattern variables are renamed to fresh internal names during expansion, so they do not capture variables from the call site.
Top-level names such as `defun`, `export`, and `data` definitions are not renamed automatically.

== String and Character

_chars_ converts String to (List Char).

[source, lisp]
----
; (Pure (-> (String) (List Char)))
(chars "Hello") ; '(`H` `e` `l` `l` `o`)
----

_str_ converts (List Char) to String.

[source, lisp]
----
; (Pure (-> ((List Char)) String))
(str '(`H` `e` `l` `l` `o`)) ; "Hello"
----

== Foreign Function Interface

_blisp::embedded_ is a macro for foreign function interface.
By using this, Rust's functions can be called from BLisp easily.

For example, first of all, define a Rust function as follows.

[source, rust]
----
use blisp::embedded;
use num_bigint::{BigInt, ToBigInt};

#[embedded]
fn add_four_ints(a: BigInt, b: (BigInt, BigInt), c: Option<BigInt>) -> Result<BigInt, String> {
    let mut result = a + b.0 + b.1;
    if let Some(n) = c {
        result += n;
    }

    Ok(result)
}
----

_blisp::embedded_ macro generates a type definition for FFI.
This function can be called from BLisp as follows.

[source, lisp]
----
(export call_add_four_ints (n)
    (IO (-> ((Option Int)) (Result Int String)))
    (add_four_ints 1 [2 3] n))
----

To register FFIs, a vector of the definition generated by _embedded_ macro
must be passed to _blisp::init_ as follows.

[source, rust]
----
// add_for_ints
let code = "(export call_add_four_ints (n)
    (IO (-> ((Option Int)) (Result Int String)))
    (add_four_ints 1 [2 3] n)
)";
let exprs = blisp::init(code, vec![Box::new(AddFourInts)]).unwrap();
let ctx = blisp::typing(exprs).unwrap();
let result = blisp::eval("(call_add_four_ints (Some 4))", &ctx).unwrap();
----

The function name is _add_four_ints_, then _AddFourInts_, which is camel case,
must be passed to _blisp::init_ capsulated by _Box_ and _Vec_.

FFIs in Rust take and return only types described as follows.
Other types, like _Vec<u64>_, are not supported,
but _Vec<Option<bool>>_ is accepted.
Types between BLisp and Rust are automatically converted by
the function generated by _embedded_ macro.

.Type Conversion between BLisp and Rust
|===
|BLisp          | Rust

|_Int_          | _BigInt_
|_Bool_         | _bool_
|_Char_         | _char_
|_String_       | _String_
|_'(T)_         | _Vec<T>_
|_[T0, T1]_     | _(T0, T1)_
|_(Option T)_   | _Option<T>_
|_(Result T E)_ | _Result<T, E>_
|===

Note that every FFI is treated as IO functions.

== Transpilation to Coq (Experimental)

BLisp experimentally implements a transpiler to Coq.
It can be invoked by calling _blisp::transpile_ as follows.

[source, coq]
----
let expr = "
(defun snoc (l y)
(Pure (-> (
    '(t) t)
'(t)))
(match l
    (nil (Cons y nil))
    ((Cons h b) (Cons h (snoc b y)))))

(defun rev (l)
(Pure (-> (
    '(t))
'(t)))
(match l
    (nil nil)
    ((Cons h t) (snoc (rev t) h))))
    ";
let exprs = blisp::init(expr, vec![]).unwrap();
let ctx = blisp::typing(exprs).unwrap();

println!("{}", blisp::transpile(&ctx));
----

This outputs Coq code as follows.
It includes as well as the prelude of BLisp.

[source, coq]
----
Require Import ZArith.
Require Import Coq.Lists.List.

Inductive Option (t: Type): Type :=
| Some (x0: t)
| None.

Arguments Some{t}.
Arguments None{t}.

Inductive Result (t e: Type): Type :=
| Ok (x0: t)
| Err (x0: e).

Arguments Ok{t e}.
Arguments Err{t e}.

Definition car {t: Type} (x: list t): Option t :=
match x with
  | (cons n _) => (Some n)
  | _ => (None)
  end.

Definition cdr {t: Type} (x: list t): list t :=
match x with
  | (cons _ l) => l
  | _ => nil
  end.

Definition filter {t: Type} (f: t -> bool) (x: list t): list t :=
(reverse (filter' f x nil ) ).

Fixpoint filter' {t: Type} (f: t -> bool) (x l: list t): list t :=
match x with
  | (cons h a) => match (f h ) with
    | true => (filter' f a (cons h l) )
    | false => (filter' f a l )
    end
  | _ => l
  end.

Fixpoint fold {a b: Type} (f: a -> b -> b) (init: b) (x: list a): b :=
match x with
  | (cons h l) => (fold f (f h init ) l )
  | _ => init
  end.

Fixpoint map {a b: Type} (f: a -> b) (x: list a): list b :=
match x with
  | (cons h l) => (cons (f h ) (map f l ))
  | _ => nil
  end.

Fixpoint rev {t: Type} (l: list t): list t :=
match l with
  | nil => nil
  | (cons h t) => (snoc (rev t ) h )
  end.

Definition reverse {t: Type} (x: list t): list t :=
(reverse' x nil ).

Fixpoint reverse' {t: Type} (x l: list t): list t :=
match x with
  | (cons h a) => (reverse' a (cons h l) )
  | _ => l
  end.

Fixpoint snoc {t: Type} (l: list t) (y: t): list t :=
match l with
  | nil => (cons y nil)
  | (cons h b) => (cons h (snoc b y ))
  end.
----

Not that this transpiler is experimental.
So, Coq cannot interpret some outputs.
Please fix it manually when you encounter that situation.
It is probably easy.

== Examples

=== Reverse

_reverse_ is a internally defined function. It reverses order of a list.

[source, lisp]
----
(reverse '(1 2 3 4 5 6 7 8 9))
----

This outputs as follows.

 '(9 8 7 6 5 4 3 2 1)

=== Filter

_filter_ is a internally defined function. It filters the elements in a list.

[source, lisp]
----
(filter (lambda (x) (= (% x 2) 0)) '(1 2 3 4 5 6 7 8 9))
----

This outputs as follows.

 '(2 4 6 8)

_filter_'s type is as follows.

[source, lisp]
----
(Pure (->
    ((Pure (-> (t) Bool)) ; take a function
     '(t))                ; take a list
    '(t))) ; return a list
----

=== Factorial

Tail call factorial can be coded as follows.

[source, lisp]
----
(export factorial (n) (Pure (-> (Int) Int))
    (fact n 1))

(defun fact (n total) (Pure (-> (Int Int) Int))
    (if (<= n 0)
        total
        (fact (- n 1) (* n total))))
----

This function can be called as follows.

 >> (factorial 10)
 3628800
 >>
 >> (factorial 1000)
 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 >>
 >> (factorial 100)
 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
 >>
 >> (factorial 500)
 1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000


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<body class="article">
<div id="header">
<h1>BLisp: A Statically Typed Lisp Like Language</h1>
<div class="details">
<span id="author" class="author">Yuuki Takano</span><br>
<span id="email" class="email"><a href="mailto:ytakano@wide.ad.jp">ytakano@wide.ad.jp</a></span><br>
<span id="revnumber">version 0.4.0,</span>
<span id="revdate">2023-02</span>
</div>
<div id="toc" class="toc">
<div id="toctitle">Table of Contents</div>
<ul class="sectlevel1">
<li><a href="#_features">1. Features</a></li>
<li><a href="#_values">2. Values</a></li>
<li><a href="#_basic_types">3. Basic Types</a></li>
<li><a href="#_function_definition">4. Function Definition</a></li>
<li><a href="#_arithmetic_operations">5. Arithmetic Operations</a></li>
<li><a href="#_boolean_operations">6. Boolean Operations</a></li>
<li><a href="#_comparison">7. Comparison</a></li>
<li><a href="#_bitwise_operations">8. Bitwise Operations</a></li>
<li><a href="#_mathematical_operations">9. Mathematical Operations</a></li>
<li><a href="#_algebraic_data_type">10. Algebraic Data Type</a></li>
<li><a href="#_generics">11. Generics</a></li>
<li><a href="#_generic_function">12. Generic Function</a></li>
<li><a href="#_if_expression">13. If Expression</a></li>
<li><a href="#_match_expression">14. Match Expression</a></li>
<li><a href="#_let_expression">15. Let Expression</a></li>
<li><a href="#_lambda_expression">16. Lambda Expression</a></li>
<li><a href="#_macro">17. Macro</a></li>
<li><a href="#_string_and_character">18. String and Character</a></li>
<li><a href="#_foreign_function_interface">19. Foreign Function Interface</a></li>
<li><a href="#_transpilation_to_coq_experimental">20. Transpilation to Coq (Experimental)</a></li>
<li><a href="#_examples">21. Examples</a>
<ul class="sectlevel2">
<li><a href="#_reverse">21.1. Reverse</a></li>
<li><a href="#_filter">21.2. Filter</a></li>
<li><a href="#_factorial">21.3. Factorial</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph">
<p>BLisp is a statically typed Lisp like programming language which adopts effect system for no_std environments.
BLisp supports higher order RPC like higher order functions of functional programming languages.</p>
</div>
<div class="ulist">
<ul>
<li>
<p><a href="https://github.com/ytakano/blisp">GitHub&#8217;s Repository</a></p>
</li>
<li>
<p><a href="https://crates.io/crates/blisp">BLisp&#8217;s crates.io</a></p>
</li>
</ul>
</div>
<div class="paragraph">
<p>This repository provides only a library crate.
Please see <a href="https://github.com/ytakano/blisp-repl">blisp-repl</a> to use BLisp,
and <a href="https://github.com/ytakano/baremetalisp">baremetalisp</a> which is a toy OS.</p>
</div>
<div class="paragraph">
<p><a href="https://ytakano.github.io/blisp/index.ja.html">日本語版はこちら</a></p>
</div>
<div class="paragraph">
<div class="title">BLisp on no_std Environment</div>
<p><span class="image"><img src="https://cdn-ak.f.st-hatena.com/images/fotolife/y/ytakano/20210221/20210221155657.gif" alt="BLisp on no_std Environment"></span></p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_features">1. Features</h2>
<div class="sectionbody">
<div class="ulist">
<ul>
<li>
<p>Algebraic data type</p>
</li>
<li>
<p>Generics</p>
</li>
<li>
<p>Hindley–Milner based type inference</p>
</li>
<li>
<p>Effect system to separate side effects from pure functions</p>
</li>
<li>
<p>Big integer</p>
</li>
<li>
<p>Supporting no_std environments</p>
</li>
</ul>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_values">2. Values</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="title">values</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-o">`</span><span class="tok-nv">A</span><span class="tok-o">`</span><span class="tok-w">       </span><span class="tok-c1">; character literal</span>
<span class="tok-s">&quot;Hello&quot;</span><span class="tok-w">   </span><span class="tok-c1">; string literal</span>
<span class="tok-mi">144</span><span class="tok-w">       </span><span class="tok-c1">; integer value</span>
<span class="tok-nv">0xabcDEF</span><span class="tok-w">  </span><span class="tok-c1">; hexadecimal</span>
<span class="tok-nv">0o777</span><span class="tok-w">     </span><span class="tok-c1">; octal</span>
<span class="tok-nv">0b1001</span><span class="tok-w">    </span><span class="tok-c1">; binary</span>
<span class="tok-nv">true</span><span class="tok-w">      </span><span class="tok-c1">; boolean value</span>
<span class="tok-nv">false</span><span class="tok-w">     </span><span class="tok-c1">; boolean value</span>
<span class="tok-nv">[true</span><span class="tok-w"> </span><span class="tok-nv">10]</span><span class="tok-w"> </span><span class="tok-c1">; tuple</span>
<span class="tok-nv">[]</span><span class="tok-w">        </span><span class="tok-c1">; empty tuple</span>
<span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span><span class="tok-w">  </span><span class="tok-c1">; list</span>
<span class="tok-o">&#39;</span><span class="tok-p">()</span><span class="tok-w">       </span><span class="tok-c1">; empty list, Nil</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_basic_types">3. Basic Types</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="title">types</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-nv">Char</span><span class="tok-w">       </span><span class="tok-c1">; character</span>
<span class="tok-nv">String</span><span class="tok-w">     </span><span class="tok-c1">; string</span>
<span class="tok-nv">Int</span><span class="tok-w">        </span><span class="tok-c1">; signed integer</span>
<span class="tok-nv">Bool</span><span class="tok-w">       </span><span class="tok-c1">; boolean</span>
<span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w">     </span><span class="tok-c1">; list of Int</span>
<span class="tok-nv">[Int</span><span class="tok-w"> </span><span class="tok-nv">Bool]</span><span class="tok-w"> </span><span class="tok-c1">; tuple of Int and Bool</span>
<span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Bool</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; Pure function, which takes 2 integers and return boolean value</span>
<span class="tok-p">(</span><span class="tok-nv">IO</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">[]</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; IO function, which takes an integer and return []</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Pure and IO are function effects.
In IO functions, both Pure and IO functions can be called.
However, in Pure functions, calling only Pure functions is permitted.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_function_definition">4. Function Definition</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Functions can be defined by defun or export.
"defun" defines a local function which cannot be called from Rust&#8217;s eval function.</p>
</div>
<div class="paragraph">
<p>Suppose following 2 functions.</p>
</div>
<div class="listingblock">
<div class="title">defun</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">defun</span><span class="tok-w"> </span><span class="tok-nv">double</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w">         </span><span class="tok-c1">; function name is &quot;double&quot; and &quot;x&quot; is an argument</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; function Type</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">))</span><span class="tok-w">              </span><span class="tok-c1">; function body</span></code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">export</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">quad</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w">          </span><span class="tok-c1">; function name is &quot;quad&quot; and &quot;x&quot; is an argument</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; function Type</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">double</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">double</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)))</span><span class="tok-w">  </span><span class="tok-c1">; function body</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>double cannot be called from Rust&#8217;s eval, but can be called from internally defined functions.
quad can be called from Rust&#8217;s eval, and it calls double internally.</p>
</div>
<div class="paragraph">
<p>This is the code what actually do in Rust.</p>
</div>
<div class="listingblock">
<div class="title">Rust&#8217;s eval</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-k">use</span><span class="tok-w"> </span><span class="tok-n">blisp</span><span class="tok-p">;</span>

<span class="tok-k">fn</span> <span class="tok-nf">eval</span><span class="tok-p">(</span><span class="tok-n">e</span>: <span class="tok-kp">&amp;</span><span class="tok-kt">str</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">ctx</span>: <span class="tok-kp">&amp;</span><span class="tok-nc">blisp</span>::<span class="tok-n">semantics</span>::<span class="tok-n">Context</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">    </span><span class="tok-c1">// evaluate expressions</span>
<span class="tok-w">    </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">exprs</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-k">match</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">eval</span><span class="tok-p">(</span><span class="tok-n">e</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">ctx</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">        </span><span class="tok-nb">Ok</span><span class="tok-p">(</span><span class="tok-n">es</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=&gt;</span><span class="tok-w"> </span><span class="tok-n">es</span><span class="tok-p">,</span>
<span class="tok-w">        </span><span class="tok-nb">Err</span><span class="tok-p">(</span><span class="tok-n">err</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=&gt;</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">            </span><span class="tok-fm">println!</span><span class="tok-p">(</span><span class="tok-s">&quot;error:{}:{}: {}&quot;</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">err</span><span class="tok-p">.</span><span class="tok-n">pos</span><span class="tok-p">.</span><span class="tok-n">line</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">err</span><span class="tok-p">.</span><span class="tok-n">pos</span><span class="tok-p">.</span><span class="tok-n">column</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">err</span><span class="tok-p">.</span><span class="tok-n">msg</span><span class="tok-p">);</span>
<span class="tok-w">            </span><span class="tok-k">return</span><span class="tok-p">;</span>
<span class="tok-w">        </span><span class="tok-p">}</span>
<span class="tok-w">    </span><span class="tok-p">};</span>

<span class="tok-w">    </span><span class="tok-k">for</span><span class="tok-w"> </span><span class="tok-n">r</span><span class="tok-w"> </span><span class="tok-k">in</span><span class="tok-w"> </span><span class="tok-n">exprs</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">        </span><span class="tok-k">match</span><span class="tok-w"> </span><span class="tok-n">r</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">            </span><span class="tok-nb">Ok</span><span class="tok-p">(</span><span class="tok-n">msg</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=&gt;</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">                </span><span class="tok-fm">println!</span><span class="tok-p">(</span><span class="tok-s">&quot;{}&quot;</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">msg</span><span class="tok-p">);</span>
<span class="tok-w">            </span><span class="tok-p">}</span>
<span class="tok-w">            </span><span class="tok-nb">Err</span><span class="tok-p">(</span><span class="tok-n">msg</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=&gt;</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">                </span><span class="tok-fm">println!</span><span class="tok-p">(</span><span class="tok-s">&quot;error: {}&quot;</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">msg</span><span class="tok-p">);</span>
<span class="tok-w">            </span><span class="tok-p">}</span>
<span class="tok-w">        </span><span class="tok-p">}</span>
<span class="tok-w">    </span><span class="tok-p">}</span>
<span class="tok-p">}</span>

<span class="tok-k">fn</span> <span class="tok-nf">main</span><span class="tok-p">()</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">    </span><span class="tok-c1">// internal code</span>
<span class="tok-w">    </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">code</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-s">&quot;</span>
<span class="tok-s">(defun double (x)         ; function name is double and x is an argument</span>
<span class="tok-s">    (Pure (-&gt; (Int) Int)) ; function Type</span>
<span class="tok-s">    (* 2 x))              ; function body</span>

<span class="tok-s">(export quad (x)          ; function name is quad and x is an argument</span>
<span class="tok-s">    (Pure (-&gt; (Int) Int)) ; function Type</span>
<span class="tok-s">    (double (double x)))  ; function body</span>
<span class="tok-s">&quot;</span><span class="tok-p">;</span>
<span class="tok-w">    </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">exprs</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">init</span><span class="tok-p">(</span><span class="tok-n">code</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-fm">vec!</span><span class="tok-p">[]).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span>
<span class="tok-w">    </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">ctx</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">typing</span><span class="tok-p">(</span><span class="tok-o">&amp;</span><span class="tok-n">exprs</span><span class="tok-p">).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span>

<span class="tok-w">    </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">e</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-s">&quot;(double 10) ; error&quot;</span><span class="tok-p">;</span>
<span class="tok-w">    </span><span class="tok-n">eval</span><span class="tok-p">(</span><span class="tok-n">e</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-o">&amp;</span><span class="tok-n">ctx</span><span class="tok-p">);</span>

<span class="tok-w">    </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">e</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-s">&quot;(quad 10) ; OK&quot;</span><span class="tok-p">;</span>
<span class="tok-w">    </span><span class="tok-n">eval</span><span class="tok-p">(</span><span class="tok-n">e</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-o">&amp;</span><span class="tok-n">ctx</span><span class="tok-p">);</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This code output as follows.</p>
</div>
<div class="literalblock">
<div class="content">
<pre>error:0:1: Typing Error: double is not defined
40</pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_arithmetic_operations">5. Arithmetic Operations</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="title">basic</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; (Int Int) Int))</span>
<span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">-</span><span class="tok-w"> </span><span class="tok-mi">30</span><span class="tok-w"> </span><span class="tok-mi">40</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">/</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nv">%</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_boolean_operations">6. Boolean Operations</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="title">logical</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; (Bool Bool) Bool))</span>
<span class="tok-p">(</span><span class="tok-nb">and</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-w"> </span><span class="tok-nv">false</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">or</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-w"> </span><span class="tok-nv">false</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nv">xor</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-w"> </span><span class="tok-nv">false</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">negation</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; (Bool) Bool))</span>
<span class="tok-p">(</span><span class="tok-nb">not</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-p">)</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_comparison">7. Comparison</h2>
<div class="sectionbody">
<div class="paragraph">
<p>=, !=, &lt;, &gt;, &lt;=, &gt;= can be used for 2 values whose types are same.</p>
</div>
<div class="listingblock">
<div class="title">comparison between 2 values whose types are same</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; (t t) Bool))</span>
<span class="tok-p">(</span><span class="tok-nb">=</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w">               </span><span class="tok-c1">; true</span>
<span class="tok-p">(</span><span class="tok-nv">!=</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w">              </span><span class="tok-c1">; false</span>
<span class="tok-p">(</span><span class="tok-nb">=</span><span class="tok-w"> </span><span class="tok-s">&quot;Hello&quot;</span><span class="tok-w"> </span><span class="tok-s">&quot;Hello&quot;</span><span class="tok-p">)</span><span class="tok-w">   </span><span class="tok-c1">; true</span>
<span class="tok-p">(</span><span class="tok-nb">=</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; false</span>
<span class="tok-p">(</span><span class="tok-nb">&lt;</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">7</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">&gt;</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">7</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">&lt;=</span><span class="tok-w"> </span><span class="tok-mi">30</span><span class="tok-w"> </span><span class="tok-mi">40</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">&gt;=</span><span class="tok-w"> </span><span class="tok-mi">30</span><span class="tok-w"> </span><span class="tok-mi">40</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">&lt;</span><span class="tok-w"> </span><span class="tok-s">&quot;Hello&quot;</span><span class="tok-w"> </span><span class="tok-s">&quot;World&quot;</span><span class="tok-p">)</span>
<span class="tok-p">(</span><span class="tok-nb">&lt;=</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>eq</em>, <em>neq</em>, <em>lt</em>, <em>gt</em>, <em>leq</em>, <em>geq</em> can be used for any 2 values</p>
</div>
<div class="listingblock">
<div class="title">comparison between any 2 values</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; (t1 t1) Bool))</span>
<span class="tok-p">(</span><span class="tok-nv">geq</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-s">&quot;Hello&quot;</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some 1) is greater than or qeual to &quot;Hello&quot;</span>
<span class="tok-p">(</span><span class="tok-nb">eq</span><span class="tok-w"> </span><span class="tok-s">&quot;Hello&quot;</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-p">)</span><span class="tok-w">       </span><span class="tok-c1">; Is &quot;Hello&quot; qeual to 100?</span>
<span class="tok-p">(</span><span class="tok-nv">neq</span><span class="tok-w"> </span><span class="tok-s">&quot;Hello&quot;</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-p">)</span><span class="tok-w">      </span><span class="tok-c1">; Is &quot;Hello&quot; not equal to 100?</span>
<span class="tok-p">(</span><span class="tok-nv">lt</span><span class="tok-w"> </span><span class="tok-mi">100</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">))</span><span class="tok-w">     </span><span class="tok-c1">; Is 100 less than (Some 20)?</span>
<span class="tok-p">(</span><span class="tok-nv">gt</span><span class="tok-w"> </span><span class="tok-mi">200</span><span class="tok-w"> </span><span class="tok-s">&quot;Hello&quot;</span><span class="tok-p">)</span><span class="tok-w">       </span><span class="tok-c1">; Is 200 greater than &quot;Hello&quot;</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_bitwise_operations">8. Bitwise Operations</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">band</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; bitwise and</span>
<span class="tok-p">(</span><span class="tok-nv">band</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; bitwise and</span>
<span class="tok-p">(</span><span class="tok-nv">bor</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">)</span><span class="tok-w">  </span><span class="tok-c1">; bitwise or</span>
<span class="tok-p">(</span><span class="tok-nv">bor</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w">  </span><span class="tok-c1">; bitwise or</span>
<span class="tok-p">(</span><span class="tok-nv">bxor</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; bitwise xor</span></code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">bit shift</div>
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; (Int Int) (Option Int)))</span>
<span class="tok-p">(</span><span class="tok-nv">&lt;&lt;</span><span class="tok-w"> </span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w">   </span><span class="tok-c1">; (Some 128)</span>
<span class="tok-p">(</span><span class="tok-nv">&gt;&gt;</span><span class="tok-w"> </span><span class="tok-mi">128</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some 8)</span>
<span class="tok-p">(</span><span class="tok-nv">&gt;&gt;</span><span class="tok-w"> </span><span class="tok-mi">-128</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some -8)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>If 2nd argument is greater or equal to 2<sup>64</sup>, then these function return None.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_mathematical_operations">9. Mathematical Operations</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; (Int Int) (Option Int)))</span>
<span class="tok-p">(</span><span class="tok-nv">pow</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; (Some 100000000000000000000)</span>

<span class="tok-c1">; (Pure (-&gt; (Int) (Option Int)))</span>
<span class="tok-p">(</span><span class="tok-nb">sqrt</span><span class="tok-w"> </span><span class="tok-mi">16</span><span class="tok-p">)</span><span class="tok-w">   </span><span class="tok-c1">; (Some 4)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>If <em>pow</em>'s exponent portion is greater or equal to 2<sup>32</sup>, then <em>pow</em> returns None.</p>
</div>
<div class="paragraph">
<p>If <em>sqrt</em>'s argument is less than 0. then <em>sqrt</em> returns None.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_algebraic_data_type">10. Algebraic Data Type</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Algebraic data type can be defined as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; in BLisp</span>
<span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-nv">Cardinal</span><span class="tok-w"> </span><span class="tok-c1">; type name</span>
<span class="tok-w">    </span><span class="tok-nv">East</span><span class="tok-w">       </span><span class="tok-c1">; value</span>
<span class="tok-w">    </span><span class="tok-nv">North</span><span class="tok-w">      </span><span class="tok-c1">; value</span>
<span class="tok-w">    </span><span class="tok-nv">West</span><span class="tok-w">       </span><span class="tok-c1">; value</span>
<span class="tok-w">    </span><span class="tok-nv">South</span><span class="tok-p">)</span><span class="tok-w">     </span><span class="tok-c1">; value</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Type name&#8217;s and its value&#8217;s first character must be uppercase.
This is equivalent to Rust&#8217;s following code.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-c1">// in Rust</span>
<span class="tok-k">enum</span> <span class="tok-nc">Cardinal</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">    </span><span class="tok-n">East</span><span class="tok-p">,</span>
<span class="tok-w">    </span><span class="tok-n">North</span><span class="tok-p">,</span>
<span class="tok-w">    </span><span class="tok-n">West</span><span class="tok-p">,</span>
<span class="tok-w">    </span><span class="tok-n">South</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Each element can have values as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; in BLisp</span>
<span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-nv">Dim2</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">Dim2</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; Dim2 has integers</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Dim2 can be instantiated as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">Dim2</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This type is equivalent to Rust&#8217;s following type.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-c1">// in Rust</span>
<span class="tok-k">use</span><span class="tok-w"> </span><span class="tok-n">num_bigint</span>::<span class="tok-n">BigInt</span><span class="tok-p">;</span>
<span class="tok-k">enum</span> <span class="tok-nc">Dim2</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">    </span><span class="tok-n">Dim2</span><span class="tok-p">(</span><span class="tok-n">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">BigInt</span><span class="tok-p">)</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_generics">11. Generics</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Option and Result types are defined internally.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Option</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-nv">None</span><span class="tok-p">)</span>

<span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Result</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-w"> </span><span class="tok-nv">e</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">Ok</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">Err</span><span class="tok-w"> </span><span class="tok-nv">e</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>t</em> and <em>e</em> are type variables.
This code is equivalent to Rust&#8217;s following code.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-c1">// in Rust</span>
<span class="tok-k">enum</span> <span class="tok-nb">Option</span><span class="tok-o">&lt;</span><span class="tok-n">T</span><span class="tok-o">&gt;</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">    </span><span class="tok-nb">Some</span><span class="tok-p">(</span><span class="tok-n">T</span><span class="tok-p">),</span>
<span class="tok-w">    </span><span class="tok-nb">None</span><span class="tok-p">,</span>
<span class="tok-p">}</span>

<span class="tok-k">enum</span> <span class="tok-nb">Result</span><span class="tok-o">&lt;</span><span class="tok-n">T</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">E</span><span class="tok-o">&gt;</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">    </span><span class="tok-nb">Ok</span><span class="tok-p">(</span><span class="tok-n">T</span><span class="tok-p">),</span>
<span class="tok-w">    </span><span class="tok-nb">Err</span><span class="tok-p">(</span><span class="tok-n">E</span><span class="tok-p">),</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>List type is a built-in type as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">data</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">List</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">List</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">))</span>
<span class="tok-w">    </span><span class="tok-no">Nil</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>So, following 2 lists are equivalent.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-no">Nil</span><span class="tok-p">)))</span>
<span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_generic_function">12. Generic Function</h2>
<div class="sectionbody">
<div class="paragraph">
<p><em>car</em> and <em>cdr</em> are internally defined generic functions.
These definitions are as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nb">car</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Option</span><span class="tok-w"> </span><span class="tok-no">t</span><span class="tok-p">)))</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">x</span>
<span class="tok-w">        </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-nv">_</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-p">))</span>
<span class="tok-w">        </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">None</span><span class="tok-p">)))</span>

<span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nb">cdr</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">)))</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">x</span>
<span class="tok-w">        </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)</span>
<span class="tok-w">        </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">())))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>t</em> is a type variable. These functions can be used as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">car</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">9</span><span class="tok-p">))</span><span class="tok-w">  </span><span class="tok-c1">; returns (Some 3)</span>
<span class="tok-p">(</span><span class="tok-nb">cdr</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; returns &#39;(10 4)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Normal and type variables' first character must be lowercase.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_if_expression">13. If Expression</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Straightforward.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-k">if</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">&lt;</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-o">&#39;</span><span class="tok-p">())</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_match_expression">14. Match Expression</h2>
<div class="sectionbody">
<div class="paragraph">
<p>A list can be matched as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-nv">_</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-o">&#39;</span><span class="tok-p">()</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>The expression</p>
</div>
<div class="literalblock">
<div class="content">
<pre>(Cons n _)</pre>
</div>
</div>
<div class="paragraph">
<p>is a pattern.
If the pattern is matched to '(1 2 3), 1 is assigned to a variable <em>n</em>. Then, <em>n</em>, namely 1, is returned.</p>
</div>
<div class="paragraph">
<p>This is an example of pattern matching of tuple.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">[1</span><span class="tok-w"> </span><span class="tok-nv">3]</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">[x</span><span class="tok-w"> </span><span class="tok-nv">y]</span><span class="tok-w"> </span><span class="tok-nv">[y</span><span class="tok-w"> </span><span class="tok-nv">x]</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This code swap 1st and 2nd elements of the tuple.</p>
</div>
<div class="paragraph">
<p>Integer values can be also used for pattern matching.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-mi">20</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-mi">20</span><span class="tok-w"> </span><span class="tok-nv">true</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">false</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>More complex example is a as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">[</span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">true]</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">[</span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">false]</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">[</span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">true]</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>BLisp checks exhaustively of pattern.
So, following code will be rejected.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-o">&#39;</span><span class="tok-p">()</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">))</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_let_expression">15. Let Expression</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Let expression is used to bind variables as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">y</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; x is 10, y is 20</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))</span>

<span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)))</span><span class="tok-w"> </span><span class="tok-c1">; x = 10, x = x * x, x = x * x</span>
<span class="tok-w">    </span><span class="tok-nv">x</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Destructuring can be also performed as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">(((</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Some</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-p">)))</span><span class="tok-w"> </span><span class="tok-c1">; x is 10</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">))</span>

<span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">[x</span><span class="tok-w"> </span><span class="tok-nv">y]</span><span class="tok-w"> </span><span class="tok-nv">[10</span><span class="tok-w"> </span><span class="tok-nv">20]</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; x is 10, y is 20</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_lambda_expression">16. Lambda Expression</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Lambda expression is defined as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This lambda takes 2 integers and return the multiplication.
Applying arguments to this is simple as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">((</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-mi">10</span><span class="tok-w"> </span><span class="tok-mi">20</span><span class="tok-p">)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Every lambda expression is Pure.
IO functions cannot be called in any lambda expressions.</p>
</div>
<div class="paragraph">
<p><em>map</em> and <em>fold</em> functions are internally defined as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nb">map</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">a</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-nv">a</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-nv">b</span><span class="tok-p">)))</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">x</span>
<span class="tok-w">        </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">h</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">h</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">map</span><span class="tok-w"> </span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)))</span>
<span class="tok-w">        </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">())))</span>

<span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">fold</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">init</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">a</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-nv">a</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-nv">b</span><span class="tok-p">))</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">match</span><span class="tok-w"> </span><span class="tok-nv">x</span>
<span class="tok-w">        </span><span class="tok-p">((</span><span class="tok-nv">Cons</span><span class="tok-w"> </span><span class="tok-nv">h</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">fold</span><span class="tok-w"> </span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">h</span><span class="tok-w"> </span><span class="tok-nv">init</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">))</span>
<span class="tok-w">        </span><span class="tok-p">(</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">init</span><span class="tok-p">)))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>map</em> can be used to apply functions to elements of a list as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; square each element</span>
<span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">l</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-p">))</span>
<span class="tok-w">      </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-p">))))</span>
<span class="tok-w">        </span><span class="tok-p">(</span><span class="tok-nb">map</span><span class="tok-w"> </span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>fold</em> can be used to calculate over elements of a list.
For example, summation can be computed as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; summation</span>
<span class="tok-p">(</span><span class="tok-k">let</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">l</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">20</span><span class="tok-w"> </span><span class="tok-mi">50</span><span class="tok-w"> </span><span class="tok-mi">60</span><span class="tok-p">))</span>
<span class="tok-w">      </span><span class="tok-p">(</span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-nv">y</span><span class="tok-p">))))</span>
<span class="tok-w">        </span><span class="tok-p">(</span><span class="tok-nv">fold</span><span class="tok-w"> </span><span class="tok-nv">f</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-w"> </span><span class="tok-nv">l</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; 0 is an initial value</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Of course, this can be written as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; summation</span>
<span class="tok-p">(</span><span class="tok-nv">fold</span><span class="tok-w"> </span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">20</span><span class="tok-w"> </span><span class="tok-mi">50</span><span class="tok-w"> </span><span class="tok-mi">60</span><span class="tok-p">))</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_macro">17. Macro</h2>
<div class="sectionbody">
<div class="paragraph">
<p>Macros can be defined by <code>macro</code>.
Each rule consists of a pattern and a template, and the first matching rule is expanded.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">macro</span><span class="tok-w"> </span><span class="tok-nv">add</span>
<span class="tok-w">    </span><span class="tok-p">((</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-nv">$e1</span><span class="tok-w"> </span><span class="tok-nv">$e2</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-nv">$e1</span><span class="tok-w"> </span><span class="tok-nv">$e2</span><span class="tok-p">))</span>
<span class="tok-w">    </span><span class="tok-p">((</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-nv">$e1</span><span class="tok-w"> </span><span class="tok-nv">$e2</span><span class="tok-w"> </span><span class="tok-nv">$e3</span><span class="tok-w"> </span><span class="tok-o">...</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-nv">$e1</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-nv">$e2</span><span class="tok-w"> </span><span class="tok-nv">$e3</span><span class="tok-w"> </span><span class="tok-o">...</span><span class="tok-p">))))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Identifiers beginning with <code>$</code> are pattern variables.
They are substituted with the expressions matched at the call site.
<code>&#8230;&#8203;</code> can be used after a pattern variable or a template fragment to match and expand the remaining arguments.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span><span class="tok-w">         </span><span class="tok-c1">; 3</span>
<span class="tok-p">(</span><span class="tok-nv">add</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">5</span><span class="tok-p">)</span><span class="tok-w">   </span><span class="tok-c1">; 15</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Macros can also generate expressions that introduce local bindings.
For example, a temporary variable can be introduced in a lambda expression.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">macro</span><span class="tok-w"> </span><span class="tok-nv">with_tmp</span>
<span class="tok-w">    </span><span class="tok-p">((</span><span class="tok-nv">_</span><span class="tok-w"> </span><span class="tok-nv">$x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">tmp</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">+</span><span class="tok-w"> </span><span class="tok-nv">tmp</span><span class="tok-w"> </span><span class="tok-nv">$x</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)))</span>

<span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">test</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">tmp</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">with_tmp</span><span class="tok-w"> </span><span class="tok-nv">tmp</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>BLisp macros are hygienic for local binders introduced by macro templates.
Variables introduced by <code>lambda</code> arguments, <code>let</code> bindings, and <code>match</code> pattern variables are renamed to fresh internal names during expansion, so they do not capture variables from the call site.
Top-level names such as <code>defun</code>, <code>export</code>, and <code>data</code> definitions are not renamed automatically.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_string_and_character">18. String and Character</h2>
<div class="sectionbody">
<div class="paragraph">
<p><em>chars</em> converts String to (List Char).</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; (String) (List Char)))</span>
<span class="tok-p">(</span><span class="tok-nv">chars</span><span class="tok-w"> </span><span class="tok-s">&quot;Hello&quot;</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-c1">; &#39;(`H` `e` `l` `l` `o`)</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>str</em> converts (List Char) to String.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-c1">; (Pure (-&gt; ((List Char)) String))</span>
<span class="tok-p">(</span><span class="tok-nv">str</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-o">`</span><span class="tok-nv">H</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-o">`</span><span class="tok-nv">e</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-o">`</span><span class="tok-nv">l</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-o">`</span><span class="tok-nv">l</span><span class="tok-o">`</span><span class="tok-w"> </span><span class="tok-o">`</span><span class="tok-nv">o</span><span class="tok-o">`</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; &quot;Hello&quot;</span></code></pre>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_foreign_function_interface">19. Foreign Function Interface</h2>
<div class="sectionbody">
<div class="paragraph">
<p><em>blisp::embedded</em> is a macro for foreign function interface.
By using this, Rust&#8217;s functions can be called from BLisp easily.</p>
</div>
<div class="paragraph">
<p>For example, first of all, define a Rust function as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-k">use</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">embedded</span><span class="tok-p">;</span>
<span class="tok-k">use</span><span class="tok-w"> </span><span class="tok-n">num_bigint</span>::<span class="tok-p">{</span><span class="tok-n">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">ToBigInt</span><span class="tok-p">};</span>

<span class="tok-cp">#[embedded]</span>
<span class="tok-k">fn</span> <span class="tok-nf">add_four_ints</span><span class="tok-p">(</span><span class="tok-n">a</span>: <span class="tok-nc">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">b</span>: <span class="tok-p">(</span><span class="tok-n">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-n">BigInt</span><span class="tok-p">),</span><span class="tok-w"> </span><span class="tok-n">c</span>: <span class="tok-nb">Option</span><span class="tok-o">&lt;</span><span class="tok-n">BigInt</span><span class="tok-o">&gt;</span><span class="tok-p">)</span><span class="tok-w"> </span>-&gt; <span class="tok-nb">Result</span><span class="tok-o">&lt;</span><span class="tok-n">BigInt</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-nb">String</span><span class="tok-o">&gt;</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">    </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-k">mut</span><span class="tok-w"> </span><span class="tok-n">result</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">a</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-n">b</span><span class="tok-p">.</span><span class="tok-mi">0</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-n">b</span><span class="tok-p">.</span><span class="tok-mi">1</span><span class="tok-p">;</span>
<span class="tok-w">    </span><span class="tok-k">if</span><span class="tok-w"> </span><span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-nb">Some</span><span class="tok-p">(</span><span class="tok-n">n</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">c</span><span class="tok-w"> </span><span class="tok-p">{</span>
<span class="tok-w">        </span><span class="tok-n">result</span><span class="tok-w"> </span><span class="tok-o">+=</span><span class="tok-w"> </span><span class="tok-n">n</span><span class="tok-p">;</span>
<span class="tok-w">    </span><span class="tok-p">}</span>

<span class="tok-w">    </span><span class="tok-nb">Ok</span><span class="tok-p">(</span><span class="tok-n">result</span><span class="tok-p">)</span>
<span class="tok-p">}</span></code></pre>
</div>
</div>
<div class="paragraph">
<p><em>blisp::embedded</em> macro generates a type definition for FFI.
This function can be called from BLisp as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">call_add_four_ints</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">n</span><span class="tok-p">)</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">IO</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">((</span><span class="tok-nv">Option</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Result</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-nv">String</span><span class="tok-p">)))</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">add_four_ints</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-nv">[2</span><span class="tok-w"> </span><span class="tok-nv">3]</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>To register FFIs, a vector of the definition generated by <em>embedded</em> macro
must be passed to <em>blisp::init</em> as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="rust"><span></span><span class="tok-c1">// add_for_ints</span>
<span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">code</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-s">&quot;(export call_add_four_ints (n)</span>
<span class="tok-s">    (IO (-&gt; ((Option Int)) (Result Int String)))</span>
<span class="tok-s">    (add_four_ints 1 [2 3] n)</span>
<span class="tok-s">)&quot;</span><span class="tok-p">;</span>
<span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">exprs</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">init</span><span class="tok-p">(</span><span class="tok-n">code</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-fm">vec!</span><span class="tok-p">[</span><span class="tok-nb">Box</span>::<span class="tok-n">new</span><span class="tok-p">(</span><span class="tok-n">AddFourInts</span><span class="tok-p">)]).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span>
<span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">ctx</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">typing</span><span class="tok-p">(</span><span class="tok-n">exprs</span><span class="tok-p">).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span>
<span class="tok-kd">let</span><span class="tok-w"> </span><span class="tok-n">result</span><span class="tok-w"> </span><span class="tok-o">=</span><span class="tok-w"> </span><span class="tok-n">blisp</span>::<span class="tok-n">eval</span><span class="tok-p">(</span><span class="tok-s">&quot;(call_add_four_ints (Some 4))&quot;</span><span class="tok-p">,</span><span class="tok-w"> </span><span class="tok-o">&amp;</span><span class="tok-n">ctx</span><span class="tok-p">).</span><span class="tok-n">unwrap</span><span class="tok-p">();</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>The function name is <em>add_four_ints</em>, then <em>AddFourInts</em>, which is camel case,
must be passed to <em>blisp::init</em> capsulated by <em>Box</em> and <em>Vec</em>.</p>
</div>
<div class="paragraph">
<p>FFIs in Rust take and return only types described as follows.
Other types, like <em>Vec&lt;u64&gt;</em>, are not supported,
but <em>Vec&lt;Option&lt;bool&gt;&gt;</em> is accepted.
Types between BLisp and Rust are automatically converted by
the function generated by <em>embedded</em> macro.</p>
</div>
<table class="tableblock frame-all grid-all stretch">
<caption class="title">Table 1. Type Conversion between BLisp and Rust</caption>
<colgroup>
<col style="width: 50%;">
<col style="width: 50%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top">BLisp</th>
<th class="tableblock halign-left valign-top">Rust</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Int</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>BigInt</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Bool</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>bool</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Char</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>char</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>String</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>String</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>'(T)</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Vec&lt;T&gt;</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>[T0, T1]</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>(T0, T1)</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>(Option T)</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Option&lt;T&gt;</em></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>(Result T E)</em></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>Result&lt;T, E&gt;</em></p></td>
</tr>
</tbody>
</table>
<div class="paragraph">
<p>Note that every FFI is treated as IO functions.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_transpilation_to_coq_experimental">20. Transpilation to Coq (Experimental)</h2>
<div class="sectionbody">
<div class="paragraph">
<p>BLisp experimentally implements a transpiler to Coq.
It can be invoked by calling <em>blisp::transpile</em> as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="coq"><span></span><span class="tok-k">let</span> <span class="tok-n">expr</span> <span class="tok-o">=</span> <span class="tok-s2">&quot;</span>
<span class="tok-s2">(defun snoc (l y)</span>
<span class="tok-s2">(Pure (-&gt; (</span>
<span class="tok-s2">    &#39;(t) t)</span>
<span class="tok-s2">&#39;(t)))</span>
<span class="tok-s2">(match l</span>
<span class="tok-s2">    (nil (Cons y nil))</span>
<span class="tok-s2">    ((Cons h b) (Cons h (snoc b y)))))</span>

<span class="tok-s2">(defun rev (l)</span>
<span class="tok-s2">(Pure (-&gt; (</span>
<span class="tok-s2">    &#39;(t))</span>
<span class="tok-s2">&#39;(t)))</span>
<span class="tok-s2">(match l</span>
<span class="tok-s2">    (nil nil)</span>
<span class="tok-s2">    ((Cons h t) (snoc (rev t) h))))</span>
<span class="tok-s2">    &quot;</span><span class="tok-o">;</span>
<span class="tok-k">let</span> <span class="tok-n">exprs</span> <span class="tok-o">=</span> <span class="tok-n">blisp</span><span class="tok-o">::</span><span class="tok-n">init</span><span class="tok-o">(</span><span class="tok-n">expr</span><span class="tok-o">,</span> <span class="tok-n">vec</span><span class="tok-o">!</span><span class="tok-bp">[]</span><span class="tok-o">).</span><span class="tok-n">unwrap</span><span class="tok-bp">()</span><span class="tok-o">;</span>
<span class="tok-k">let</span> <span class="tok-n">ctx</span> <span class="tok-o">=</span> <span class="tok-n">blisp</span><span class="tok-o">::</span><span class="tok-n">typing</span><span class="tok-o">(</span><span class="tok-n">exprs</span><span class="tok-o">).</span><span class="tok-n">unwrap</span><span class="tok-bp">()</span><span class="tok-o">;</span>

<span class="tok-n">println</span><span class="tok-o">!(</span><span class="tok-s2">&quot;{}&quot;</span><span class="tok-o">,</span> <span class="tok-n">blisp</span><span class="tok-o">::</span><span class="tok-n">transpile</span><span class="tok-o">(&amp;</span><span class="tok-n">ctx</span><span class="tok-o">));</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This outputs Coq code as follows.
It includes as well as the prelude of BLisp.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="coq"><span></span><span class="tok-kn">Require</span> <span class="tok-kn">Import</span> <span class="tok-n">ZArith</span><span class="tok-o">.</span>
<span class="tok-kn">Require</span> <span class="tok-kn">Import</span> <span class="tok-n">Coq.Lists.List</span><span class="tok-o">.</span>

<span class="tok-kn">Inductive</span> <span class="tok-n">Option</span> <span class="tok-o">(</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">):</span> <span class="tok-kt">Type</span> <span class="tok-o">:=</span>
<span class="tok-o">|</span> <span class="tok-n">Some</span> <span class="tok-o">(</span><span class="tok-n">x0</span><span class="tok-o">:</span> <span class="tok-n">t</span><span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-n">None</span><span class="tok-o">.</span>

<span class="tok-kn">Arguments</span> <span class="tok-n">Some</span><span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">}.</span>
<span class="tok-kn">Arguments</span> <span class="tok-n">None</span><span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">}.</span>

<span class="tok-kn">Inductive</span> <span class="tok-n">Result</span> <span class="tok-o">(</span><span class="tok-n">t</span> <span class="tok-n">e</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">):</span> <span class="tok-kt">Type</span> <span class="tok-o">:=</span>
<span class="tok-o">|</span> <span class="tok-n">Ok</span> <span class="tok-o">(</span><span class="tok-n">x0</span><span class="tok-o">:</span> <span class="tok-n">t</span><span class="tok-o">)</span>
<span class="tok-o">|</span> <span class="tok-n">Err</span> <span class="tok-o">(</span><span class="tok-n">x0</span><span class="tok-o">:</span> <span class="tok-n">e</span><span class="tok-o">).</span>

<span class="tok-kn">Arguments</span> <span class="tok-n">Ok</span><span class="tok-o">{</span><span class="tok-n">t</span> <span class="tok-n">e</span><span class="tok-o">}.</span>
<span class="tok-kn">Arguments</span> <span class="tok-n">Err</span><span class="tok-o">{</span><span class="tok-n">t</span> <span class="tok-n">e</span><span class="tok-o">}.</span>

<span class="tok-kn">Definition</span> <span class="tok-n">car</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">Option</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
  <span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">n</span> <span class="tok-o">_)</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">Some</span> <span class="tok-n">n</span><span class="tok-o">)</span>
  <span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">None</span><span class="tok-o">)</span>
  <span class="tok-k">end</span><span class="tok-o">.</span>

<span class="tok-kn">Definition</span> <span class="tok-n">cdr</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
  <span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-o">_</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">=&gt;</span> <span class="tok-n">l</span>
  <span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=&gt;</span> <span class="tok-n">nil</span>
  <span class="tok-k">end</span><span class="tok-o">.</span>

<span class="tok-kn">Definition</span> <span class="tok-n">filter</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">f</span><span class="tok-o">:</span> <span class="tok-n">t</span> <span class="tok-o">-&gt;</span> <span class="tok-n">bool</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-o">(</span><span class="tok-n">reverse</span> <span class="tok-o">(</span><span class="tok-n">filter&#39;</span> <span class="tok-n">f</span> <span class="tok-n">x</span> <span class="tok-n">nil</span> <span class="tok-o">)</span> <span class="tok-o">).</span>

<span class="tok-kn">Fixpoint</span> <span class="tok-n">filter&#39;</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">f</span><span class="tok-o">:</span> <span class="tok-n">t</span> <span class="tok-o">-&gt;</span> <span class="tok-n">bool</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">x</span> <span class="tok-n">l</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
  <span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">a</span><span class="tok-o">)</span> <span class="tok-o">=&gt;</span> <span class="tok-k">match</span> <span class="tok-o">(</span><span class="tok-n">f</span> <span class="tok-n">h</span> <span class="tok-o">)</span> <span class="tok-k">with</span>
    <span class="tok-o">|</span> <span class="tok-bp">true</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">filter&#39;</span> <span class="tok-n">f</span> <span class="tok-n">a</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">)</span>
    <span class="tok-o">|</span> <span class="tok-bp">false</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">filter&#39;</span> <span class="tok-n">f</span> <span class="tok-n">a</span> <span class="tok-n">l</span> <span class="tok-o">)</span>
    <span class="tok-k">end</span>
  <span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=&gt;</span> <span class="tok-n">l</span>
  <span class="tok-k">end</span><span class="tok-o">.</span>

<span class="tok-kn">Fixpoint</span> <span class="tok-k">fold</span> <span class="tok-o">{</span><span class="tok-n">a</span> <span class="tok-n">b</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">f</span><span class="tok-o">:</span> <span class="tok-n">a</span> <span class="tok-o">-&gt;</span> <span class="tok-n">b</span> <span class="tok-o">-&gt;</span> <span class="tok-n">b</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">init</span><span class="tok-o">:</span> <span class="tok-n">b</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">a</span><span class="tok-o">):</span> <span class="tok-n">b</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
  <span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-k">fold</span> <span class="tok-n">f</span> <span class="tok-o">(</span><span class="tok-n">f</span> <span class="tok-n">h</span> <span class="tok-n">init</span> <span class="tok-o">)</span> <span class="tok-n">l</span> <span class="tok-o">)</span>
  <span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=&gt;</span> <span class="tok-n">init</span>
  <span class="tok-k">end</span><span class="tok-o">.</span>

<span class="tok-kn">Fixpoint</span> <span class="tok-n">map</span> <span class="tok-o">{</span><span class="tok-n">a</span> <span class="tok-n">b</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">f</span><span class="tok-o">:</span> <span class="tok-n">a</span> <span class="tok-o">-&gt;</span> <span class="tok-n">b</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">a</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">b</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
  <span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-o">(</span><span class="tok-n">f</span> <span class="tok-n">h</span> <span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">map</span> <span class="tok-n">f</span> <span class="tok-n">l</span> <span class="tok-o">))</span>
  <span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=&gt;</span> <span class="tok-n">nil</span>
  <span class="tok-k">end</span><span class="tok-o">.</span>

<span class="tok-kn">Fixpoint</span> <span class="tok-n">rev</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">l</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">l</span> <span class="tok-k">with</span>
  <span class="tok-o">|</span> <span class="tok-n">nil</span> <span class="tok-o">=&gt;</span> <span class="tok-n">nil</span>
  <span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">t</span><span class="tok-o">)</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">snoc</span> <span class="tok-o">(</span><span class="tok-n">rev</span> <span class="tok-n">t</span> <span class="tok-o">)</span> <span class="tok-n">h</span> <span class="tok-o">)</span>
  <span class="tok-k">end</span><span class="tok-o">.</span>

<span class="tok-kn">Definition</span> <span class="tok-n">reverse</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">x</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-o">(</span><span class="tok-n">reverse&#39;</span> <span class="tok-n">x</span> <span class="tok-n">nil</span> <span class="tok-o">).</span>

<span class="tok-kn">Fixpoint</span> <span class="tok-n">reverse&#39;</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">x</span> <span class="tok-n">l</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">x</span> <span class="tok-k">with</span>
  <span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">a</span><span class="tok-o">)</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">reverse&#39;</span> <span class="tok-n">a</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">l</span><span class="tok-o">)</span> <span class="tok-o">)</span>
  <span class="tok-o">|</span> <span class="tok-o">_</span> <span class="tok-o">=&gt;</span> <span class="tok-n">l</span>
  <span class="tok-k">end</span><span class="tok-o">.</span>

<span class="tok-kn">Fixpoint</span> <span class="tok-n">snoc</span> <span class="tok-o">{</span><span class="tok-n">t</span><span class="tok-o">:</span> <span class="tok-kt">Type</span><span class="tok-o">}</span> <span class="tok-o">(</span><span class="tok-n">l</span><span class="tok-o">:</span> <span class="tok-n">list</span> <span class="tok-n">t</span><span class="tok-o">)</span> <span class="tok-o">(</span><span class="tok-n">y</span><span class="tok-o">:</span> <span class="tok-n">t</span><span class="tok-o">):</span> <span class="tok-n">list</span> <span class="tok-n">t</span> <span class="tok-o">:=</span>
<span class="tok-k">match</span> <span class="tok-n">l</span> <span class="tok-k">with</span>
  <span class="tok-o">|</span> <span class="tok-n">nil</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">y</span> <span class="tok-n">nil</span><span class="tok-o">)</span>
  <span class="tok-o">|</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-n">b</span><span class="tok-o">)</span> <span class="tok-o">=&gt;</span> <span class="tok-o">(</span><span class="tok-n">cons</span> <span class="tok-n">h</span> <span class="tok-o">(</span><span class="tok-n">snoc</span> <span class="tok-n">b</span> <span class="tok-n">y</span> <span class="tok-o">))</span>
  <span class="tok-k">end</span><span class="tok-o">.</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>Not that this transpiler is experimental.
So, Coq cannot interpret some outputs.
Please fix it manually when you encounter that situation.
It is probably easy.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_examples">21. Examples</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_reverse">21.1. Reverse</h3>
<div class="paragraph">
<p><em>reverse</em> is a internally defined function. It reverses order of a list.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">reverse</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">5</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">7</span><span class="tok-w"> </span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">9</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This outputs as follows.</p>
</div>
<div class="literalblock">
<div class="content">
<pre>'(9 8 7 6 5 4 3 2 1)</pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_filter">21.2. Filter</h3>
<div class="paragraph">
<p><em>filter</em> is a internally defined function. It filters the elements in a list.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">filter</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-k">lambda</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">x</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">=</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">%</span><span class="tok-w"> </span><span class="tok-nv">x</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-mi">1</span><span class="tok-w"> </span><span class="tok-mi">2</span><span class="tok-w"> </span><span class="tok-mi">3</span><span class="tok-w"> </span><span class="tok-mi">4</span><span class="tok-w"> </span><span class="tok-mi">5</span><span class="tok-w"> </span><span class="tok-mi">6</span><span class="tok-w"> </span><span class="tok-mi">7</span><span class="tok-w"> </span><span class="tok-mi">8</span><span class="tok-w"> </span><span class="tok-mi">9</span><span class="tok-p">))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This outputs as follows.</p>
</div>
<div class="literalblock">
<div class="content">
<pre>'(2 4 6 8)</pre>
</div>
</div>
<div class="paragraph">
<p><em>filter</em>'s type is as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span>
<span class="tok-w">    </span><span class="tok-p">((</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Bool</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-c1">; take a function</span>
<span class="tok-w">     </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">))</span><span class="tok-w">                </span><span class="tok-c1">; take a list</span>
<span class="tok-w">    </span><span class="tok-o">&#39;</span><span class="tok-p">(</span><span class="tok-no">t</span><span class="tok-p">)))</span><span class="tok-w"> </span><span class="tok-c1">; return a list</span></code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_factorial">21.3. Factorial</h3>
<div class="paragraph">
<p>Tail call factorial can be coded as follows.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="pygments highlight"><code data-lang="lisp"><span></span><span class="tok-p">(</span><span class="tok-nb">export</span><span class="tok-w"> </span><span class="tok-nv">factorial</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">n</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-nv">fact</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">))</span>

<span class="tok-p">(</span><span class="tok-nb">defun</span><span class="tok-w"> </span><span class="tok-nv">fact</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-nv">total</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Pure</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">-&gt;</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nv">Int</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-nv">Int</span><span class="tok-p">))</span>
<span class="tok-w">    </span><span class="tok-p">(</span><span class="tok-k">if</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">&lt;=</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-mi">0</span><span class="tok-p">)</span>
<span class="tok-w">        </span><span class="tok-nv">total</span>
<span class="tok-w">        </span><span class="tok-p">(</span><span class="tok-nv">fact</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">-</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-mi">1</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-nb">*</span><span class="tok-w"> </span><span class="tok-nv">n</span><span class="tok-w"> </span><span class="tok-nv">total</span><span class="tok-p">))))</span></code></pre>
</div>
</div>
<div class="paragraph">
<p>This function can be called as follows.</p>
</div>
<div class="literalblock">
<div class="content">
<pre>&gt;&gt; (factorial 10)
3628800
&gt;&gt;
&gt;&gt; (factorial 1000)
402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
&gt;&gt;
&gt;&gt; (factorial 100)
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
&gt;&gt;
&gt;&gt; (factorial 500)
1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000</pre>
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================================================
FILE: docs/index.ja.adoc
================================================
= BLisp: Lispっぽい静的型付け言語
Yuuki Takano <ytakano@wide.ad.jp>
v0.4.0, 2023-02
:doctype: article
:toc:
:sectnums:
:lang: ja
:encoding: utf-8
:stem: latexmath
:source-highlighter: pygments


BLispは静的型付けされたLispライクなプログラミング言語で、no_std環境用のエフェクトシステムを採用しています。BLispは関数型プログラミング言語の高階関数のような高階のRPCをサポートしています。

* https://github.com/ytakano/blisp[GitHubリポジトリ]
* https://crates.io/crates/blisp[BLispのcrates.io]

本リポジトリではライブラリクレートのみを提供しています。BLispを利用するには https://github.com/ytakano/blisp-repl[blisp-repl] か、おもちゃのOSである https://github.com/ytakano/baremetalisp[baremetalisp] を参照してください。

https://ytakano.github.io/blisp/[English version is here.]

.no_stdで動くBLisp
image:https://cdn-ak.f.st-hatena.com/images/fotolife/y/ytakano/20210221/20210221155657.gif[no_stdで動くBLisp]

== 特徴

* 代数的データ型
* ジェネリクス
* 型推論
* IOと純粋な関数を分離するためのエフェクトシステム
* 多倍長整数
* no_std環境のサポート

== 値

.values
[source, lisp]
----
`A`       ; 文字リテラル
"Hello"   ; 文字列リテラル
144       ; 整数値
0xabcDEF  ; 16進数
0o777     ; 8進数
0b1001    ; 2進数
true      ; 真偽値
false     ; 真偽値
[true 10] ; タプル
[]        ; 空のタプル
'(1 2 3)  ; リスト
'()       ; 空のリスト、Nil
----

== 基本型

.types
[source, lisp]
----
Char       ; 文字型
String     ; 文字列型
Int        ; 整数型
Bool       ; 真偽値型
'(Int)     ; Int型のリスト型
[Int Bool] ; Int型とBool型のタプル型
(Pure (-> (Int Int) Bool)) ; Int型の値を2つとり、Bool型の値をリターンする純粋な関数
(IO (-> (Int) [])) ; Int型の値をとり[]をリターンするIOのある関数
----

PureとIOは関数の効果です。IO関数内では、Pure関数とIO関数の両方を呼び出すことができます。しかし、Pure関数内では、Pure関数の呼び出しのみ許可されています。

== 関数定義

関数はdefunやexportで定義することができます。"defun"はRustのeval関数からは呼び出せないローカル関数を定義します。

以下の2つの関数があるとしましょう。

.defun
[source, lisp]
----
(defun double (x)         ; 関数名がdoubleでxは引数
    (Pure (-> (Int) Int)) ; 関数の型
    (* 2 x))              ; 関数の中身
----

.export
[source, lisp]
----
(export quad (x)          ; 関数名がquadで引数はx
    (Pure (-> (Int) Int)) ; 関数の型
    (double (double x)))  ; 関数の中身
----

doubleはRustのevalからは呼び出せませんが、内部で定義された関数からは呼び出せます。quadはRustのevalから呼び出すことができ、内部的にdoubleを呼び出します。

これはRustで実際に行うコードです。

.Rust's eval
[source, rust]
----
use blisp;

fn eval(e: &str, ctx: &blisp::semantics::Context) {
    // evaluate expressions
    let exprs = match blisp::eval(e, ctx) {
        Ok(es) => es,
        Err(err) => {
            println!("error:{}:{}: {}", err.pos.line, err.pos.column, err.msg);
            return;
        }
    };

    for r in exprs {
        match r {
            Ok(msg) => {
                println!("{}", msg);
            }
            Err(msg) => {
                println!("error: {}", msg);
            }
        }
    }
}

fn main() {
    // internal code
    let code = "
(defun double (x)         ; 関数名がdoubleでxは引数
    (Pure (-> (Int) Int)) ; 関数の型
    (* 2 x))              ; 関数の中身

(export quad (x)          ; 関数名がquadで引数はx
    (Pure (-> (Int) Int)) ; 関数の型
    (double (double x)))  ; 関数の中身
";
    let exprs = blisp::init(code, vec![]).unwrap();
    let ctx = blisp::typing(exprs).unwrap();

    let e = "(double 10) ; エラー";
    eval(e, &ctx);

    let e = "(quad 10) ; OK";
    eval(e, &ctx);
}
----

このコードは以下のように出力します。

 error:0:1: Typing Error: double is not defined
 40

== 算術演算

.基本
[source, lisp]
----
; (Pure (-> (Int Int) Int))
(+ 10 20)
(- 30 40)
(* 6 100)
(/ 100 2)
(% 10 3)
----

== 真偽値演算

.logical
[source, lisp]
----
; (Pure (-> (Bool Bool) Bool))
(and true false)
(or true false)
(xor true false)
----

.negation
[source, lisp]
----
; (Pure (-> (Bool) Bool))
(not true)
----

== 比較演算

=, !=, <, >, \<=, >= といった関数は、同じ型の2つの値に対して適用できます。

.comparison between 2 values whose types are same
[source, lisp]
----
; (Pure (-> (t t) Bool))
(= 4 4)               ; true
(!= 4 4)              ; false
(= "Hello" "Hello")   ; true
(= (Some 1) (Some 2)) ; false
(< 6 7)
(> 6 7)
(<= 30 40)
(>= 30 40)
(< "Hello" "World")
(<= (Some 1) (Some 2))
----

_eq_, _neq_, _lt_, _gt_, _leq_, _geq_ といった関数は、異なる型同士の値でも比較可能です。

.comparison between any 2 values
[source, lisp]
----
; (Pure (-> (t1 t1) Bool))
(geq (Some 1) "Hello") ; (Some 1)は"Hello"より大きい、もしくは等しいか？
(eq "Hello" 100)       ; "Hello"と100は等しいか？
(neq "Hello" 100)      ; "Hello"と100は等しくないか？
(lt 100 (Some 20))     ; 100は(Some 20)より小さいか？
(gt 200 "Hello")       ; 200は"Hello"より大きいか？
----

== ビット演算

[source, lisp]
----
(band 1 0) ; ビット積
(band 1 1) ; ビット積
(bor 1 0)  ; ビット和
(bor 1 1)  ; ビット和
(bxor 1 0) ; ビット排他的論理和
----

.ビットシフト
[source, lisp]
----
; (Pure (-> (Int Int) (Option Int)))
(<< 8 4)   ; (Some 128)
(>> 128 4) ; (Some 8)
(>> -128 4) ; (Some -8)
----

2番目の引数が2^64^以上の場合はNoneをリターンします。

== 数学的演算

[source, lisp]
----
; (Pure (-> (Int Int) (Option Int)))
(pow 10 20) ; (Some 100000000000000000000) namely 10^20

; (Pure (-> (Int) (Option Int)))
(sqrt 16)   ; (Some 4)
----

powの指数部が2^32^以上の場合は、powはNoneをリターンします。

sqrtの引数が0以下の場合は、sqrtはNoneをリターンします。

== 代数的データ型

代数的データ型は以下のように定義できます。

[source, lisp]
----
; in BLisp
(data Cardinal ; 型名
    East       ; 値
    North      ; 値
    West       ; 値
    South)     ; 値
----

型名とその値の最初の文字は大文字でなければなりません。これはRustの以下のコードと同等です。

[source, rust]
----
// in Rust
enum Cardinal {
    East,
    North,
    West,
    South
}
----

各要素は以下のような値を持つことができます。

[source, lisp]
----
; in BLisp
(data Dim2
    (Dim2 Int Int)) ; Dim2は2つのInt型の値を持つ
----

Dim2は以下のようにインスタンス化することができます。

[source, lisp]
----
(Dim2 10 20)
----

この型はRustの以下の型と同等です。

[source, rust]
----
// in Rust
use num_bigint::BigInt;
enum Dim2 {
    Dim2(BigInt, BigInt)
}
----

== ジェネリクス

Option型とResult型は内部で定義されています。

[source, lisp]
----
(data (Option t)
    (Some t)
    None)

(data (Result t e)
    (Ok t)
    (Err e))
----


_t_ と _e_ は型変数です。このコードは、Rustの以下のコードと同等です。

[source, rust]
----
// in Rust
enum Option<T> {
    Some(T),
    None,
}

enum Result<T, E> {
    Ok(T),
    Err(E),
}
----

リスト型は以下のような組み込み型です。

[source, lisp]
----
(data (List t)
    (Cons t (List t))
    Nil)
----

したがって、以下の2つのリストは等価です。

[source, lisp]
----
(Cons 1 (Cons 2 (Cons 3 Nil)))
'(1 2 3)
----

== ジェネリック関数

_car_ と _cdr_ は内部的に定義されたジェネリック関数です。これらの定義は以下の通りです。

[source, lisp]
----
(export car (x) (Pure (-> ('(t)) (Option t)))
    (match x
        ((Cons n _) (Some n))
        (_ None)))

(export cdr (x) (Pure (-> ('(t)) '(t)))
    (match x
        ((Cons _ l) l)
        (_ '())))
----

t_は型変数です。これらの関数は以下のように使うことができます。

[source, lisp]
----
(car '(3 8 9))  ; returns (Some 3)
(cdr '(8 10 4)) ; returns '(10 4)
----

通常変数と型変数の最初の文字は小文字でなければなりません。

== If式

単純です.

[source, lisp]
----
(if (< 10 20)
    '(1 2 3)
    '())
----

== Match式

リストは以下のようにマッチさせることができます。

[source, lisp]
----
(match '(1 2 3)
    ((Cons n _) n)
    ('() 0))
----

この、

 (Cons n _)

という式はパターンです。
パターンが '(1 2 3) にマッチした場合、1は可変変数 _n_ に代入されます。そうすると、_n_ つまり1が返されます。

タプルのパターンマッチングの例です。

[source, lisp]
----
(match [1 3]
    ([x y] [y x]))
----

このコードはタプルの第1要素と第2要素を入れ替えます。

整数値はパターンマッチングにも使用できます。

[source, lisp]
----
(match 20
    (20 true)
    (_ false))
----

より複雑な例としては、以下のようなものがあります。

[source, lisp]
----
(match [(Some 10) true]
    ([(Some 10) false] 1)
    ([(Some 10) true] 2)
    (_ 0))
----

BLispはパターンを網羅的にチェックします。そのため、以下のコードは拒否されます。

[source, lisp]
----
(match '(1 2)
    ('() 0))
----

== Let式

変数のバインドには、以下のようにLet式を使用します。

[source, lisp]
----
(let ((x 10) (y 20)) ; x is 10, y is 20
    (* x y))

(let ((x 10) (x (* x x)) (x (* x x))) ; x = 10, x = x * x, x = x * x
    x)
----

また、以下のように分配束縛を行うこともできます。

[source, lisp]
----
(let (((Some x) (Some 10))) ; x is 10
    (* x 2))

(let (([x y] [10 20])) ; x is 10, y is 20
    (* x y))
----

== ラムダ式

ラムダ式は以下のように定義されます。

[source, lisp]
----
(lambda (x y) (* x y))
----

このラムダは2つの整数を受け取り、それらの乗算を返します。これに引数を適用するのは次のように簡単に行えます。

[source, lisp]
----
((lambda (x y) (* x y)) 10 20)
----

すべてのラムダ式は純粋です。よって、ラムダ式からIO関数を呼び出すことはできません。

_map_ と _fold_ 関数は内部的に以下のように定義されています。

[source, lisp]
----
(export map (f x) (Pure (-> ((Pure (-> (a) b)) '(a)) '(b)))
    (match x
        ((Cons h l) (Cons (f h) (map f l)))
        (_ '())))

(export fold (f init x) (Pure (-> ((Pure (-> (a b) b)) b '(a)) b))
    (match x
        ((Cons h l) (fold f (f h init) l))
        (_ init)))
----

_map_ を使うと、以下のようにリストの要素に関数を適用することができます。

[source, lisp]
----
; それぞれをの要素を2乗
(let ((l '(1 2 3))
      (f (lambda (x) (* x x))))
        (map f l))
----

_fold_ を使用して、リストの要素にまたがって計算することができます。例えば、合計は以下のように計算できます。

[source, lisp]
----
; 合計
(let ((l '(20 50 60))
      (f (lambda (x y) (+ x y))))
        (fold f 0 l)) ; 0 is an initial value
----

当然、これは以下のようにも記述できます。

[source, lisp]
----
; summation
(fold + 0 '(20 50 60))
----

== マクロ

マクロは `macro` で定義できます。
各ルールはパターンとテンプレートの組からなり、最初に一致したルールが展開されます。

[source, lisp]
----
(macro add
    ((add $e1 $e2) (+ $e1 $e2))
    ((add $e1 $e2 $e3 ...) (+ $e1 (add $e2 $e3 ...))))
----

`$` で始まる識別子はパターン変数です。
パターン変数には、マクロ呼び出し側で一致した式がそのまま代入されます。
`...` は、パターン変数やテンプレート断片の後ろに置くことで、残りの引数を可変長部分としてまとめて扱えます。

[source, lisp]
----
(add 1 2)         ; 3
(add 1 2 3 4 5)   ; 15
----

マクロは局所変数を導入する式も生成できます。
たとえば、一時変数を含むラムダ式は以下のように書けます。

[source, lisp]
----
(macro with_tmp
    ((_ $x) ((lambda (tmp) (+ tmp $x)) 1)))

(export test (tmp) (Pure (-> (Int) Int))
    (with_tmp tmp))
----

BLispのマクロは、テンプレートが導入する局所 binder に対して衛生的です。
`lambda` の引数、`let` の束縛、`match` のパターン変数は展開時に fresh な内部名へ自動的にリネームされるため、呼び出し側の同名変数を変数捕捉しません。
一方で、`defun`、`export`、`data` のようなトップレベル名は自動では改名されません。

== 文字列と文字

_chars_ はStringから(List Char)へ変換します。

[source, lisp]
----
; (Pure (-> (String) (List Char)))
(chars "Hello") ; '(`H` `e` `l` `l` `o`)
----

_str_ は(List Char)からStringへ変換します。

[source, lisp]
----
; (Pure (-> ((List Char)) String))
(str '(`H` `e` `l` `l` `o`)) ; "Hello"
----

== 外部関数呼び出し

_blisp::embedded_ は、外部関数呼び出し用のマクロです。
このマクロを利用すると、Rustの関数をBLispから容易に呼び出せるようになります。

たとえば、はじめに、Rustの関数を以下のように定義します。

[source, rust]
----
use blisp::embedded;
use num_bigint::{BigInt, ToBigInt};

#[embedded]
fn add_four_ints(a: BigInt, b: (BigInt, BigInt), c: Option<BigInt>) -> Result<BigInt, String> {
    let mut result = a + b.0 + b.1;
    if let Some(n) = c {
        result += n;
    }

    Ok(result)
}
----

_blisp::embedded_ マクロは外部関数呼び出し用の型定義を生成します。
この関数は、以下のようにBLispから呼び出せます。

[source, lisp]
----
(export call_add_four_ints (n)
    (IO (-> ((Option Int)) (Result Int String)))
    (add_four_ints 1 [2 3] n))
----

外部関数を登録するためには、以下のように、 _embedded_ によって生成される型定義のベクタを
_blisp::init_ に渡します。

[source, rust]
----
// add_for_ints
let code = "(export call_add_four_ints (n)
    (IO (-> ((Option Int)) (Result Int String)))
    (add_four_ints 1 [2 3] n)
)";
let exprs = blisp::init(code, vec![Box::new(AddFourInts)]).unwrap();
let ctx = blisp::typing(exprs).unwrap();
let result = blisp::eval("(call_add_four_ints (Some 4))", &ctx).unwrap();
----

ここでは、関数名が _add_four_ints_ のため、そのキャメルケースの _AddFourInts_
を _Box_ と _Vec_ に包んで _blisp::init_ に渡さなければなりません。

Rustの外部関数は以下に示される型のみ引数と返り値で利用可能です。
_Vec<u64>_ のような他の型はサポート外ですが、
_Vec<Option<bool>>_ のような型はOKです。
BLispとRustの間の型変換は _embedded_ マクロが生成する関数によって自動的に行われます。

.Type Conversion between BLisp and Rust
|===
|BLisp          | Rust

|_Int_          | _BigInt_
|_Bool_         | _bool_
|_Char_         | _char_
|_String_       | _String_
|_'(T)_         | _Vec<T>_
|_[T0, T1]_     | _(T0, T1)_
|_(Option T)_   | _Option<T>_
|_(Result T E)_ | _Result<T, E>_
|===

== Coqへのトランスパイラ (実験的)

BLispは実験的にCoqへのトランスパイラを実装しています。
トランスパイラは、以下のように _blisp::transpile_ を呼び出すことで実行されます。

[source, coq]
----
let expr = "
(defun snoc (l y)
(Pure (-> (
    '(t) t)
'(t)))
(match l
    (nil (Cons y nil))
    ((Cons h b) (Cons h (snoc b y)))))

(defun rev (l)
(Pure (-> (
    '(t))
'(t)))
(match l
    (nil nil)
    ((Cons h t) (snoc (rev t) h))))
    ";
let exprs = blisp::init(expr, vec![]).unwrap();
let ctx = blisp::typing(exprs).unwrap();

println!("{}", blisp::transpile(&ctx));
----

これは以下のようなCoqのコードを出力します。
この出力には、BLispのプレリュードも含まれます。

[source, coq]
----
Require Import ZArith.
Require Import Coq.Lists.List.

Inductive Option (t: Type): Type :=
| Some (x0: t)
| None.

Arguments Some{t}.
Arguments None{t}.

Inductive Result (t e: Type): Type :=
| Ok (x0: t)
| Err (x0: e).

Arguments Ok{t e}.
Arguments Err{t e}.

Definition car {t: Type} (x: list t): Option t :=
match x with
  | (cons n _) => (Some n)
  | _ => (None)
  end.

Definition cdr {t: Type} (x: list t): list t :=
match x with
  | (cons _ l) => l
  | _ => nil
  end.

Definition filter {t: Type} (f: t -> bool) (x: list t): list t :=
(reverse (filter' f x nil ) ).

Fixpoint filter' {t: Type} (f: t -> bool) (x l: list t): list t :=
match x with
  | (cons h a) => match (f h ) with
    | true => (filter' f a (cons h l) )
    | false => (filter' f a l )
    end
  | _ => l
  end.

Fixpoint fold {a b: Type} (f: a -> b -> b) (init: b) (x: list a): b :=
match x with
  | (cons h l) => (fold f (f h init ) l )
  | _ => init
  end.

Fixpoint map {a b: Type} (f: a -> b) (x: list a): list b :=
match x with
  | (cons h l) => (cons (f h ) (map f l ))
  | _ => nil
  end.

Fixpoint rev {t: Type} (l: list t): list t :=
match l with
  | nil => nil
  | (cons h t) => (snoc (rev t ) h )
  end.

Definition reverse {t: Type} (x: list t): list t :=
(reverse' x nil ).

Fixpoint reverse' {t: Type} (x l: list t): list t :=
match x with
  | (cons h a) => (reverse' a (cons h l) )
  | _ => l
  end.

Fixpoint snoc {t: Type} (l: list t) (y: t): list t :=
match l with
  | nil => (cons y nil)
  | (cons h b) => (cons h (snoc b y ))
  end.
----

このトランスパイラは実験的なものであることに注意してください。
よって、いくつかの出力はCoqが解釈できません。
その場合は、手動でソースコードを修正してください。
簡単にできるはずです。

== 例

=== リバース

_reverse_ は内部で定義されている関数です。この関数はリストを反転します。

[source, lisp]
----
(reverse '(1 2 3 4 5 6 7 8 9))
----

このコードの出力は以下の通りです。

 '(9 8 7 6 5 4 3 2 1)

=== Filter

_filter_ は内部で定義されている関数です。この関数はリストの中身をフィルターします。

[source, lisp]
----
(filter (lambda (x) (= (% x 2) 0)) '(1 2 3 4 5 6 7 8 9))
----

このコードの出力は以下の通りです。

 '(2 4 6 8)

_filter_' の型は以下の通りです。

[source, lisp]
----
(Pure (->
    ((Pure (-> (t) Bool)) ; 関数を引数にとる
     '(t))                ; リストを引数にとる
    '(t))) ; リストをリターン
----

=== 階乗

末尾呼び出し版の階乗関数は、以下のように実装できます。

[source, lisp]
----
(export factorial (n) (Pure (-> (Int) Int))
    (fact n 1))

(defun fact (n total) (Pure (-> (Int Int) Int))
    (if (<= n 0)
        total
        (fact (- n 1) (* n total))))
----

この関数は以下のように呼び出すことができます。

 >> (factorial 10)
 3628800
 >>
 >> (factorial 1000)
 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 >>
 >> (factorial 100)
 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
 >>
 >> (factorial 500)
 1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000


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