Repository: p-e-w/savage
Branch: master
Commit: 24e25a6a5add
Files: 29
Total size: 179.6 KB
Directory structure:
gitextract_86suw3hs/
├── .github/
│ ├── dependabot.yml
│ └── workflows/
│ └── continuous_integration.yml
├── .gitignore
├── CHANGELOG.md
├── Cargo.toml
├── LICENSE
├── README.md
├── savage/
│ ├── Cargo.toml
│ ├── help/
│ │ ├── footer.md
│ │ └── header.md
│ └── src/
│ ├── command.rs
│ ├── help.rs
│ ├── input.rs
│ └── main.rs
├── savage_core/
│ ├── Cargo.toml
│ └── src/
│ ├── evaluate.rs
│ ├── expression.rs
│ ├── functions/
│ │ ├── combinatorics.rs
│ │ ├── linear_algebra.rs
│ │ ├── logic.rs
│ │ ├── mod.rs
│ │ └── number_theory.rs
│ ├── helpers.rs
│ ├── lib.rs
│ ├── parse.rs
│ ├── print.rs
│ └── simplify.rs
└── savage_macros/
├── Cargo.toml
└── src/
└── lib.rs
================================================
FILE CONTENTS
================================================
================================================
FILE: .github/dependabot.yml
================================================
# Please see the documentation for all configuration options:
# https://docs.github.com/github/administering-a-repository/configuration-options-for-dependency-updates
version: 2
updates:
- package-ecosystem: "cargo"
directory: "/"
schedule:
interval: "weekly"
================================================
FILE: .github/workflows/continuous_integration.yml
================================================
# Based on https://github.com/actions-rs/meta/blob/master/recipes/msrv.md
on: [push, pull_request]
name: Continuous integration
jobs:
check:
name: Check
runs-on: ubuntu-latest
strategy:
matrix:
rust:
- stable
- 1.56.0
steps:
- uses: actions/checkout@v2
- uses: actions-rs/toolchain@v1
with:
profile: minimal
toolchain: ${{ matrix.rust }}
override: true
- uses: actions-rs/cargo@v1
with:
command: check
test:
name: Test Suite
runs-on: ubuntu-latest
strategy:
matrix:
rust:
- stable
- 1.56.0
steps:
- uses: actions/checkout@v2
- uses: actions-rs/toolchain@v1
with:
profile: minimal
toolchain: ${{ matrix.rust }}
override: true
- uses: actions-rs/cargo@v1
with:
command: test
fmt:
name: Rustfmt
runs-on: ubuntu-latest
strategy:
matrix:
rust:
- stable
steps:
- uses: actions/checkout@v2
- uses: actions-rs/toolchain@v1
with:
profile: minimal
toolchain: ${{ matrix.rust }}
override: true
- run: rustup component add rustfmt
- uses: actions-rs/cargo@v1
with:
command: fmt
args: --all -- --check
clippy:
name: Clippy
runs-on: ubuntu-latest
strategy:
matrix:
rust:
- stable
steps:
- uses: actions/checkout@v2
- uses: actions-rs/toolchain@v1
with:
profile: minimal
toolchain: ${{ matrix.rust }}
override: true
- run: rustup component add clippy
- uses: actions-rs/cargo@v1
with:
command: clippy
args: -- -D warnings
================================================
FILE: .gitignore
================================================
/target
================================================
FILE: CHANGELOG.md
================================================
# Changelog
All notable changes to this project will be documented in this file.
The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
## [Unreleased]
### Added
#### REPL
- Basic help system
- Ability to define custom variables and functions
- Proper formatting for parse errors
### Changed
### Fixed
## [0.2.0] - 2022-03-13
### Added
#### Core
- Basic support for vectors and matrices
- Algebraic simplification during evaluation
- Infrastructure for evaluating functions
- Macro-based function dispatch system
- New built-in functions:
- `and`
- `det`
- `factorial`
- `is_prime`
- `nth_prime`
- `prime_pi`
#### REPL
- Persistent input history
- Multi-line editing mode
- Syntax highlighting for input and output
- Highlighting of matching brackets in input
### Fixed
#### Core
- Type inflation in parser
- Exponential blowup in parser
#### REPL
- Error on empty input
## [0.1.0] - 2021-11-28
Initial release with basic REPL and support for elementary arithmetic and logic.
[unreleased]: https://github.com/p-e-w/savage/compare/v0.2.0...HEAD
[0.2.0]: https://github.com/p-e-w/savage/compare/v0.1.0...v0.2.0
[0.1.0]: https://github.com/p-e-w/savage/releases/tag/v0.1.0
================================================
FILE: Cargo.toml
================================================
[workspace]
members = [
"savage_macros",
"savage_core",
"savage",
]
[profile.release]
codegen-units = 1
opt-level = 3
lto = true
#strip = true
================================================
FILE: LICENSE
================================================
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shall include the Corresponding Source for any work covered by version 3
of the GNU General Public License that is incorporated pursuant to the
following paragraph.
Notwithstanding any other provision of this License, you have
permission to link or combine any covered work with a work licensed
under version 3 of the GNU General Public License into a single
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License will continue to apply to the part which is the covered work,
but the work with which it is combined will remain governed by version
3 of the GNU General Public License.
14. Revised Versions of this License.
The Free Software Foundation may publish revised and/or new versions of
the GNU Affero General Public License from time to time. Such new versions
will be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.
Each version is given a distinguishing version number. If the
Program specifies that a certain numbered version of the GNU Affero General
Public License "or any later version" applies to it, you have the
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version or of any later version published by the Free Software
Foundation. If the Program does not specify a version number of the
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If the Program specifies that a proxy can decide which future
versions of the GNU Affero General Public License can be used, that proxy's
public statement of acceptance of a version permanently authorizes you
to choose that version for the Program.
Later license versions may give you additional or different
permissions. However, no additional obligations are imposed on any
author or copyright holder as a result of your choosing to follow a
later version.
15. Disclaimer of Warranty.
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
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IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
16. Limitation of Liability.
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WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
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17. Interpretation of Sections 15 and 16.
If the disclaimer of warranty and limitation of liability provided
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reviewing courts shall apply local law that most closely approximates
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Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.
END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail.
If your software can interact with users remotely through a computer
network, you should also make sure that it provides a way for users to
get its source. For example, if your program is a web application, its
interface could display a "Source" link that leads users to an archive
of the code. There are many ways you could offer source, and different
solutions will be better for different programs; see section 13 for the
specific requirements.
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU AGPL, see
<https://www.gnu.org/licenses/>.
================================================
FILE: README.md
================================================
# Savage Computer Algebra System
Savage is a new computer algebra system written from scratch in pure Rust.
Its goals are correctness, simplicity, and usability, in that order.
The entire system compiles to a single, dependency-free executable just
2.5 MB in size. While that executable will of course grow as Savage matures,
the plan is to eventually deliver a useful computer algebra system in 5 MB
or less.
The name "Savage" is a reference/homage to [Sage](https://www.sagemath.org/),
the leading open-source computer algebra system. Since Sage already exists
and works very well, it would make no sense to attempt to create a clone of it.
Instead, Savage aims to be something of an antithesis to Sage: Where Sage is
a unified frontend to dozens of mathematics packages, Savage is a tightly-integrated,
monolithic system. Where Sage covers many areas of mathematics, including cutting-edge
research topics, Savage will focus on the "bread and butter" math employed by
engineers and other people who *use*, rather than develop, mathematical concepts.
Where Sage features amazingly sophisticated implementations of countless functions,
Savage has code that is savagely primitive, getting the job done naively but correctly,
without worrying whether the performance is still optimal when the input is
a million-digit number.
**Savage is in early development and is not yet ready to be used for serious work.**
It is, however, ready to play around with, and is happily accepting contributions
to move the project forward.
## Features
This is what Savage offers **today:**
* Arbitrary-precision integer, rational, and complex arithmetic
* Input, simplification, and evaluation of symbolic expressions
* First-class support for vectors and matrices, with coefficients being arbitrary expressions
* REPL with syntax and bracket highlighting, persistent history, and automatic multi-line input
* Macro-based system for defining functions with metadata and automatic type checking
* [Usable as a library](#savage-as-a-library) from any Rust program
The following features are **planned,** with some of the groundwork already done:
* User-defined variables and functions
* Built-in help system
* Many more functions from various areas of math
* More powerful expression simplification
* Jupyter kernel
By contrast, the following are considered **non-features** for Savage,
and there are no plans to add them either now or in the future:
* *Advanced/research-level mathematics:* As a rule of thumb, if it doesn't belong
in a typical undergraduate course, it probably doesn't belong in Savage.
* *Physics/finance/machine learning/other areas adjacent to math:* The scope would
grow without bounds and that is exactly what Savage aims to avoid.
* *Formal verification of implementations:* The required technologies aren't mature yet
and Savage is not a research project.
* *Performance at the expense of simplicity:* Yes, I know that multiplication
can be done faster using some fancy Fourier tricks. No, I won't implement that.
* *General-purpose programming:* Too complex, and not the focus of this project.
* *File/network I/O:* Savage performs computations, nothing more and nothing less.
Functions have no side effects.
* *Modules/packages/extensions/plugins:* The world is complicated enough.
Either something is built in, or Savage doesn't have it at all.
* *GUI:* Although it's possible to create a GUI frontend backed by the `savage_core`
crate, there are no plans to do so within the Savage project itself.
## Installation
Building Savage from source requires [Rust](https://www.rust-lang.org/) **1.56 or later.**
Once a supported version of Rust is installed on your system, you only need to run
```
cargo install savage
```
to install the Savage REPL to your Cargo binary directory (usually `$HOME/.cargo/bin`).
Of course, you can also just clone this repository and `cargo run` the REPL from the
repository root.
In the future, there will be pre-built executables for major platforms
available with every Savage release.
## Tour
### Arithmetic
Arithmetic operations in Savage have no precision limits (other than the amount
of memory available in your system):
```
in: 1 + 1
out: 2
in: 1.1 ^ 100
out: 13780.612339822270184118337172089636776264331200038466433146477552154985209
5523076769401159497458526446001
in: 3 ^ 4 ^ 5
out: 373391848741020043532959754184866588225409776783734007750636931722079040617
26525122999368893880397722046876506543147515810872705459216085858135133698280918
73141917485942625809388070199519564042855718180410466812887974029255176680123406
17298396574731619152386723046235125934896058590588284654793540505936202376547807
44273058214452705898875625145281779341335214192074462302751872918543286237573706
39854853194764169262638199728870069070138992565242971985276987492741962768110607
02333710356481
```
Results are automatically printed in either fractional or decimal form,
depending on whether the input contained fractions or decimal numbers:
```
in: 6/5 * 3
out: 18/5
in: 1.2 * 3
out: 3.6
```
The variable `i` is predefined to represent the imaginary unit, allowing for
complex numbers to be entered using standard notation:
```
in: (1 + i) ^ 12
out: -64
```
### Linear algebra
Vectors and matrices are first-class citizens in Savage and support the standard
addition, subtraction, multiplication, and exponentiation operators. Coefficients
can be arbitrary expressions:
```
in: [a, b] - [a, c]
out: [0, b - c]
in: [a, b, c] * 3
out: [a * 3, b * 3, c * 3]
in: [[1, 2], [3, 4]] * [5, 6]
out: [17, 39]
```
Determinants are evaluated symbolically:
```
in: det([[a, 2], [3, a]])
out: a ^ 2 - 6
```
### Logic
The standard `&&`, `||`, `!`, and comparison operators are available. Savage
automatically evaluates many tautologies and contradictions, even in the presence
of undefined variables:
```
in: a && true
out: a
in: a || true
out: true
in: a || !a
out: true
in: a < a
out: false
```
### Number theory
Verify that the Mersenne number *M<sub>31</sub>* is a prime number:
```
in: is_prime(2^31 - 1)
out: true
```
Compute the ten millionth prime number:
```
in: nth_prime(10^7)
out: 179424673
```
Compute the number of primes up to ten million:
```
in: prime_pi(10^7)
out: 664579
```
These functions for dealing with prime numbers are powered by the ultra-fast
[`primal`](https://crates.io/crates/primal) crate. Many more functions from
number theory will be added to Savage in the future.
## Savage as a library
All of Savage's actual computer algebra functionality is contained in the
[`savage_core`](https://crates.io/crates/savage_core) crate. That crate exposes
everything necessary to build software that leverages symbolic math capabilities.
Assuming `savage_core` has been added as a dependency to a crate's `Cargo.toml`,
it can be used like this:
```rust
use std::collections::HashMap;
use savage_core::{expression::Expression, helpers::*};
fn main() {
// Expressions can be constructed by parsing a string literal...
let lhs = "det([[a, 2], [3, a]])".parse::<Expression>().unwrap();
// ... or directly from code using helper functions.
let rhs = pow(var("a"), int(2)) - int(6);
let mut context = HashMap::new();
// The context can be used to set the values of variables during evaluation.
// Change "b" to "a" to see this in action!
context.insert("b".to_owned(), int(3));
assert_eq!(lhs.evaluate(context), Ok(rhs));
}
```
Please note that at this point, the primary purpose of the `savage_core` crate is
to power the Savage REPL, so any use by third-party crates should be considered
somewhat experimental. Note also that like the rest of Savage, `savage_core` is
licensed under the terms of the [AGPL](LICENSE), which imposes conditions on any
dependent software that go beyond what is required by the more common permissive
licenses. Make sure you understand the AGPL and its implications before adding
`savage_core` as a dependency to your crate.
## Acknowledgments
Savage stands on the shoulders of the giant that is the Rust ecosystem. Among the
many third-party crates that Savage relies on, I want to highlight two that play
a particularly important role:
* [`num`](https://crates.io/crates/num) is the fundamental crate for all numeric
computations in Savage. It provides the crucial `BigInt` type that enables
standard arithmetic operations to be performed with arbitrary precision.
`num`'s code is of high quality and extremely well tested.
* [`chumsky`](https://crates.io/crates/chumsky) is the magic behind Savage's expression
parser. I have looked at every parser crate currently available and found Chumsky's
API to be by far the most intuitive. Furthermore, Chumsky's author is highly
responsive on the issue tracker, and has personally helped me understand and resolve
two major issues that arose during the development of Savage's parser.
## License
Copyright © 2021-2022 Philipp Emanuel Weidmann (<pew@worldwidemann.com>)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
**By contributing to this project, you agree to release your
contributions under the same license.**
================================================
FILE: savage/Cargo.toml
================================================
[package]
name = "savage"
version = "0.2.0"
authors = ["Philipp Emanuel Weidmann <pew@worldwidemann.com>"]
description = "A primitive computer algebra system (REPL)"
repository = "https://github.com/p-e-w/savage"
readme = "README.md"
license = "AGPL-3.0-or-later"
edition = "2021"
[dependencies]
lazy_static = "1.4.0"
directories = "4.0.1"
crossterm = "0.25.0"
ansi_term = "0.12.1"
rustyline = "9.0.0"
rustyline-derive = "0.7.0"
termimad = "0.20.2"
regex = "1.6.0"
chumsky = "0.8.0"
ariadne = "0.1.5"
savage_core = { path = "../savage_core", version = "0.2.0" }
================================================
FILE: savage/help/footer.md
================================================
## License
Copyright (C) 2021-2022 Philipp Emanuel Weidmann (**pew@worldwidemann.com**)
This program is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License along with this program. If not, see **https://www.gnu.org/licenses/**.
================================================
FILE: savage/help/header.md
================================================
# Savage Computer Algebra System
Savage is a new computer algebra system written from scratch in pure Rust. Its goals are correctness, simplicity, and usability, in that order.
This is Savage's documentation, which may be viewed at any time by entering `?` in the REPL (**r**ead-**e**val-**p**rint **l**oop, i.e. the Savage command interpreter). You can also directly view the documentation for a specific built-in function by entering `?` followed by the name of the function, e.g. `? det` for the determinant function.
For more information, visit **https://github.com/p-e-w/savage**. Note that Savage is in early development. If you encounter bugs or other problems, please don't hesitate to file an issue.
## Basic usage
Type mathematical expressions in the REPL using standard notation and press *Enter* to evaluate them:
```
in: 1 + 1
out: 2
```
Savage supports integer (`123`), fractional (`1/2`), decimal (`1.23`), and complex (`1 + 2*i`) number literals, as well as the sum (`+`), difference (`-`), product (`*`), quotient (`/`), remainder (`%`), and power (`^`) binary operators, and the negation (`-`) prefix operator:
```
in: 6/5 * 3
out: 18/5
in: 1.2 * 3
out: 3.6
in: (1 + i) ^ 12
out: -64
```
It also supports boolean (`true`/`false`) literals, and the conjunction ("and", `&&`), disjunction ("or", `||`), and logical negation ("not", `!`) operators. The standard comparison operators (`==`, `!=`, `<`, `<=`, `>`, `>=`) are available as well:
```
in: a && true
out: a
in: a || true
out: true
in: a || !a
out: true
in: a < a
out: false
```
## Vectors and matrices
A comma-separated list of expressions surrounded by square brackets (e.g. `[1, 2, 3]`) represents a column vector with the expressions as elements. A vector of vectors, all of which have the same size (e.g. `[[1, 2], [3, 4]]`), is interpreted as a column-major matrix whose rows are the constitutent vectors.
Vectors and matrices support the standard arithmetic operations:
```
in: [a, b] - [a, c]
out: [0, b - c]
in: [a, b, c] * 3
out: [a * 3, b * 3, c * 3]
in: [[1, 2], [3, 4]] * [5, 6]
out: [17, 39]
```
Individual elements of vectors and matrices can be accessed using the index notation familiar from many programming languages:
```
in: v = [1, 2, 3]
in: v[1]
out: 2
in: m = [[1, 2], [3, 4]]
in: m[1, 0]
out: 3
```
## Variables and functions
Symbolic names like `a`, `b`, and `c` are by default interpreted as expression placeholders. They can, however, be assigned specific values, at which point they become defined variables:
```
in: a = 1
in: b = 2
in: a + b
out: 3
```
Functions can also be defined with a syntax that is essentially identical to that used in standard mathematical notation:
```
in: sum(x, y) = x + y
in: sum(1, 2)
out: 3
```
## Built-in functions
The following named functions are available in the REPL without needing to be explicitly loaded or manually defined:
================================================
FILE: savage/src/command.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use std::str::FromStr;
use chumsky::prelude::*;
use savage_core::{
expression::Expression,
parse::{parser as expression, Error},
};
#[derive(PartialEq, Eq, Clone, Debug)]
pub enum Command {
EvaluateExpression(Expression),
DefineVariable(String, Expression),
DefineFunction(String, Vec<String>, Expression),
ShowHelp(Option<String>),
}
fn parser() -> impl Parser<char, Command, Error = Error> {
text::ident()
.padded()
.then_ignore(just('='))
.then(expression())
.map(|(identifier, expression)| Command::DefineVariable(identifier, expression))
.or(text::ident()
.padded()
.then(
text::ident()
.padded()
.separated_by(just(','))
.padded()
.delimited_by(just('('), just(')'))
.padded(),
)
.then_ignore(just('='))
.then(expression())
.map(|((identifier, argument_identifiers), expression)| {
Command::DefineFunction(identifier, argument_identifiers, expression)
}))
.or(expression().map(Command::EvaluateExpression))
.or(just('?')
.padded()
.ignore_then(text::ident().padded().or_not())
.map(Command::ShowHelp))
}
impl FromStr for Command {
type Err = Vec<Error>;
fn from_str(string: &str) -> Result<Self, Self::Err> {
parser().then_ignore(end()).parse(string)
}
}
#[cfg(test)]
mod tests {
use savage_core::helpers::*;
use crate::command::{Command, Command::*};
#[track_caller]
fn t(string: &str, command: Command) {
assert_eq!(string.parse(), Ok(command));
}
#[test]
fn parse() {
t(" a ", EvaluateExpression(var("a")));
t("a ==b ", EvaluateExpression(eq(var("a"), var("b"))));
t(" a=1", DefineVariable("a".to_owned(), int(1)));
t(
"a =b== c",
DefineVariable("a".to_owned(), eq(var("b"), var("c"))),
);
t("f( )= 1", DefineFunction("f".to_owned(), vec![], int(1)));
t(
" f (x) =x ^ 2",
DefineFunction("f".to_owned(), vec!["x".to_owned()], pow(var("x"), int(2))),
);
t(
"f( x )=( (x)== (y)) ",
DefineFunction("f".to_owned(), vec!["x".to_owned()], eq(var("x"), var("y"))),
);
t(
"f( x ,y)= g(x, y)",
DefineFunction(
"f".to_owned(),
vec!["x".to_owned(), "y".to_owned()],
fun(var("g"), [var("x"), var("y")]),
),
);
t(" ? ", ShowHelp(None));
t("?is_prime ", ShowHelp(Some("is_prime".to_owned())));
t("? is_prime", ShowHelp(Some("is_prime".to_owned())));
}
}
================================================
FILE: savage/src/help.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use std::{
collections::HashMap,
io::{stdout, Write},
};
use crossterm::{
cursor,
event::{self, Event, KeyEvent},
queue,
style::Stylize,
terminal::{
self, ClearType, DisableLineWrap, EnableLineWrap, EnterAlternateScreen,
LeaveAlternateScreen,
},
};
use lazy_static::lazy_static;
use savage_core::functions::functions;
use termimad::{Area, Error, MadSkin, MadView};
const HELP_HEADER: &str = include_str!("../help/header.md");
const HELP_FOOTER: &str = include_str!("../help/footer.md");
lazy_static! {
pub static ref FUNCTION_HELP_TEXTS: HashMap<String, String> = {
let mut texts = HashMap::new();
for function in functions() {
let metadata = function.metadata;
let text = format!(
"**{}** - {}\n\n*Syntax:*\n```\n{}({})\n```\n\n*Examples:*\n```\n{}\n```\n\n*Categories:*\n{}\n",
metadata.name,
metadata.description,
metadata.name,
metadata
.parameters
.iter()
.map(|p| format!("{:?}", p))
.collect::<Vec<_>>()
.join(", "),
metadata
.examples
.iter()
.map(|(i, o)| format!("in: {}\nout: {}", i, o))
.collect::<Vec<_>>()
.join("\n\n"),
metadata.categories.join(", "),
);
texts.insert(metadata.name.to_owned(), text);
}
texts
};
pub static ref HELP_TEXT: String = {
let mut text = String::from(HELP_HEADER);
text.push_str("\n---\n\n");
for function in functions() {
text.push_str(&FUNCTION_HELP_TEXTS[function.metadata.name]);
text.push_str("\n---\n\n");
}
text.push('\n');
text.push_str(HELP_FOOTER);
text.push('\n');
text
};
}
fn view_area() -> Area {
let mut area = Area::full_screen();
area.pad_for_max_width(120);
// Make space for bottom bar.
area.height -= 1;
area
}
pub fn show_help(text: String) -> Result<(), Error> {
// Based on https://github.com/Canop/termimad/blob/5ab13e600f05c0217e270181dd5d9288210f893f/examples/scrollable/main.rs
use crossterm::event::KeyCode::*;
let mut stdout = stdout();
queue!(stdout, EnterAlternateScreen, DisableLineWrap, cursor::Hide)?;
terminal::enable_raw_mode()?;
let mut view = MadView::from(text, view_area(), MadSkin::default());
loop {
view.write_on(&mut stdout)?;
print!(
"\n\r{}{}{}{}{}{}{}{}",
"Press ".reverse(),
"\u{2191}".bold().reverse(),
" and ".reverse(),
"\u{2193}".bold().reverse(),
" to scroll, ".reverse(),
"Q".bold().reverse(),
" to quit".reverse(),
" ".repeat(view_area().width as usize).reverse(),
);
stdout.flush()?;
match event::read() {
Ok(Event::Key(KeyEvent { code, .. })) => match code {
Up | Char('k') => view.try_scroll_lines(-1),
Down | Char('j') | Enter => view.try_scroll_lines(1),
PageUp => view.try_scroll_pages(-1),
PageDown | Char(' ') => view.try_scroll_pages(1),
Char('q') | Esc => break,
_ => {}
},
Ok(Event::Resize(..)) => {
queue!(stdout, terminal::Clear(ClearType::All))?;
view.resize(&view_area());
}
_ => {}
}
}
terminal::disable_raw_mode()?;
queue!(stdout, cursor::Show, EnableLineWrap, LeaveAlternateScreen)?;
stdout.flush()?;
Ok(())
}
================================================
FILE: savage/src/input.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use std::borrow::Cow;
use ansi_term::Style;
use lazy_static::lazy_static;
use regex::Regex;
use rustyline::{
highlight::Highlighter,
validate::{ValidationContext, ValidationResult, Validator},
Result,
};
use rustyline_derive::{Completer, Helper, Hinter};
use savage_core::{expression::Expression, parse::ErrorReason};
enum TokenType {
Literal,
Variable,
Operator,
Bracket,
Separator,
Whitespace,
Invalid,
}
fn tokenize(input: &str) -> Vec<(String, TokenType)> {
use TokenType::*;
lazy_static! {
static ref REGEX: Regex = Regex::new(
&[
r"(?P<literal>[0-9]+(?:\.[0-9]+)?|true|false)",
r"(?P<variable>[a-zA-Z_][a-zA-Z0-9_]*)",
r"(?P<operator>[+\-*/%^!=<>&|]+)",
r"(?P<bracket>[()\[\]])",
r"(?P<separator>,)",
r"(?P<whitespace>\s+)",
]
.join("|"),
)
.unwrap();
}
let mut tokens = Vec::new();
let mut last_token_end = 0;
for captures in REGEX.captures_iter(input) {
let token_type = if captures.name("literal").is_some() {
Literal
} else if captures.name("variable").is_some() {
Variable
} else if captures.name("operator").is_some() {
Operator
} else if captures.name("bracket").is_some() {
Bracket
} else if captures.name("separator").is_some() {
Separator
} else if captures.name("whitespace").is_some() {
Whitespace
} else {
unreachable!()
};
let token_range = captures.get(0).unwrap().range();
if last_token_end < token_range.start {
tokens.push((input[last_token_end..token_range.start].to_owned(), Invalid));
}
last_token_end = token_range.end;
tokens.push((input[token_range].to_owned(), token_type));
}
if last_token_end < input.len() {
tokens.push((input[last_token_end..].to_owned(), Invalid));
}
tokens
}
#[derive(Completer, Helper, Hinter)]
pub struct InputHelper {}
impl Highlighter for InputHelper {
fn highlight_prompt<'b, 's: 'b, 'p: 'b>(
&'s self,
prompt: &'p str,
_default: bool,
) -> Cow<'b, str> {
Cow::Owned(Style::new().bold().paint(prompt).to_string())
}
fn highlight<'l>(&self, line: &'l str, pos: usize) -> Cow<'l, str> {
use ansi_term::Colour::*;
use TokenType::*;
let matching_pos = if pos < line.len() {
let line_bytes = line.as_bytes();
let mut matching_pos = None;
'outer: for (open, close) in [(b'(', b')'), (b'[', b']')] {
let (range, open, close): (Box<dyn Iterator<Item = usize>>, _, _) =
if line_bytes[pos] == open {
(Box::new(pos + 1..line_bytes.len()), open, close)
} else if line_bytes[pos] == close {
(Box::new((0..pos).rev()), close, open)
} else {
continue;
};
let mut closes_needed = 1;
for i in range {
if line_bytes[i] == open {
closes_needed += 1;
} else if line_bytes[i] == close {
closes_needed -= 1;
if closes_needed == 0 {
matching_pos = Some(i);
break 'outer;
}
}
}
}
matching_pos
} else {
None
};
let mut highlighted_line = String::new();
let mut token_pos = 0;
for (token, token_type) in tokenize(line) {
let mut style = match token_type {
Literal => Cyan.into(),
Variable => Green.into(),
Operator => Purple.into(),
Bracket => Style::new(),
Separator => Style::new(),
Whitespace => Style::new(),
Invalid => Red.into(),
};
if Some(token_pos) == matching_pos {
style = style.bold();
}
token_pos += token.len();
// https://github.com/rust-lang/rust-clippy/issues/9317
#[allow(clippy::unnecessary_to_owned)]
highlighted_line.push_str(&style.paint(token).to_string());
}
Cow::Owned(highlighted_line)
}
fn highlight_char(&self, _line: &str, _pos: usize) -> bool {
true
}
}
impl Validator for InputHelper {
fn validate(&self, ctx: &mut ValidationContext) -> Result<ValidationResult> {
// This implementation distinguishes only between "incomplete"
// (unexpected end of input) and "valid" (everything else),
// because actual input validation is performed by the REPL
// as part of the regular input processing step.
let input = ctx.input();
if input.trim().is_empty() || input.ends_with('\n') {
return Ok(ValidationResult::Valid(None));
}
if let Err(errors) = input.parse::<Expression>() {
for error in errors {
if error.reason() == &ErrorReason::Unexpected && error.found() == None {
return Ok(ValidationResult::Incomplete);
}
}
}
Ok(ValidationResult::Valid(None))
}
}
================================================
FILE: savage/src/main.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
mod command;
mod help;
mod input;
use std::{
collections::{HashMap, HashSet},
fs,
iter::FromIterator,
rc::Rc,
};
use ansi_term::Style;
use ariadne::{Color, Fmt, Label, Report, ReportKind, Source};
use directories::ProjectDirs;
use lazy_static::lazy_static;
use rustyline::{error::ReadlineError, highlight::Highlighter, Editor};
use savage_core::{
evaluate::{default_context, Error as EvaluateError},
expression::{Expression, Vector},
parse::{Error as ParseError, ErrorReason},
};
use crate::{
command::Command,
help::{show_help, FUNCTION_HELP_TEXTS, HELP_TEXT},
input::InputHelper,
};
lazy_static! {
static ref RESERVED_IDENTIFIERS: HashSet<String> =
HashSet::from(["true", "false", "out"].map(str::to_owned));
}
fn format_parse_error(error: ParseError) -> Report {
// Heavily based on https://github.com/zesterer/chumsky/blob/463226372cf293d45bd5df52bf25d5028243066e/examples/json.rs#L114-L173
let message = if let ErrorReason::Custom(message) = error.reason() {
message.clone()
} else {
format!(
"{}, expected {}",
if error.found().is_some() {
"Unexpected token"
} else {
"Unexpected end of input"
},
if error.expected().len() == 0 {
"something else".to_string()
} else {
error
.expected()
.map(|expected| match expected {
Some(expected) => expected.to_string(),
None => "end of input".to_string(),
})
.collect::<Vec<_>>()
.join(", ")
},
)
};
let report = Report::build(ReportKind::Error, (), error.span().start)
.with_message(message)
.with_label(
Label::new(error.span())
.with_message(match error.reason() {
ErrorReason::Custom(message) => message.clone(),
_ => format!(
"Unexpected {}",
error
.found()
.map(|c| format!("token {}", c.fg(Color::Red)))
.unwrap_or_else(|| "end of input".to_string()),
),
})
.with_color(Color::Red),
);
let report = match error.reason() {
ErrorReason::Unclosed { span, delimiter } => report.with_label(
Label::new(span.clone())
.with_message(format!(
"Unclosed delimiter {}",
delimiter.fg(Color::Yellow),
))
.with_color(Color::Yellow),
),
ErrorReason::Unexpected => report,
ErrorReason::Custom(_) => report,
};
report.finish()
}
fn main() {
use crate::command::Command::*;
let history_path = ProjectDirs::from("com.worldwidemann", "", "Savage")
.expect("unable to locate data directory")
.data_dir()
.join("history");
let mut editor = Editor::new();
editor.set_helper(Some(InputHelper {}));
editor.load_history(&history_path).ok();
println!(
"Savage Computer Algebra System {}",
env!("CARGO_PKG_VERSION"),
);
println!(
"Enter {} for help, press {} to quit, {} to cancel evaluation",
Style::new().bold().paint("?"),
Style::new().bold().paint("Ctrl+D"),
Style::new().bold().paint("Ctrl+C"),
);
let mut outputs = Vec::new();
let mut context = default_context();
context.insert(
"out".to_owned(),
Expression::Vector(Vector::from_vec(outputs.clone())),
);
'outer: loop {
println!();
match editor.readline("in: ") {
Ok(line) => {
let line = line.trim();
if line.is_empty() {
continue;
}
editor.add_history_entry(line);
match line.parse::<Command>() {
Ok(EvaluateExpression(expression)) => match expression.evaluate(&context) {
Ok(output) => {
println!(
"{}{}",
Style::new()
.bold()
.paint(format!("out[{}]: ", outputs.len())),
editor
.helper()
.unwrap()
.highlight(&output.to_string(), usize::MAX),
);
outputs.push(output);
context.insert(
"out".to_owned(),
Expression::Vector(Vector::from_vec(outputs.clone())),
);
}
Err(error) => println!("Error: {:#?}", error),
},
Ok(DefineVariable(identifier, expression)) => {
if RESERVED_IDENTIFIERS.contains(&identifier) {
println!("Error: \"{}\" is a reserved identifier and cannot be used as a variable name.", identifier);
continue;
}
match expression.evaluate(&context) {
Ok(expression) => {
let variables = expression.variables();
if !variables.is_empty() {
println!("Error: The assigned expression contains the undefined variable(s) {}.", Vec::from_iter(variables).join(", "));
continue;
}
context.insert(identifier, expression);
}
Err(error) => println!("Error: {:#?}", error),
}
}
Ok(DefineFunction(identifier, argument_identifiers, expression)) => {
if RESERVED_IDENTIFIERS.contains(&identifier) {
println!("Error: \"{}\" is a reserved identifier and cannot be used as a function name.", identifier);
continue;
}
let mut inner_context = context.clone();
for argument_identifier in &argument_identifiers {
if RESERVED_IDENTIFIERS.contains(argument_identifier) {
println!("Error: \"{}\" is a reserved identifier and cannot be used as an argument name.", argument_identifier);
continue 'outer;
}
if argument_identifiers
.iter()
.filter(|&id| id == argument_identifier)
.count()
> 1
{
println!(
"Error: The name \"{}\" is used for more than one argument.",
argument_identifier,
);
continue 'outer;
}
inner_context.remove(argument_identifier);
}
match expression.evaluate(&inner_context) {
Ok(expression) => {
let mut variables = expression.variables();
for argument_identifier in &argument_identifiers {
variables.remove(argument_identifier);
}
if !variables.is_empty() {
println!("Error: The assigned expression contains the undefined variable(s) {}.", Vec::from_iter(variables).join(", "));
continue;
}
context.insert(
identifier.clone(),
Expression::Function(
identifier,
Rc::new(move |self_expression, arguments, _| {
if arguments.len() != argument_identifiers.len() {
return Err(
EvaluateError::InvalidNumberOfArguments {
expression: self_expression.clone(),
min_number: argument_identifiers.len(),
max_number: argument_identifiers.len(),
given_number: arguments.len(),
},
);
}
// Both the default context and the outer context the function is being
// evaluated in can be ignored, since it was already checked that the
// expression contains no variables other than the argument identifiers.
let mut context = HashMap::new();
for (identifier, argument) in
argument_identifiers.iter().zip(arguments)
{
context
.insert(identifier.clone(), argument.clone());
}
expression.evaluate(&context)
}),
),
);
}
Err(error) => println!("Error: {:#?}", error),
}
}
Ok(ShowHelp(function_name)) => {
if let Some(function_name) = function_name {
if let Some(function_help_text) =
FUNCTION_HELP_TEXTS.get(&function_name)
{
show_help(function_help_text.clone()).expect("unable to show help");
} else {
println!(
"Error: No help text available for the function {}.",
function_name,
);
}
} else {
show_help(HELP_TEXT.clone()).expect("unable to show help");
}
}
Err(errors) => {
for error in errors {
format_parse_error(error)
.print(Source::from(line))
.expect("unable to print parse error");
}
}
}
}
Err(ReadlineError::Interrupted | ReadlineError::Eof) => {
break;
}
Err(error) => {
println!("Error: {:#?}", error);
break;
}
}
}
fs::create_dir_all(
history_path
.parent()
.expect("unable to determine parent directory of history file"),
)
.expect("unable to create data directory");
editor
.save_history(&history_path)
.expect("unable to save input history");
}
================================================
FILE: savage_core/Cargo.toml
================================================
[package]
name = "savage_core"
version = "0.2.0"
authors = ["Philipp Emanuel Weidmann <pew@worldwidemann.com>"]
description = "A primitive computer algebra system (library)"
repository = "https://github.com/p-e-w/savage"
readme = "README.md"
license = "AGPL-3.0-or-later"
edition = "2021"
[dependencies]
num = "0.4.0"
nalgebra = "0.31.1"
permutohedron = "0.2.4"
primal = "0.3.0"
chumsky = "0.8.0"
derivative = "2.2.0"
savage_macros = { path = "../savage_macros", version = "0.1.0" }
================================================
FILE: savage_core/src/evaluate.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use std::collections::HashMap;
use num::{One, ToPrimitive, Zero};
use crate::{
expression::{Complex, Expression, RationalRepresentation},
functions::functions,
};
/// Error that occurred while trying to evaluate an expression.
#[derive(PartialEq, Eq, Clone, Debug)]
pub enum Error {
/// Operation on an expression that the operation is not defined for.
InvalidOperand {
expression: Expression,
operand: Expression,
},
/// Operation on two expressions that cannot be combined using the operation.
IncompatibleOperands {
expression: Expression,
operand_1: Expression,
operand_2: Expression,
},
/// Division by an expression that evaluates to zero (undefined).
DivisionByZero {
expression: Expression,
dividend: Expression,
divisor: Expression,
},
/// An expression that evaluates to zero raised to the power of
/// another expression that evaluates to zero (undefined).
ZeroToThePowerOfZero {
expression: Expression,
base: Expression,
exponent: Expression,
},
/// Vector or matrix expression indexed by an expression that evaluates to
/// an integer outside the range of valid indices for that vector or matrix.
IndexOutOfBounds {
expression: Expression,
vector_or_matrix: Expression,
index: Expression,
},
/// Function expression evaluated with a number of arguments
/// that is invalid for the function.
InvalidNumberOfArguments {
expression: Expression,
min_number: usize,
max_number: usize,
given_number: usize,
},
/// Function expression evaluated with an argument
/// that is invalid for the function in that position.
InvalidArgument {
expression: Expression,
argument: Expression,
},
}
/// Returns an evaluation context populated with standard variable and function definitions.
pub fn default_context() -> HashMap<String, Expression> {
let mut default_context = HashMap::new();
default_context.insert(
"i".to_owned(),
Expression::Complex(Complex::i(), RationalRepresentation::Fraction),
);
for function in functions() {
default_context.insert(
function.metadata.name.to_owned(),
Expression::Function(function.metadata.name.to_owned(), function.implementation),
);
}
default_context
}
impl Expression {
/// Returns the result of performing a single evaluation step on
/// the unary operator expression `self` with operand `a`, or an error
/// if the expression cannot be evaluated. The `context` argument can be
/// used to set the values of variables by their identifiers.
fn evaluate_step_unary(
&self,
a: &Self,
context: &HashMap<String, Self>,
) -> Result<Self, Error> {
use crate::expression::Expression::*;
use crate::expression::Type::{Arithmetic, Boolean as Bool, Matrix as Mat, Number as Num};
use Error::*;
let a_original = a;
let a = a.evaluate_step(context)?;
match (self, a.typ()) {
(Negation(_), Bool(_)) | (Not(_), Num(_, _) | Mat(_) | Arithmetic) => {
Err(InvalidOperand {
expression: self.clone(),
operand: a_original.clone(),
})
}
(Negation(_), Num(a, representation)) => Ok(Complex(-a, representation)),
(Negation(_), Mat(a)) => Ok(Matrix(-a)),
(Negation(_), _) => Ok(Negation(Box::new(a))),
(Not(_), Bool(Some(a))) => Ok(Boolean(!a)),
(Not(_), _) => Ok(Not(Box::new(a))),
(
Variable(_)
| Function(_, _)
| FunctionValue(_, _)
| Integer(_)
| Rational(_, _)
| Complex(_, _)
| Vector(_)
| VectorElement(_, _)
| Matrix(_)
| MatrixElement(_, _, _)
| Boolean(_)
| Sum(_, _)
| Difference(_, _)
| Product(_, _)
| Quotient(_, _)
| Remainder(_, _)
| Power(_, _)
| Equal(_, _)
| NotEqual(_, _)
| LessThan(_, _)
| LessThanOrEqual(_, _)
| GreaterThan(_, _)
| GreaterThanOrEqual(_, _)
| And(_, _)
| Or(_, _),
_,
) => unreachable!(),
}
}
/// Returns the result of performing a single evaluation step on
/// the binary operator expression `self` with operands `a` and `b`,
/// or an error if the expression cannot be evaluated. The `context`
/// argument can be used to set the values of variables by their
/// identifiers.
fn evaluate_step_binary(
&self,
a: &Self,
b: &Self,
context: &HashMap<String, Self>,
) -> Result<Self, Error> {
use crate::expression::Expression::*;
use crate::expression::Type::{Arithmetic, Boolean as Bool, Matrix as Mat, Number as Num};
use Error::*;
let a_original = a;
let b_original = b;
let a = a.evaluate_step(context)?;
let b = b.evaluate_step(context)?;
let a_evaluated = &a;
let b_evaluated = &b;
match (self, a.typ(), b.typ()) {
(
Sum(_, _)
| Difference(_, _)
| Product(_, _)
| Quotient(_, _)
| Remainder(_, _)
| Power(_, _),
Bool(_),
_,
)
| (
LessThan(_, _)
| LessThanOrEqual(_, _)
| GreaterThan(_, _)
| GreaterThanOrEqual(_, _),
Mat(_) | Bool(_),
_,
)
| (And(_, _) | Or(_, _), Num(_, _) | Mat(_) | Arithmetic, _) => Err(InvalidOperand {
expression: self.clone(),
operand: a_original.clone(),
}),
(
Sum(_, _)
| Difference(_, _)
| Product(_, _)
| Quotient(_, _)
| Remainder(_, _)
| Power(_, _),
_,
Bool(_),
)
| (
LessThan(_, _)
| LessThanOrEqual(_, _)
| GreaterThan(_, _)
| GreaterThanOrEqual(_, _),
_,
Mat(_) | Bool(_),
)
| (And(_, _) | Or(_, _), _, Num(_, _) | Mat(_) | Arithmetic) => Err(InvalidOperand {
expression: self.clone(),
operand: b_original.clone(),
}),
(Sum(_, _) | Difference(_, _) | Equal(_, _) | NotEqual(_, _), Num(_, _), Mat(_))
| (Sum(_, _) | Difference(_, _) | Equal(_, _) | NotEqual(_, _), Mat(_), Num(_, _))
| (Equal(_, _) | NotEqual(_, _), Num(_, _) | Mat(_), Bool(_))
| (Equal(_, _) | NotEqual(_, _), Bool(_), Num(_, _) | Mat(_)) => {
Err(IncompatibleOperands {
expression: self.clone(),
operand_1: a_original.clone(),
operand_2: b_original.clone(),
})
}
(
Sum(_, _)
| Difference(_, _)
| Product(_, _)
| Quotient(_, _)
| Remainder(_, _)
| Power(_, _)
| Equal(_, _)
| NotEqual(_, _)
| LessThan(_, _)
| LessThanOrEqual(_, _)
| GreaterThan(_, _)
| GreaterThanOrEqual(_, _),
Num(a, a_representation),
Num(b, b_representation),
) => {
let representation = a_representation.merge(b_representation);
match self {
Sum(_, _) => Ok(Complex(a + b, representation)),
Difference(_, _) => Ok(Complex(a - b, representation)),
Product(_, _) => Ok(Complex(a * b, representation)),
Quotient(_, _) | Remainder(_, _) => {
if b.is_zero() {
Err(DivisionByZero {
expression: self.clone(),
dividend: a_original.clone(),
divisor: b_original.clone(),
})
} else {
Ok(Complex(
match self {
Quotient(_, _) => a / b,
Remainder(_, _) => a % b,
_ => unreachable!(),
},
representation,
))
}
}
Power(_, _) => {
if a.is_zero() && b.is_zero() {
Err(ZeroToThePowerOfZero {
expression: self.clone(),
base: a_original.clone(),
exponent: b_original.clone(),
})
} else if let Some(b) = b.to_i32() {
Ok(Complex(a.powi(b), representation))
} else {
// TODO
Ok(Power(
Box::new(a_evaluated.clone()),
Box::new(b_evaluated.clone()),
))
}
}
Equal(_, _) => Ok(Boolean(a == b)),
NotEqual(_, _) => Ok(Boolean(a != b)),
LessThan(_, _)
| LessThanOrEqual(_, _)
| GreaterThan(_, _)
| GreaterThanOrEqual(_, _) => {
if !a.im.is_zero() {
Err(InvalidOperand {
expression: self.clone(),
operand: a_original.clone(),
})
} else if !b.im.is_zero() {
Err(InvalidOperand {
expression: self.clone(),
operand: b_original.clone(),
})
} else {
let a = a.re;
let b = b.re;
Ok(Boolean(match self {
LessThan(_, _) => a < b,
LessThanOrEqual(_, _) => a <= b,
GreaterThan(_, _) => a > b,
GreaterThanOrEqual(_, _) => a >= b,
_ => unreachable!(),
}))
}
}
_ => unreachable!(),
}
}
(Sum(_, _) | Difference(_, _), Mat(a), Mat(b)) => {
if a.shape() == b.shape() {
Ok(Matrix(match self {
Sum(_, _) => a + b,
Difference(_, _) => a - b,
_ => unreachable!(),
}))
} else {
Err(IncompatibleOperands {
expression: self.clone(),
operand_1: a_original.clone(),
operand_2: b_original.clone(),
})
}
}
(Product(_, _), Mat(a), Mat(b)) => {
if a.is_empty() && b.is_empty() {
Ok(Matrix(a))
} else if !a.is_empty() && !b.is_empty() && a.ncols() == b.nrows() {
Ok(Matrix(crate::expression::Matrix::from_fn(
a.nrows(),
b.ncols(),
|i, j| {
(0..a.ncols())
.map(|k| a[(i, k)].clone() * b[(k, j)].clone())
.reduce(|a, b| a + b)
.unwrap()
},
)))
} else {
Err(IncompatibleOperands {
expression: self.clone(),
operand_1: a_original.clone(),
operand_2: b_original.clone(),
})
}
}
(Product(_, _), Mat(a), _) => Ok(Matrix(a.map(|element| element * b.clone()))),
(Product(_, _), _, Mat(b)) => Ok(Matrix(b.map(|element| a.clone() * element))),
(Equal(_, _), Bool(Some(a)), Bool(Some(b))) => Ok(Boolean(a == b)),
(NotEqual(_, _), Bool(Some(a)), Bool(Some(b))) => Ok(Boolean(a != b)),
(And(_, _), Bool(Some(a)), Bool(Some(b))) => Ok(Boolean(a && b)),
(Or(_, _), Bool(Some(a)), Bool(Some(b))) => Ok(Boolean(a || b)),
(Sum(_, _), _, _) => Ok(Sum(Box::new(a), Box::new(b))), // TODO
(Difference(_, _), _, _) => Ok(Difference(Box::new(a), Box::new(b))), // TODO
(Product(_, _), _, _) => Ok(Product(Box::new(a), Box::new(b))), // TODO
(Quotient(_, _), _, _) => Ok(Quotient(Box::new(a), Box::new(b))), // TODO
(Remainder(_, _), _, _) => Ok(Remainder(Box::new(a), Box::new(b))), // TODO
(Power(_, _), _, _) => Ok(Power(Box::new(a), Box::new(b))), // TODO
(Equal(_, _), _, _) => Ok(Equal(Box::new(a), Box::new(b))), // TODO
(NotEqual(_, _), _, _) => Ok(NotEqual(Box::new(a), Box::new(b))), // TODO
(LessThan(_, _), _, _) => Ok(LessThan(Box::new(a), Box::new(b))), // TODO
(LessThanOrEqual(_, _), _, _) => Ok(LessThanOrEqual(Box::new(a), Box::new(b))), // TODO
(GreaterThan(_, _), _, _) => Ok(GreaterThan(Box::new(a), Box::new(b))), // TODO
(GreaterThanOrEqual(_, _), _, _) => Ok(GreaterThanOrEqual(Box::new(a), Box::new(b))), // TODO
(And(_, _), _, _) => Ok(And(Box::new(a), Box::new(b))), // TODO
(Or(_, _), _, _) => Ok(Or(Box::new(a), Box::new(b))), // TODO
(
Variable(_)
| Function(_, _)
| FunctionValue(_, _)
| Integer(_)
| Rational(_, _)
| Complex(_, _)
| Vector(_)
| VectorElement(_, _)
| Matrix(_)
| MatrixElement(_, _, _)
| Boolean(_)
| Negation(_)
| Not(_),
_,
_,
) => unreachable!(),
}
}
/// Returns the result of performing a single evaluation step on the expression,
/// or an error if the expression cannot be evaluated. The `context` argument
/// can be used to set the values of variables by their identifiers.
fn evaluate_step(&self, context: &HashMap<String, Self>) -> Result<Self, Error> {
use crate::expression::Expression::*;
use crate::expression::Type::{
Boolean as Bool, Function as Fun, Matrix as Mat, Number as Num,
};
use Error::*;
let expression = self.simplify();
match &expression {
Variable(identifier) => context
.get(identifier)
.map_or_else(|| Ok(expression), |x| x.evaluate_step(context)),
Function(_, _) => Ok(expression),
FunctionValue(function, arguments) => {
let function_original = function;
let function = function.evaluate_step(context)?;
let mut arguments_evaluated = Vec::new();
for argument in arguments {
arguments_evaluated.push(argument.evaluate_step(context)?);
}
match function.typ() {
Num(_, _) | Mat(_) | Bool(_) => Err(InvalidOperand {
expression: expression.clone(),
operand: *function_original.clone(),
}),
Fun(_, f) => f(&expression, &arguments_evaluated, context),
_ => Ok(FunctionValue(Box::new(function), arguments_evaluated)),
}
}
Integer(_) => Ok(expression),
Rational(x, _) => Ok(if x.denom().is_one() {
Integer(x.numer().clone())
} else {
expression
}),
Complex(z, representation) => Ok(if z.im.is_zero() {
Rational(z.re.clone(), *representation)
} else {
expression
}),
Vector(v) => {
let mut elements = Vec::new();
for element in v.iter() {
elements.push(element.evaluate_step(context)?);
}
Ok(Vector(crate::expression::Vector::from_vec(elements)))
}
VectorElement(vector, i) => {
let vector_original = vector;
let i_original = i;
let vector = vector.evaluate_step(context)?;
let i = i.evaluate_step(context)?;
match (vector.typ(), i.typ()) {
(Num(_, _) | Bool(_), _) => Err(InvalidOperand {
expression: expression.clone(),
operand: *vector_original.clone(),
}),
(_, Mat(_) | Bool(_)) => Err(InvalidOperand {
expression: expression.clone(),
operand: *i_original.clone(),
}),
(Mat(vector), Num(i, _)) => {
if vector.ncols() != 1 {
Err(InvalidOperand {
expression: expression.clone(),
operand: *vector_original.clone(),
})
} else if let Some(i) = i.to_usize() {
if i >= vector.nrows() {
Err(IndexOutOfBounds {
expression: expression.clone(),
vector_or_matrix: *vector_original.clone(),
index: *i_original.clone(),
})
} else {
Ok(vector[(i, 0)].clone())
}
} else {
Err(InvalidOperand {
expression: expression.clone(),
operand: *i_original.clone(),
})
}
}
_ => Ok(VectorElement(Box::new(vector), Box::new(i))),
}
}
Matrix(m) => {
let mut columns = Vec::new();
for column in m.column_iter() {
let mut elements = Vec::new();
for element in column.iter() {
elements.push(element.evaluate_step(context)?);
}
columns.push(crate::expression::Vector::from_vec(elements));
}
Ok(if columns.is_empty() {
Vector(crate::expression::Vector::from_vec(Vec::new()))
} else if columns.len() == 1 {
Vector(columns.remove(0))
} else {
Matrix(crate::expression::Matrix::from_columns(&columns))
})
}
MatrixElement(matrix, i, j) => {
let matrix_original = matrix;
let i_original = i;
let j_original = j;
let matrix = matrix.evaluate_step(context)?;
let i = i.evaluate_step(context)?;
let j = j.evaluate_step(context)?;
match (matrix.typ(), i.typ(), j.typ()) {
(Num(_, _) | Bool(_), _, _) => Err(InvalidOperand {
expression: expression.clone(),
operand: *matrix_original.clone(),
}),
(_, Mat(_) | Bool(_), _) => Err(InvalidOperand {
expression: expression.clone(),
operand: *i_original.clone(),
}),
(_, _, Mat(_) | Bool(_)) => Err(InvalidOperand {
expression: expression.clone(),
operand: *j_original.clone(),
}),
(Mat(matrix), Num(i, _), Num(j, _)) => {
if let Some(i) = i.to_usize() {
if let Some(j) = j.to_usize() {
if i >= matrix.nrows() {
Err(IndexOutOfBounds {
expression: expression.clone(),
vector_or_matrix: *matrix_original.clone(),
index: *i_original.clone(),
})
} else if j >= matrix.ncols() {
Err(IndexOutOfBounds {
expression: expression.clone(),
vector_or_matrix: *matrix_original.clone(),
index: *j_original.clone(),
})
} else {
Ok(matrix[(i, j)].clone())
}
} else {
Err(InvalidOperand {
expression: expression.clone(),
operand: *j_original.clone(),
})
}
} else {
Err(InvalidOperand {
expression: expression.clone(),
operand: *i_original.clone(),
})
}
}
_ => Ok(MatrixElement(Box::new(matrix), Box::new(i), Box::new(j))),
}
}
Boolean(_) => Ok(expression),
Negation(a) => expression.evaluate_step_unary(a, context),
Not(a) => expression.evaluate_step_unary(a, context),
Sum(a, b) => expression.evaluate_step_binary(a, b, context),
Difference(a, b) => expression.evaluate_step_binary(a, b, context),
Product(a, b) => expression.evaluate_step_binary(a, b, context),
Quotient(a, b) => expression.evaluate_step_binary(a, b, context),
Remainder(a, b) => expression.evaluate_step_binary(a, b, context),
Power(a, b) => expression.evaluate_step_binary(a, b, context),
Equal(a, b) => expression.evaluate_step_binary(a, b, context),
NotEqual(a, b) => expression.evaluate_step_binary(a, b, context),
LessThan(a, b) => expression.evaluate_step_binary(a, b, context),
LessThanOrEqual(a, b) => expression.evaluate_step_binary(a, b, context),
GreaterThan(a, b) => expression.evaluate_step_binary(a, b, context),
GreaterThanOrEqual(a, b) => expression.evaluate_step_binary(a, b, context),
And(a, b) => expression.evaluate_step_binary(a, b, context),
Or(a, b) => expression.evaluate_step_binary(a, b, context),
}
}
/// Returns the result of evaluating the expression, or an error
/// if the expression cannot be evaluated. The `context` argument
/// can be used to set the values of variables by their identifiers.
pub fn evaluate(&self, context: &HashMap<String, Self>) -> Result<Self, Error> {
let mut old_expression: Self = self.clone();
loop {
let new_expression = old_expression.evaluate_step(context)?;
if new_expression == old_expression {
return Ok(new_expression);
}
old_expression = new_expression;
}
}
}
#[cfg(test)]
mod tests {
use crate::evaluate::default_context;
use crate::expression::Expression;
#[track_caller]
fn t(expression: &str, result: &str) {
assert_eq!(
expression
.parse::<Expression>()
.unwrap()
.evaluate(&default_context())
.unwrap()
.to_string(),
result,
);
}
#[test]
fn arithmetic() {
t("-(-1)", "1");
t("-0", "0");
t("1 + 2", "3");
t("1 + -1", "0");
t("1/2 + 0.5", "1");
t(
"123456789987654321 + 987654321123456789",
"1111111111111111110",
);
t("1 - 2", "-1");
t("1 - -1", "2");
t("1/2 - 0.5", "0");
t(
"123456789987654321 - 987654321123456789",
"-864197531135802468",
);
t("1 * 2", "2");
t("1 * -1", "-1");
t("1/2 * 0.5", "0.25");
t(
"123456789987654321 * 987654321123456789",
"121932632103337905662094193112635269",
);
t("1 / 2", "1/2");
t("1 / -1", "-1");
t("1/2 / 0.5", "1");
t(
"123456789987654321 / 987654321123456789",
"101010101/808080809",
);
t("4 % 2", "0");
t("0 % 2", "0");
t("5 % 2", "1");
t("-5 % 2", "-1");
t("-5 % -2", "-1");
t("0.75 % (1/4)", "0");
t("0.75 % (1/3)", "1/12");
t("987654321123456789 % 123456789987654321", "1222222221");
t("i ^ 2", "-1");
t("2 ^ 3", "8");
t("2 ^ (-3)", "1/8");
t("-2 ^ 4", "-16");
t("(-2) ^ 4", "16");
t("0.5 ^ 4", "0.0625");
t(
"987654321123456789 ^ 5",
"939777062588963894467852986656442266299580252508947542802086985660852317355013741720482949",
);
t(
"3 ^ 4 ^ 5",
"373391848741020043532959754184866588225409776783734007750636931722079040617265251229993688938803977220468765065431475158108727054592160858581351336982809187314191748594262580938807019951956404285571818041046681288797402925517668012340617298396574731619152386723046235125934896058590588284654793540505936202376547807442730582144527058988756251452817793413352141920744623027518729185432862375737063985485319476416926263819972887006907013899256524297198527698749274196276811060702333710356481",
);
}
#[test]
fn linear_algebra() {
t("[1] + [2]", "[3]");
t("[1] - [2]", "[-1]");
t("[1] * [2]", "[2]");
t("[1] * 2", "[2]");
t("1 * [2]", "[2]");
t("[1, 2] + [3, 4]", "[4, 6]");
t("[1, 2] - [3, 4]", "[-2, -2]");
t("[1, 2] * [[3, 4]]", "[[3, 4], [6, 8]]");
t("[[1, 2]] * [3, 4]", "[11]");
t("2 * [3, 4]", "[6, 8]");
t("[2, 3] * 4", "[8, 12]");
t(
"[[a, b], [c, d], [e, f]] * [[5, 6], [7, 8]]",
"[[a * 5 + b * 7, a * 6 + b * 8], [c * 5 + d * 7, c * 6 + d * 8], [e * 5 + f * 7, e * 6 + f * 8]]",
);
}
#[test]
fn indices() {
t("[a][0]", "a");
t("[a, b, c][2]", "c");
t("[1 + 2, 2 + 3, 3 + 4, 4 + 5][1 + 2]", "9");
t("[[a]][0, 0]", "a");
t("[[a, b, c], [d, e, f]][1, 2]", "f");
t("[[1 + 2, 2 + 3], [3 + 4, 4 + 5]][0 + 0, 0 + 1]", "5");
}
#[test]
fn logic() {
t("!true", "false");
t("!false", "true");
t("true && true", "true");
t("true && false", "false");
t("false && true", "false");
t("false && false", "false");
t("true || true", "true");
t("true || false", "true");
t("false || true", "true");
t("false || false", "false");
}
#[test]
fn comparisons() {
t("0 == 0", "true");
t("0 == 0.0", "true");
t("0.5 == 1/2", "true");
t("1/2 == 2/4", "true");
t("3 ^ 4 ^ 5 == 5 ^ 4 ^ 3", "false");
t("0 != 0", "false");
t("0 != 0.0", "false");
t("0.5 != 1/2", "false");
t("1/2 != 2/4", "false");
t("3 ^ 4 ^ 5 != 5 ^ 4 ^ 3", "true");
t("0 < 0", "false");
t("0 < 0.0", "false");
t("0.5 < 1/2", "false");
t("1/2 < 2/4", "false");
t("3 ^ 4 ^ 5 < 5 ^ 4 ^ 3", "false");
t("0 <= 0", "true");
t("0 <= 0.0", "true");
t("0.5 <= 1/2", "true");
t("1/2 <= 2/4", "true");
t("3 ^ 4 ^ 5 <= 5 ^ 4 ^ 3", "false");
t("0 > 0", "false");
t("0 > 0.0", "false");
t("0.5 > 1/2", "false");
t("1/2 > 2/4", "false");
t("3 ^ 4 ^ 5 > 5 ^ 4 ^ 3", "true");
t("0 >= 0", "true");
t("0 >= 0.0", "true");
t("0.5 >= 1/2", "true");
t("1/2 >= 2/4", "true");
t("3 ^ 4 ^ 5 >= 5 ^ 4 ^ 3", "true");
t("true == true", "true");
t("true == false", "false");
t("false == true", "false");
t("false == false", "true");
t("true != true", "false");
t("true != false", "true");
t("false != true", "true");
t("false != false", "false");
}
}
================================================
FILE: savage_core/src/expression.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use std::{
collections::{HashMap, HashSet},
rc::Rc,
};
use derivative::*;
use num::{Signed, Zero};
use crate::evaluate::Error;
/// Function implementation.
pub type Function =
dyn Fn(&Expression, &[Expression], &HashMap<String, Expression>) -> Result<Expression, Error>;
/// Arbitrary-precision integer.
pub type Integer = num::bigint::BigInt;
/// Arbitrary-precision rational number.
pub type Rational = num::rational::Ratio<Integer>;
/// Arbitrary-precision complex number (i.e. real and imaginary parts are arbitrary-precision rational numbers).
pub type Complex = num::complex::Complex<Rational>;
/// Column vector with expressions as components.
pub type Vector = nalgebra::DVector<Expression>;
/// Column-major matrix with expressions as components.
pub type Matrix = nalgebra::DMatrix<Expression>;
/// Preferred representation when printing a rational number.
#[derive(PartialEq, Eq, Clone, Copy, Debug)]
pub enum RationalRepresentation {
/// Fraction (numerator/denominator).
Fraction,
/// Decimal, falling back to fraction representation
/// if the number cannot be represented as a finite decimal.
Decimal,
}
impl RationalRepresentation {
/// Returns the preferred representation for the result of an operation
/// on two numbers with representations `self` and `other`.
pub(crate) fn merge(self, other: Self) -> Self {
use RationalRepresentation::*;
if self == Decimal || other == Decimal {
Decimal
} else {
Fraction
}
}
}
/// Symbolic expression.
#[derive(Derivative)]
#[derivative(PartialEq, Eq, Clone, Debug)]
pub enum Expression {
/// Variable with identifier.
Variable(String),
/// Function with identifier and implementation.
Function(
String,
#[derivative(PartialEq = "ignore", Debug = "ignore")] Rc<Function>,
),
/// Value of a function expression at the given arguments.
FunctionValue(Box<Self>, Vec<Self>),
/// Integer.
Integer(Integer),
/// Rational number with preferred representation.
Rational(Rational, RationalRepresentation),
/// Complex number with preferred representation for real and imaginary parts.
Complex(Complex, RationalRepresentation),
/// Column vector.
Vector(Vector),
/// Element of a column vector expression given by an index expression.
VectorElement(Box<Self>, Box<Self>),
/// Column-major matrix.
Matrix(Matrix),
/// Element of a column-major matrix expression given by row and column index expressions.
MatrixElement(Box<Self>, Box<Self>, Box<Self>),
/// Boolean value.
Boolean(bool),
/// Arithmetic negation of an expression.
Negation(Box<Self>),
/// Logical negation (NOT) of an expression.
Not(Box<Self>),
/// Sum of two expressions.
Sum(Box<Self>, Box<Self>),
/// Difference of two expressions.
Difference(Box<Self>, Box<Self>),
/// Product of two expressions.
Product(Box<Self>, Box<Self>),
/// Quotient of two expressions.
Quotient(Box<Self>, Box<Self>),
/// Remainder of the Euclidean division of the first expression by the second.
Remainder(Box<Self>, Box<Self>),
/// The first expression raised to the power of the second.
Power(Box<Self>, Box<Self>),
/// Whether two expressions are equal.
Equal(Box<Self>, Box<Self>),
/// Whether two expressions are not equal.
NotEqual(Box<Self>, Box<Self>),
/// Whether the first expression is less than the second.
LessThan(Box<Self>, Box<Self>),
/// Whether the first expression is less than or equal to the second.
LessThanOrEqual(Box<Self>, Box<Self>),
/// Whether the first expression is greater than the second.
GreaterThan(Box<Self>, Box<Self>),
/// Whether the first expression is greater than or equal to the second.
GreaterThanOrEqual(Box<Self>, Box<Self>),
/// Logical conjunction (AND) of two expressions.
And(Box<Self>, Box<Self>),
/// Logical disjunction (OR) of two expressions.
Or(Box<Self>, Box<Self>),
}
/// Basic expression type designed to make evaluating expressions easier.
#[derive(Derivative)]
#[derivative(PartialEq, Eq, Clone, Debug)]
pub(crate) enum Type {
/// Function with identifier and implementation.
Function(
String,
#[derivative(PartialEq = "ignore", Debug = "ignore")] Rc<Function>,
),
/// Number with preferred representation for rational parts.
Number(Complex, RationalRepresentation),
/// Column-major matrix.
Matrix(Matrix),
/// Boolean expression with value (if available).
Boolean(Option<bool>),
/// Arithmetic expression (in particular, this expression does *not* have a boolean value).
Arithmetic,
/// Expression that cannot be assigned to any of the above types with certainty.
Unknown,
}
/// Associativity of an operator expression.
#[allow(clippy::enum_variant_names)]
#[derive(PartialEq, Eq, Clone, Copy, Debug)]
pub(crate) enum Associativity {
/// `a OP b OP c == (a OP b) OP c`.
LeftAssociative,
/// `a OP b OP c == a OP (b OP c)`.
RightAssociative,
/// `a OP b OP c == (a OP b) OP c == a OP (b OP c)`.
Associative,
}
impl Expression {
/// Returns the basic type of the expression.
pub(crate) fn typ(&self) -> Type {
use Expression::*;
use RationalRepresentation::*;
use Type::{
Arithmetic, Boolean as Bool, Function as Fun, Matrix as Mat, Number as Num, Unknown,
};
match self {
Variable(_) => Unknown,
Function(identifier, f) => Fun(identifier.clone(), f.clone()),
FunctionValue(_, _) => Unknown,
Integer(n) => Num(self::Rational::from_integer(n.clone()).into(), Fraction),
Rational(x, representation) => Num(x.into(), *representation),
Complex(z, representation) => Num(z.clone(), *representation),
Vector(v) => Mat(self::Matrix::from_columns(&[v.clone()])),
VectorElement(_, _) => Unknown,
Matrix(m) => Mat(m.clone()),
MatrixElement(_, _, _) => Unknown,
Boolean(boolean) => Bool(Some(*boolean)),
Negation(_) => Arithmetic,
Not(_) => Bool(None),
Sum(_, _) => Arithmetic,
Difference(_, _) => Arithmetic,
Product(_, _) => Arithmetic,
Quotient(_, _) => Arithmetic,
Remainder(_, _) => Arithmetic,
Power(_, _) => Arithmetic,
Equal(_, _) => Bool(None),
NotEqual(_, _) => Bool(None),
LessThan(_, _) => Bool(None),
LessThanOrEqual(_, _) => Bool(None),
GreaterThan(_, _) => Bool(None),
GreaterThanOrEqual(_, _) => Bool(None),
And(_, _) => Bool(None),
Or(_, _) => Bool(None),
}
}
/// Returns the precedence (as an integer intended for comparison)
/// and associativity of the expression. For unary or non-operator
/// expressions, to which the concept of associativity doesn't apply,
/// `Associative` is returned.
pub(crate) fn precedence_and_associativity(&self) -> (isize, Associativity) {
use Associativity::*;
use Expression::*;
match self {
Variable(_) => (isize::MAX, Associative),
Function(_, _) => (isize::MAX, Associative),
FunctionValue(_, _) => (5, Associative),
Integer(n) => {
if n.is_negative() {
(2, Associative)
} else {
(isize::MAX, Associative)
}
}
Rational(x, _) => {
if self.to_string().contains('/') {
(2, LeftAssociative)
} else if x.is_negative() {
(2, Associative)
} else {
(isize::MAX, Associative)
}
}
Complex(z, _) => {
if !z.re.is_zero() && !z.im.is_zero() {
if self.to_string().contains('+') {
(1, Associative)
} else {
(1, LeftAssociative)
}
} else if self.to_string().contains('/') {
(2, LeftAssociative)
} else if z.re.is_negative() || !z.im.is_zero() {
(2, Associative)
} else {
(isize::MAX, Associative)
}
}
Vector(_) => (isize::MAX, Associative),
VectorElement(_, _) => (5, Associative),
Matrix(_) => (isize::MAX, Associative),
MatrixElement(_, _, _) => (5, Associative),
Boolean(_) => (isize::MAX, Associative),
Negation(_) => (3, Associative),
Not(_) => (3, Associative),
Sum(_, _) => (1, Associative),
Difference(_, _) => (1, LeftAssociative),
Product(_, _) => (2, Associative),
Quotient(_, _) => (2, LeftAssociative),
Remainder(_, _) => (2, LeftAssociative),
Power(_, _) => (4, RightAssociative),
Equal(_, _) => (0, Associative),
NotEqual(_, _) => (0, Associative),
LessThan(_, _) => (0, Associative),
LessThanOrEqual(_, _) => (0, Associative),
GreaterThan(_, _) => (0, Associative),
GreaterThanOrEqual(_, _) => (0, Associative),
And(_, _) => (-1, Associative),
Or(_, _) => (-2, Associative),
}
}
/// Returns the precedence (as an integer intended for comparison) of the expression.
pub(crate) fn precedence(&self) -> isize {
self.precedence_and_associativity().0
}
/// Returns the associativity of the expression.
/// For unary or non-operator expressions, to which the concept
/// of associativity doesn't apply, `Associative` is returned.
pub(crate) fn associativity(&self) -> Associativity {
self.precedence_and_associativity().1
}
/// Returns all sub-expressions that the expression contains.
/// The returned list is built recursively and thus includes sub-expressions
/// of sub-expressions and so on, as well as the expression itself.
pub(crate) fn parts(&self) -> Vec<Self> {
use Expression::*;
let mut parts = vec![self.clone()];
match self {
Variable(_) => {}
Function(_, _) => {}
FunctionValue(function, arguments) => {
parts.append(&mut function.parts());
for argument in arguments {
parts.append(&mut argument.parts());
}
}
Integer(_) => {}
Rational(_, _) => {}
Complex(_, _) => {}
Vector(v) => {
for element in v.iter() {
parts.append(&mut element.parts());
}
}
VectorElement(vector, i) => {
parts.append(&mut vector.parts());
parts.append(&mut i.parts());
}
Matrix(m) => {
for element in m.iter() {
parts.append(&mut element.parts());
}
}
MatrixElement(matrix, i, j) => {
parts.append(&mut matrix.parts());
parts.append(&mut i.parts());
parts.append(&mut j.parts());
}
Boolean(_) => {}
Negation(a) | Not(a) => {
parts.append(&mut a.parts());
}
Sum(a, b)
| Difference(a, b)
| Product(a, b)
| Quotient(a, b)
| Remainder(a, b)
| Power(a, b)
| Equal(a, b)
| NotEqual(a, b)
| LessThan(a, b)
| LessThanOrEqual(a, b)
| GreaterThan(a, b)
| GreaterThanOrEqual(a, b)
| And(a, b)
| Or(a, b) => {
parts.append(&mut a.parts());
parts.append(&mut b.parts());
}
}
parts
}
/// Returns the identifiers of all variables that the expression contains.
pub fn variables(&self) -> HashSet<String> {
let mut identifiers = HashSet::new();
for part in self.parts() {
if let Self::Variable(identifier) = part {
identifiers.insert(identifier);
}
}
identifiers
}
}
================================================
FILE: savage_core/src/functions/combinatorics.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use num::range_inclusive;
use savage_macros::function;
use crate::{expression::Integer, functions::NonNegativeInteger};
#[function(
name = "factorial",
description = "factorial of a non-negative integer",
examples = r#"[
("factorial(0)", "1"),
("factorial(1)", "1"),
("factorial(4)", "24"),
("factorial(10)", "3628800"),
]"#,
categories = r#"[
"combinatorics",
]"#
)]
fn factorial(n: NonNegativeInteger) -> Integer {
range_inclusive::<Integer>(1.into(), n).product()
}
================================================
FILE: savage_core/src/functions/linear_algebra.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use permutohedron::heap_recursive;
use savage_macros::function;
use crate::{expression::Expression, functions::SquareMatrix, helpers::*};
#[function(
name = "det",
description = "determinant of a square matrix",
examples = r#"[
("det([[1, 2], [3, 4]])", "-2"),
("det([[a, b], [c, d]])", "a * d - b * c"),
("det([])", "1"),
]"#,
categories = r#"[
"linear algebra",
]"#
)]
fn determinant(matrix: SquareMatrix) -> Expression {
if matrix.is_empty() {
return int(1);
}
let mut indices = (0..matrix.nrows()).collect::<Vec<usize>>();
let mut products = Vec::new();
heap_recursive(indices.as_mut_slice(), |permutation| {
products.push(
(0..matrix.nrows())
.map(|i| matrix[(i, permutation[i])].clone())
.reduce(|a, b| a * b)
.unwrap(),
);
});
// The first permutation generated by Heap's algorithm is the identity,
// which has positive sign...
let mut positive = true;
products
.into_iter()
.reduce(|a, b| {
// ... and every following permutation differs from its predecessor
// by exactly one transposition, which flips the sign.
positive = !positive;
if positive {
a + b
} else {
a - b
}
})
.unwrap()
}
================================================
FILE: savage_core/src/functions/logic.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use savage_macros::function;
#[function(
name = "and",
description = "logical conjunction",
examples = r#"[
("and(true, true)", "true"),
("and(true, false)", "false"),
("and(false, true)", "false"),
("and(false, false)", "false"),
]"#,
categories = r#"[
"logic",
"boolean operators",
]"#
)]
fn and(a: bool, b: bool) -> bool {
a && b
}
================================================
FILE: savage_core/src/functions/mod.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
mod combinatorics;
mod linear_algebra;
mod logic;
mod number_theory;
use std::rc::Rc;
use num::Signed;
use savage_macros::functions;
use crate::expression::{Expression, Function as FunctionImplementation, Integer, Matrix};
/// Arbitrary-precision non-negative integer.
/// This type alias is intended for use in function signatures
/// to mark integer parameters that must be non-negative.
pub(crate) type NonNegativeInteger = Integer;
/// Arbitrary-precision positive integer.
/// This type alias is intended for use in function signatures
/// to mark integer parameters that must be positive.
pub(crate) type PositiveInteger = Integer;
/// Column-major square matrix with expressions as components.
/// This type alias is intended for use in function signatures
/// to mark matrix parameters that must be square matrices.
pub(crate) type SquareMatrix = Matrix;
/// Function parameter.
#[derive(PartialEq, Eq, Clone, Copy, Debug)]
pub enum Parameter {
/// Any symbolic expression.
Expression,
/// Integer expression, or an expression that can be interpreted as an integer.
Integer,
/// Non-negative integer expression, or an expression that can be interpreted as a non-negative integer.
NonNegativeInteger,
/// Positive integer expression, or an expression that can be interpreted as a positive integer.
PositiveInteger,
/// Rational number expression, or an expression that can be interpreted as a rational number.
Rational,
/// Complex number expression, or an expression that can be interpreted as a complex number.
Complex,
/// Vector expression, or an expression that can be interpreted as a vector.
Vector,
/// Matrix expression, or an expression that can be interpreted as a matrix.
Matrix,
/// Matrix expression containing a square matrix, or an expression that can be interpreted as a square matrix.
SquareMatrix,
/// Boolean expression, or an expression that can be interpreted as a boolean value.
Boolean,
}
/// Metadata associated with a function.
#[derive(PartialEq, Eq, Clone, Debug)]
pub struct Metadata {
/// Name used to represent the function (also, default identifier for invoking the function).
pub name: &'static str,
/// Human-readable description of the function.
pub description: &'static str,
/// Parameters expected by the function, in the expected order.
pub parameters: &'static [Parameter],
/// Usage examples for the function, as pairs of REPL input and output.
pub examples: &'static [(&'static str, &'static str)],
/// Categories associated with the function.
pub categories: &'static [&'static str],
}
/// Function definition.
pub struct Function {
/// Metadata associated with the function.
pub metadata: Metadata,
/// Implementation of the function.
pub implementation: Rc<FunctionImplementation>,
}
/// Returns a regular function implementation that type-checks its arguments
/// based on the given `parameters` and then invokes the given function `proxy`.
fn wrap_proxy(
parameters: &'static [Parameter],
proxy: impl Fn(&[Expression]) -> Result<Expression, Expression> + 'static,
) -> Rc<FunctionImplementation> {
use crate::evaluate::Error::*;
use crate::expression::Type::{Arithmetic, Boolean as Bool, Unknown};
use Parameter::*;
Rc::new(move |expression, arguments, _| {
if arguments.len() != parameters.len() {
return Err(InvalidNumberOfArguments {
expression: expression.clone(),
min_number: parameters.len(),
max_number: parameters.len(),
given_number: arguments.len(),
});
}
for (argument, parameter) in arguments.iter().zip(parameters) {
if let Bool(None) | Arithmetic | Unknown = argument.typ() {
if *parameter != Expression {
return Ok(expression.clone());
}
}
let mut argument_valid = true;
match parameter {
NonNegativeInteger => {
if let Ok(integer) = crate::expression::Integer::try_from(argument.clone()) {
argument_valid = !integer.is_negative();
}
}
PositiveInteger => {
if let Ok(integer) = crate::expression::Integer::try_from(argument.clone()) {
argument_valid = integer.is_positive();
}
}
SquareMatrix => {
if let Ok(matrix) = crate::expression::Matrix::try_from(argument.clone()) {
argument_valid = matrix.is_square() || matrix.is_empty();
}
}
_ => (),
}
if !argument_valid {
return Err(InvalidArgument {
expression: expression.clone(),
argument: argument.clone(),
});
}
}
proxy(arguments).map_err(|argument| InvalidArgument {
expression: expression.clone(),
argument,
})
})
}
/// Returns all available functions.
pub fn functions() -> Vec<Function> {
functions!(
logic::and,
combinatorics::factorial,
linear_algebra::determinant,
number_theory::is_prime,
number_theory::nth_prime,
number_theory::prime_pi,
)
}
/// Returns an expression representing the function with the given name,
/// or `None` if the function library contains no function with that name.
pub fn function_expression(name: &str) -> Option<Expression> {
for function in functions() {
if function.metadata.name == name {
return Some(Expression::Function(
function.metadata.name.to_owned(),
function.implementation,
));
}
}
None
}
#[cfg(test)]
mod tests {
use crate::evaluate::default_context;
use crate::expression::Expression;
use crate::functions::functions;
#[track_caller]
fn t(expression: &str, result: &str) {
assert_eq!(
expression
.parse::<Expression>()
.unwrap()
.evaluate(&default_context())
.unwrap()
.to_string(),
result,
);
}
#[test]
fn examples() {
for function in functions() {
for (expression, result) in function.metadata.examples {
t(expression, result);
}
}
}
}
================================================
FILE: savage_core/src/functions/number_theory.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use num::ToPrimitive;
use primal::StreamingSieve;
use savage_macros::function;
use crate::{
expression::Expression,
functions::{function_expression, NonNegativeInteger, PositiveInteger},
helpers::*,
};
#[function(
name = "is_prime",
description = "whether the given non-negative integer is a prime number",
examples = r#"[
("is_prime(0)", "false"),
("is_prime(1)", "false"),
("is_prime(2)", "true"),
("is_prime(29)", "true"),
("is_prime(2^31)", "false"),
("is_prime(2^31 - 1)", "true"),
]"#,
categories = r#"[
"number theory",
"prime numbers",
]"#
)]
fn is_prime(n: NonNegativeInteger) -> Expression {
if let Some(n) = n.to_u64() {
Expression::Boolean(primal::is_prime(n))
} else {
fun(function_expression("is_prime").unwrap(), [int(n)])
}
}
#[function(
name = "nth_prime",
description = "`n`th prime number, 1-indexed",
examples = r#"[
("nth_prime(1)", "2"),
("nth_prime(10)", "29"),
("nth_prime(100)", "541"),
("nth_prime(1000)", "7919"),
]"#,
categories = r#"[
"number theory",
"prime numbers",
]"#
)]
fn nth_prime(n: PositiveInteger) -> Expression {
if let Some(n) = n.to_usize() {
int(StreamingSieve::nth_prime(n))
} else {
fun(function_expression("nth_prime").unwrap(), [int(n)])
}
}
#[function(
name = "prime_pi",
description = "number of prime numbers less than or equal to the given non-negative integer",
examples = r#"[
("prime_pi(10)", "4"),
("prime_pi(100)", "25"),
("prime_pi(1000)", "168"),
("prime_pi(10000)", "1229"),
("prime_pi(100000)", "9592"),
]"#,
categories = r#"[
"number theory",
"prime numbers",
]"#
)]
fn prime_pi(n: NonNegativeInteger) -> Expression {
if let Some(n) = n.to_usize() {
int(StreamingSieve::prime_pi(n))
} else {
fun(function_expression("prime_pi").unwrap(), [int(n)])
}
}
================================================
FILE: savage_core/src/helpers.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
//! Operators, conversions, and helper functions to make working with expressions easier.
use std::ops::{
Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Not, Rem, RemAssign, Sub, SubAssign,
};
use num::{One, Zero};
use crate::expression::{
Complex, Expression, Integer, Matrix, Rational, RationalRepresentation, Type, Vector,
};
impl Neg for Expression {
type Output = Self;
fn neg(self) -> Self {
Expression::Negation(Box::new(self))
}
}
impl Not for Expression {
type Output = Self;
fn not(self) -> Self {
Expression::Not(Box::new(self))
}
}
impl Add for Expression {
type Output = Self;
fn add(self, other: Self) -> Self {
Expression::Sum(Box::new(self), Box::new(other))
}
}
impl AddAssign for Expression {
fn add_assign(&mut self, other: Self) {
*self = self.clone() + other;
}
}
impl Sub for Expression {
type Output = Self;
fn sub(self, other: Self) -> Self {
Expression::Difference(Box::new(self), Box::new(other))
}
}
impl SubAssign for Expression {
fn sub_assign(&mut self, other: Self) {
*self = self.clone() - other;
}
}
impl Mul for Expression {
type Output = Self;
fn mul(self, other: Self) -> Self {
Expression::Product(Box::new(self), Box::new(other))
}
}
impl MulAssign for Expression {
fn mul_assign(&mut self, other: Self) {
*self = self.clone() * other;
}
}
impl Div for Expression {
type Output = Self;
fn div(self, other: Self) -> Self {
Expression::Quotient(Box::new(self), Box::new(other))
}
}
impl DivAssign for Expression {
fn div_assign(&mut self, other: Self) {
*self = self.clone() / other;
}
}
impl Rem for Expression {
type Output = Self;
fn rem(self, other: Self) -> Self {
Expression::Remainder(Box::new(self), Box::new(other))
}
}
impl RemAssign for Expression {
fn rem_assign(&mut self, other: Self) {
*self = self.clone() % other;
}
}
impl From<&Self> for Expression {
fn from(expression: &Self) -> Self {
expression.clone()
}
}
impl From<Integer> for Expression {
fn from(integer: Integer) -> Self {
Expression::Integer(integer)
}
}
impl TryFrom<Expression> for Integer {
type Error = Expression;
fn try_from(expression: Expression) -> Result<Self, Self::Error> {
if let Type::Number(z, _) = expression.typ() {
if z.im.is_zero() && z.re.denom().is_one() {
Ok(z.re.numer().clone())
} else {
Err(expression)
}
} else {
Err(expression)
}
}
}
impl From<Rational> for Expression {
fn from(rational: Rational) -> Self {
Expression::Rational(rational, RationalRepresentation::Fraction)
}
}
impl TryFrom<Expression> for Rational {
type Error = Expression;
fn try_from(expression: Expression) -> Result<Self, Self::Error> {
if let Type::Number(z, _) = expression.typ() {
if z.im.is_zero() {
Ok(z.re)
} else {
Err(expression)
}
} else {
Err(expression)
}
}
}
impl From<Complex> for Expression {
fn from(complex: Complex) -> Self {
Expression::Complex(complex, RationalRepresentation::Fraction)
}
}
impl TryFrom<Expression> for Complex {
type Error = Expression;
fn try_from(expression: Expression) -> Result<Self, Self::Error> {
if let Type::Number(z, _) = expression.typ() {
Ok(z)
} else {
Err(expression)
}
}
}
impl From<Vector> for Expression {
fn from(vector: Vector) -> Self {
Expression::Vector(vector)
}
}
impl TryFrom<Expression> for Vector {
type Error = Expression;
fn try_from(expression: Expression) -> Result<Self, Self::Error> {
if let Type::Matrix(m) = expression.typ() {
if m.ncols() == 1 {
Ok(m.column(0).clone_owned())
} else {
Err(expression)
}
} else {
Err(expression)
}
}
}
impl From<Matrix> for Expression {
fn from(matrix: Matrix) -> Self {
Expression::Matrix(matrix)
}
}
impl TryFrom<Expression> for Matrix {
type Error = Expression;
fn try_from(expression: Expression) -> Result<Self, Self::Error> {
if let Type::Matrix(m) = expression.typ() {
Ok(m)
} else {
Err(expression)
}
}
}
impl From<bool> for Expression {
fn from(boolean: bool) -> Self {
Expression::Boolean(boolean)
}
}
impl TryFrom<Expression> for bool {
type Error = Expression;
fn try_from(expression: Expression) -> Result<Self, Self::Error> {
if let Expression::Boolean(boolean) = expression {
Ok(boolean)
} else {
Err(expression)
}
}
}
/// Returns an expression representing the variable with the given identifier.
pub fn var(identifier: impl Into<String>) -> Expression {
Expression::Variable(identifier.into())
}
/// Returns an expression representing the value of the given function at the given arguments.
pub fn fun(function: impl Into<Expression>, arguments: impl Into<Vec<Expression>>) -> Expression {
Expression::FunctionValue(Box::new(function.into()), arguments.into())
}
/// Returns an expression representing the given integer.
pub fn int(integer: impl Into<Integer>) -> Expression {
Expression::Integer(integer.into())
}
/// Returns an expression representing the rational number with
/// the given numerator and denominator, using fraction representation.
pub fn rat(numerator: impl Into<Integer>, denominator: impl Into<Integer>) -> Expression {
Expression::Rational(
Rational::new(numerator.into(), denominator.into()),
RationalRepresentation::Fraction,
)
}
/// Returns an expression representing the rational number with
/// the given numerator and denominator, using decimal representation,
/// falling back to fraction representation if the number cannot be
/// represented as a finite decimal.
pub fn ratd(numerator: impl Into<Integer>, denominator: impl Into<Integer>) -> Expression {
Expression::Rational(
Rational::new(numerator.into(), denominator.into()),
RationalRepresentation::Decimal,
)
}
/// Returns an expression representing the complex number with
/// real and imaginary parts being rational numbers described by
/// the given numerators and denominators, using fraction representation.
pub fn com(
real_numerator: impl Into<Integer>,
real_denominator: impl Into<Integer>,
imaginary_numerator: impl Into<Integer>,
imaginary_denominator: impl Into<Integer>,
) -> Expression {
Expression::Complex(
Complex::new(
Rational::new(real_numerator.into(), real_denominator.into()),
Rational::new(imaginary_numerator.into(), imaginary_denominator.into()),
),
RationalRepresentation::Fraction,
)
}
/// Returns an expression representing the complex number with
/// real and imaginary parts being rational numbers described by
/// the given numerators and denominators, using decimal representation,
/// falling back to fraction representation for parts that cannot be
/// represented as a finite decimal.
pub fn comd(
real_numerator: impl Into<Integer>,
real_denominator: impl Into<Integer>,
imaginary_numerator: impl Into<Integer>,
imaginary_denominator: impl Into<Integer>,
) -> Expression {
Expression::Complex(
Complex::new(
Rational::new(real_numerator.into(), real_denominator.into()),
Rational::new(imaginary_numerator.into(), imaginary_denominator.into()),
),
RationalRepresentation::Decimal,
)
}
/// Returns an expression representing the first expression raised to the power of the second.
pub fn pow(base: impl Into<Expression>, exponent: impl Into<Expression>) -> Expression {
Expression::Power(Box::new(base.into()), Box::new(exponent.into()))
}
/// Returns an expression representing whether two expressions are equal.
pub fn eq(left: impl Into<Expression>, right: impl Into<Expression>) -> Expression {
Expression::Equal(Box::new(left.into()), Box::new(right.into()))
}
/// Returns an expression representing whether two expressions are not equal.
pub fn ne(left: impl Into<Expression>, right: impl Into<Expression>) -> Expression {
Expression::NotEqual(Box::new(left.into()), Box::new(right.into()))
}
/// Returns an expression representing whether the first expression is less than the second.
pub fn lt(left: impl Into<Expression>, right: impl Into<Expression>) -> Expression {
Expression::LessThan(Box::new(left.into()), Box::new(right.into()))
}
/// Returns an expression representing whether the first expression is less than or equal to the second.
pub fn le(left: impl Into<Expression>, right: impl Into<Expression>) -> Expression {
Expression::LessThanOrEqual(Box::new(left.into()), Box::new(right.into()))
}
/// Returns an expression representing whether the first expression is greater than the second.
pub fn gt(left: impl Into<Expression>, right: impl Into<Expression>) -> Expression {
Expression::GreaterThan(Box::new(left.into()), Box::new(right.into()))
}
/// Returns an expression representing whether the first expression is greater than or equal to the second.
pub fn ge(left: impl Into<Expression>, right: impl Into<Expression>) -> Expression {
Expression::GreaterThanOrEqual(Box::new(left.into()), Box::new(right.into()))
}
/// Returns an expression representing the logical conjunction (AND) of two expressions.
pub fn and(a: impl Into<Expression>, b: impl Into<Expression>) -> Expression {
Expression::And(Box::new(a.into()), Box::new(b.into()))
}
/// Returns an expression representing the logical disjunction (OR) of two expressions.
pub fn or(a: impl Into<Expression>, b: impl Into<Expression>) -> Expression {
Expression::Or(Box::new(a.into()), Box::new(b.into()))
}
================================================
FILE: savage_core/src/lib.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
pub mod evaluate;
pub mod expression;
pub mod functions;
pub mod helpers;
pub mod parse;
mod print;
mod simplify;
================================================
FILE: savage_core/src/parse.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use std::{ops::Range, str::FromStr};
use chumsky::prelude::*;
use crate::{
expression::{Expression, Integer, Matrix, Vector},
helpers::*,
};
/// Error that occurred while trying to parse a character stream into an expression.
pub type Error = chumsky::error::Simple<char, Range<usize>>;
/// Reason why a parse error occurred.
pub type ErrorReason = chumsky::error::SimpleReason<char, Range<usize>>;
/// Returns a parser that produces expressions from character streams.
///
/// The purpose of this function is to be a building block for parsers that parse
/// expressions as parts of a more complex input language. If you simply want
/// to turn strings into expressions, use `"a + b".parse::<Expression>()`.
#[allow(clippy::let_and_return)]
pub fn parser() -> impl Parser<char, Expression, Error = Error> {
recursive(|expression| {
let identifier = text::ident()
.map(|identifier: String| match identifier.as_str() {
"true" => Expression::Boolean(true),
"false" => Expression::Boolean(false),
_ => var(identifier),
})
.labelled("identifier")
.boxed();
let number = text::int(10)
.chain(just('.').ignore_then(text::digits(10)).or_not())
.map(|parts: Vec<String>| match parts.as_slice() {
[integer] => int(integer.parse::<Integer>().unwrap()),
[integer_part, fractional_part] => {
let numerator = format!("{}{}", integer_part, fractional_part);
let denominator = format!("1{}", "0".repeat(fractional_part.len()));
ratd(
numerator.parse::<Integer>().unwrap(),
denominator.parse::<Integer>().unwrap(),
)
}
_ => unreachable!(),
})
.labelled("number")
.boxed();
let vector_or_matrix = expression
.clone()
.separated_by(just(','))
.padded()
.delimited_by(just('['), just(']'))
.map(|elements| {
if let Some(Expression::Vector(v)) = elements.first() {
// If all elements of the vector are themselves vectors, and have the same size,
// they are interpreted as the rows of a rectangular matrix.
let row_size = v.len();
let mut rows = Vec::new();
for element in &elements {
match element {
Expression::Vector(v) if v.len() == row_size => {
rows.push(v.transpose());
}
_ => return Expression::Vector(Vector::from_vec(elements)),
}
}
Expression::Matrix(Matrix::from_rows(&rows))
} else {
Expression::Vector(Vector::from_vec(elements))
}
})
.labelled("vector_or_matrix")
.boxed();
let atomic_expression = identifier
.or(number)
.or(vector_or_matrix)
.or(expression.clone().delimited_by(just('('), just(')')))
.padded()
.boxed();
let function_or_element = atomic_expression
.then(
expression
.clone()
.separated_by(just(','))
.padded()
.delimited_by(just('('), just(')'))
.map(|arguments| (Some(arguments), None))
.or(expression
.clone()
.separated_by(just(','))
.at_least(1)
.at_most(2)
.delimited_by(just('['), just(']'))
.map(|indices| (None, Some(indices))))
.or_not(),
)
.map(
|(expression, arguments_or_indices)| match arguments_or_indices {
Some((Some(arguments), None)) => fun(expression, arguments),
Some((None, Some(indices))) => {
if indices.len() == 1 {
Expression::VectorElement(
Box::new(expression),
Box::new(indices[0].clone()),
)
} else {
Expression::MatrixElement(
Box::new(expression),
Box::new(indices[0].clone()),
Box::new(indices[1].clone()),
)
}
}
None => expression,
_ => unreachable!(),
},
)
.padded()
.boxed();
let power = function_or_element
.separated_by(just('^'))
.at_least(1)
.map(|expressions| {
expressions
.into_iter()
.rev()
.reduce(|a, b| pow(b, a))
.unwrap()
})
.labelled("power")
.boxed();
let negation = just('-')
.ignore_then(power.clone())
.map(|a| -a)
.or(just('!').ignore_then(power.clone()).map(|a| !a))
.labelled("negation")
.or(power)
.padded()
.boxed();
let product_or_quotient_or_remainder = negation
.clone()
.then(
just('*')
.or(just('/'))
.or(just('%'))
.then(negation)
.repeated(),
)
.foldl(|a, (operator, b)| match operator {
'*' => a * b,
'/' => a / b,
'%' => a % b,
_ => unreachable!(),
})
.labelled("product_or_quotient_or_remainder")
.boxed();
let sum_or_difference = product_or_quotient_or_remainder
.clone()
.then(
just('+')
.or(just('-'))
.then(product_or_quotient_or_remainder)
.repeated(),
)
.foldl(|a, (operator, b)| match operator {
'+' => a + b,
'-' => a - b,
_ => unreachable!(),
})
.labelled("sum_or_difference")
.boxed();
let comparison = sum_or_difference
.clone()
.then(
just('=')
.chain(just('='))
.or(just('!').chain(just('=')))
.or(just('<').chain(just('=')))
.or(just('<').to(vec!['<']))
.or(just('>').chain(just('=')))
.or(just('>').to(vec!['>']))
.collect::<String>()
.then(sum_or_difference)
.repeated(),
)
.foldl(|a, (operator, b)| match operator.as_str() {
"==" => eq(a, b),
"!=" => ne(a, b),
"<" => lt(a, b),
"<=" => le(a, b),
">" => gt(a, b),
">=" => ge(a, b),
_ => unreachable!(),
})
.labelled("comparison")
.boxed();
let conjunction = comparison
.clone()
.then(
just('&')
.ignore_then(just('&'))
.ignore_then(comparison)
.repeated(),
)
.foldl(and)
.labelled("conjunction")
.boxed();
let disjunction = conjunction
.clone()
.then(
just('|')
.ignore_then(just('|'))
.ignore_then(conjunction)
.repeated(),
)
.foldl(or)
.labelled("disjunction")
.boxed();
disjunction
})
}
impl FromStr for Expression {
type Err = Vec<Error>;
fn from_str(string: &str) -> Result<Self, Self::Err> {
parser().then_ignore(end()).parse(string)
}
}
#[cfg(test)]
mod tests {
use nalgebra::{dmatrix, dvector};
use crate::expression::{Expression, Expression::*};
use crate::helpers::*;
#[track_caller]
fn t(string: &str, expression: Expression) {
assert_eq!(string.parse(), Ok(expression));
}
#[test]
fn variables() {
t("a ", var("a"));
t(" A", var("A"));
t(" Named_Variable ", var("Named_Variable"));
}
#[test]
fn functions() {
t(" f( ) ", fun(var("f"), []));
t("f ( a) ", fun(var("f"), [var("a")]));
t("f( a, 1 )", fun(var("f"), [var("a"), int(1)]));
t(
" f( g(a ),h( b ) ) ",
fun(
var("f"),
[fun(var("g"), [var("a")]), fun(var("h"), [var("b")])],
),
);
t(
" ( f ( a ) ) ( b ) ",
fun(fun(var("f"), [var("a")]), [var("b")]),
);
t("(f +g)( a)", fun(var("f") + var("g"), [var("a")]));
}
#[test]
fn integers() {
t("0", int(0));
t(" 1", int(1));
t("1234567890 ", int(1234567890));
t(" 9876543210 ", int(9876543210u64));
}
#[test]
fn rational_numbers() {
t("0.5", ratd(1, 2));
t(" 1.5", ratd(3, 2));
t("3.075 ", ratd(123, 40));
t(" 100.000 ", ratd(100, 1));
}
#[test]
fn vectors() {
t(" [ ] ", Vector(dvector![]));
t("[ 1]", Vector(dvector![int(1)]));
t(" [1,2, 3 ]", Vector(dvector![int(1), int(2), int(3)]));
t(
"[ 1,f(a,1),[ 1,2,3 ] ] ",
Vector(dvector![
int(1),
fun(var("f"), [var("a"), int(1)]),
Vector(dvector![int(1), int(2), int(3)])
]),
);
}
#[test]
fn matrices() {
t("[[1 ] ] ", Matrix(dmatrix![int(1)]));
t("[ [ 1,2,3 ] ]", Matrix(dmatrix![int(1), int(2), int(3)]));
t(
" [[ 1, 2,3 ],[ 4,5, 6]]",
Matrix(dmatrix![
int(1), int(2), int(3);
int(4), int(5), int(6)
]),
);
t(
" [[f ( ) ,2, [1 ] ], [[ [ 1]],3.075,6] ] ",
Matrix(dmatrix![
fun(var("f"), []), int(2), Vector(dvector![int(1)]);
Matrix(dmatrix![int(1)]), ratd(123, 40), int(6)
]),
);
}
#[test]
fn booleans() {
t(" true", Boolean(true));
t("false ", Boolean(false));
}
#[test]
fn operators() {
t(" - 1 ", -int(1));
t(" - (- 1 )", -(-int(1)));
t("!A ", !var("A"));
t(" !( ! A)", !(!var("A")));
t("1+2 +3 ", (int(1) + int(2)) + int(3));
t(" 1 +2- 3 ", (int(1) + int(2)) - int(3));
t("1 -2 + 3", (int(1) - int(2)) + int(3));
t("1-2-3", (int(1) - int(2)) - int(3));
t(" 1-(2 + 3)", int(1) - (int(2) + int(3)));
t("1 - (2 - 3)", int(1) - (int(2) - int(3)));
t(" 1 *2* 3 ", (int(1) * int(2)) * int(3));
t("1*2 / 3", (int(1) * int(2)) / int(3));
t("1 / 2*3 ", (int(1) / int(2)) * int(3));
t(" 1/2/3", (int(1) / int(2)) / int(3));
t("1 /( 2 *3) ", int(1) / (int(2) * int(3)));
t(" 1/ (2 /3)", int(1) / (int(2) / int(3)));
t("(1+2) /3 ", (int(1) + int(2)) / int(3));
t(" 1/ 2 +3", (int(1) / int(2)) + int(3));
t("1 + 2 / 3", int(1) + (int(2) / int(3)));
t("1/ (2+3) ", int(1) / (int(2) + int(3)));
t("(1 * 2)^3", pow(int(1) * int(2), int(3)));
t("1^2 * 3 ", pow(int(1), int(2)) * int(3));
t("1* 2 ^3", int(1) * pow(int(2), int(3)));
t(" 1^( 2 * 3 )", pow(int(1), int(2) * int(3)));
t(" (1^2) ^ 3", pow(pow(int(1), int(2)), int(3)));
t("1 ^2 ^3 ", pow(int(1), pow(int(2), int(3))));
// TODO: Comparison operators!
t("A&&B&&C", and(and(var("A"), var("B")), var("C")));
t("A && B||C", or(and(var("A"), var("B")), var("C")));
t(" ( A || B ) && C ", and(or(var("A"), var("B")), var("C")));
t("A||B ||C", or(or(var("A"), var("B")), var("C")));
t("A&& ( B|| C)", and(var("A"), or(var("B"), var("C"))));
t(" A|| B &&C", or(var("A"), and(var("B"), var("C"))));
}
// TODO: Replace with a real benchmark once `#[bench]` is stable.
#[test]
fn benchmark() {
for depth in 0..20 {
t(
&format!("{}a{}", "(".repeat(depth), ")".repeat(depth)),
var("a"),
);
}
}
}
================================================
FILE: savage_core/src/print.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use std::cmp::max;
use std::fmt::{Display, Formatter, Result};
use num::{One, Signed, Zero};
use crate::expression::{Expression, Integer, Rational};
/// Returns a pair of integers `(n, m)` such that `x = n / 10^m`,
/// or `None` if no such integers exist.
fn decimal_representation(x: &Rational) -> Option<(Integer, usize)> {
// https://en.wikipedia.org/wiki/Decimal_representation#Finite_decimal_representations
let mut denominator = x.denom().clone();
let [power_of_2, power_of_5] = [2, 5].map(|n| {
let mut power = 0;
while (denominator.clone() % Integer::from(n)).is_zero() {
denominator /= n;
power += 1;
}
power
});
if denominator.is_one() {
let multiplier = if power_of_2 < power_of_5 {
Integer::from(2).pow(power_of_5 - power_of_2)
} else {
Integer::from(5).pow(power_of_2 - power_of_5)
};
Some((x.numer() * multiplier, max(power_of_2, power_of_5) as usize))
} else {
None
}
}
impl Expression {
/// Formats the expression as a unary prefix operator with the minimally necessary parentheses.
fn fmt_prefix(&self, f: &mut Formatter<'_>, symbol: &str, a: &Self) -> Result {
let a_needs_parentheses = a.precedence() <= self.precedence();
write!(
f,
"{}{}{}{}",
symbol,
if a_needs_parentheses { "(" } else { "" },
a,
if a_needs_parentheses { ")" } else { "" },
)
}
/// Formats the expression as a binary infix operator with the minimally necessary parentheses.
fn fmt_infix(&self, f: &mut Formatter<'_>, symbol: &str, a: &Self, b: &Self) -> Result {
use crate::expression::Associativity::*;
let a_needs_parentheses = (a.precedence() < self.precedence())
|| ((a.precedence() == self.precedence())
&& (self.associativity() == RightAssociative));
let b_needs_parentheses = (b.precedence() < self.precedence())
|| ((b.precedence() == self.precedence()) && (self.associativity() == LeftAssociative));
write!(
f,
"{}{}{} {} {}{}{}",
if a_needs_parentheses { "(" } else { "" },
a,
if a_needs_parentheses { ")" } else { "" },
symbol,
if b_needs_parentheses { "(" } else { "" },
b,
if b_needs_parentheses { ")" } else { "" },
)
}
}
impl Display for Expression {
fn fmt(&self, f: &mut Formatter<'_>) -> Result {
use crate::expression::{Expression::*, RationalRepresentation::*};
match self {
Variable(identifier) => write!(f, "{}", identifier),
Function(identifier, _) => write!(f, "{}", identifier),
FunctionValue(function, arguments) => {
let function_needs_parentheses = function.precedence() < isize::MAX;
write!(
f,
"{}{}{}({})",
if function_needs_parentheses { "(" } else { "" },
function,
if function_needs_parentheses { ")" } else { "" },
arguments
.iter()
.map(|a| a.to_string())
.collect::<Vec<_>>()
.join(", "),
)
}
Integer(n) => write!(f, "{}", n),
Rational(x, representation) => {
match representation {
Fraction => write!(f, "{}", x),
Decimal => {
if let Some((mantissa, separator_position)) = decimal_representation(x) {
let mut string = mantissa.abs().to_string();
if separator_position > 0 {
if separator_position > string.len() - 1 {
// Left-pad the string with enough zeros to be able
// to insert the decimal separator at the indicated position.
string = format!(
"{}{}",
"0".repeat(separator_position - (string.len() - 1)),
string,
);
}
string.insert(string.len() - separator_position, '.');
}
write!(f, "{}{}", if x.is_negative() { "-" } else { "" }, string)
} else {
// Fall back to fraction representation.
write!(f, "{}", x)
}
}
}
}
Complex(z, representation) => {
if z.im.is_zero() {
write!(f, "{}", Rational(z.re.clone(), *representation))
} else if z.re.is_zero() {
if z.im.abs().is_one() {
write!(f, "{}i", if z.im.is_negative() { "-" } else { "" })
} else {
write!(f, "{}*i", Rational(z.im.clone(), *representation))
}
} else if z.re.is_negative() && z.im.is_positive() {
if z.im.is_one() {
write!(f, "i - {}", Rational(z.re.abs(), *representation))
} else {
write!(
f,
"{}*i - {}",
Rational(z.im.clone(), *representation),
Rational(z.re.abs(), *representation),
)
}
} else if z.im.abs().is_one() {
write!(
f,
"{} {} i",
Rational(z.re.clone(), *representation),
if z.im.is_negative() { "-" } else { "+" },
)
} else {
write!(
f,
"{} {} {}*i",
Rational(z.re.clone(), *representation),
if z.im.is_negative() { "-" } else { "+" },
Rational(z.im.abs(), *representation),
)
}
}
Vector(v) => write!(
f,
"[{}]",
v.iter()
.map(|element| element.to_string())
.collect::<Vec<_>>()
.join(", "),
),
VectorElement(vector, i) => {
let vector_needs_parentheses = vector.precedence() < isize::MAX;
write!(
f,
"{}{}{}[{}]",
if vector_needs_parentheses { "(" } else { "" },
vector,
if vector_needs_parentheses { ")" } else { "" },
i,
)
}
Matrix(m) => write!(
f,
"[{}]",
m.row_iter()
.map(|row| format!(
"[{}]",
row.iter()
.map(|element| element.to_string())
.collect::<Vec<_>>()
.join(", "),
))
.collect::<Vec<_>>()
.join(", "),
),
MatrixElement(matrix, i, j) => {
let matrix_needs_parentheses = matrix.precedence() < isize::MAX;
write!(
f,
"{}{}{}[{}, {}]",
if matrix_needs_parentheses { "(" } else { "" },
matrix,
if matrix_needs_parentheses { ")" } else { "" },
i,
j,
)
}
Boolean(boolean) => write!(f, "{}", boolean),
Negation(a) => self.fmt_prefix(f, "-", a),
Not(a) => self.fmt_prefix(f, "!", a),
Sum(a, b) => self.fmt_infix(f, "+", a, b),
Difference(a, b) => self.fmt_infix(f, "-", a, b),
Product(a, b) => self.fmt_infix(f, "*", a, b),
Quotient(a, b) => self.fmt_infix(f, "/", a, b),
Remainder(a, b) => self.fmt_infix(f, "%", a, b),
Power(a, b) => self.fmt_infix(f, "^", a, b),
Equal(a, b) => self.fmt_infix(f, "==", a, b),
NotEqual(a, b) => self.fmt_infix(f, "!=", a, b),
LessThan(a, b) => self.fmt_infix(f, "<", a, b),
LessThanOrEqual(a, b) => self.fmt_infix(f, "<=", a, b),
GreaterThan(a, b) => self.fmt_infix(f, ">", a, b),
GreaterThanOrEqual(a, b) => self.fmt_infix(f, ">=", a, b),
And(a, b) => self.fmt_infix(f, "&&", a, b),
Or(a, b) => self.fmt_infix(f, "||", a, b),
}
}
}
#[cfg(test)]
mod tests {
use nalgebra::{dmatrix, dvector};
use crate::expression::{Expression, Expression::*};
use crate::helpers::*;
#[track_caller]
fn t(expression: Expression, string: &str) {
assert_eq!(expression.to_string(), string);
}
#[test]
fn variables() {
t(var("a"), "a");
t(var("A"), "A");
t(var("Named_Variable"), "Named_Variable");
}
#[test]
fn functions() {
t(fun(var("f"), []), "f()");
t(fun(var("f"), [var("a")]), "f(a)");
t(fun(var("f"), [var("a"), int(1)]), "f(a, 1)");
t(
fun(
var("f"),
[fun(var("g"), [var("a")]), fun(var("h"), [var("b")])],
),
"f(g(a), h(b))",
);
t(fun(fun(var("f"), [var("a")]), [var("b")]), "(f(a))(b)");
t(fun(var("f") + var("g"), [var("a")]), "(f + g)(a)");
}
#[test]
fn integers() {
t(int(0), "0");
t(int(1), "1");
t(int(-1), "-1");
t(int(1234567890), "1234567890");
t(int(-1234567890), "-1234567890");
t(int(9876543210u64), "9876543210");
t(int(-9876543210i64), "-9876543210");
}
#[test]
fn rational_numbers() {
t(rat(0, 1), "0");
t(ratd(0, 1), "0");
t(rat(0, -1), "0");
t(ratd(0, -1), "0");
t(rat(1, 1), "1");
t(ratd(1, 1), "1");
t(rat(-1, 1), "-1");
t(ratd(-1, 1), "-1");
t(rat(1, 2), "1/2");
t(ratd(1, 2), "0.5");
t(rat(3, 2), "3/2");
t(ratd(3, 2), "1.5");
t(rat(1, 3), "1/3");
t(ratd(1, 3), "1/3");
t(rat(123, 40), "123/40");
t(ratd(123, 40), "3.075");
t(rat(123, -40), "-123/40");
t(ratd(123, -40), "-3.075");
t(rat(-123, -40), "123/40");
t(ratd(-123, -40), "3.075");
}
#[test]
fn complex_numbers() {
t(com(0, 1, 0, 1), "0");
t(comd(0, 1, 0, 1), "0");
t(com(1, 1, 0, 1), "1");
t(comd(1, 1, 0, 1), "1");
t(com(0, 1, 1, 1), "i");
t(comd(0, 1, 1, 1), "i");
t(com(-1, 1, 0, 1), "-1");
t(comd(-1, 1, 0, 1), "-1");
t(com(0, 1, -1, 1), "-i");
t(comd(0, 1, -1, 1), "-i");
t(com(1, 1, 1, 1), "1 + i");
t(comd(1, 1, 1, 1), "1 + i");
t(com(1, 1, -1, 1), "1 - i");
t(comd(1, 1, -1, 1), "1 - i");
t(com(-1, 1, 1, 1), "i - 1");
t(comd(-1, 1, 1, 1), "i - 1");
t(com(-1, 1, -1, 1), "-1 - i");
t(comd(-1, 1, -1, 1), "-1 - i");
t(com(123, -40, 1, 3), "1/3*i - 123/40");
t(comd(123, -40, 1, 3), "1/3*i - 3.075");
t(com(1, 3, 123, 40), "1/3 + 123/40*i");
t(comd(1, 3, 123, 40), "1/3 + 3.075*i");
}
#[test]
fn vectors() {
t(Vector(dvector![]), "[]");
t(Vector(dvector![int(1)]), "[1]");
t(Vector(dvector![int(1), int(2), int(3)]), "[1, 2, 3]");
t(
Vector(dvector![
int(1),
fun(var("f"), [var("a"), int(1)]),
Vector(dvector![int(1), int(2), int(3)])
]),
"[1, f(a, 1), [1, 2, 3]]",
);
}
#[test]
fn matrices() {
t(Matrix(dmatrix![]), "[]");
t(Matrix(dmatrix![int(1)]), "[[1]]");
t(Matrix(dmatrix![int(1), int(2), int(3)]), "[[1, 2, 3]]");
t(
Matrix(dmatrix![
int(1), int(2), int(3);
int(4), int(5), int(6)
]),
"[[1, 2, 3], [4, 5, 6]]",
);
t(
Matrix(dmatrix![
fun(var("f"), []), int(2), Vector(dvector![int(1)]);
Matrix(dmatrix![int(1)]), comd(123, -40, 1, 3), int(6)
]),
"[[f(), 2, [1]], [[[1]], 1/3*i - 3.075, 6]]",
);
}
#[test]
fn booleans() {
t(Boolean(true), "true");
t(Boolean(false), "false");
}
#[test]
fn operators() {
t(-int(1), "-1");
t(-(-int(1)), "-(-1)");
t(!var("A"), "!A");
t(!(!var("A")), "!(!A)");
t((int(1) + int(2)) + int(3), "1 + 2 + 3");
t((int(1) + int(2)) - int(3), "1 + 2 - 3");
t((int(1) - int(2)) + int(3), "1 - 2 + 3");
t((int(1) - int(2)) - int(3), "1 - 2 - 3");
t(int(1) + (int(2) + int(3)), "1 + 2 + 3");
t(int(1) + (int(2) - int(3)), "1 + 2 - 3");
t(int(1) - (int(2) + int(3)), "1 - (2 + 3)");
t(int(1) - (int(2) - int(3)), "1 - (2 - 3)");
t((int(1) * int(2)) * int(3), "1 * 2 * 3");
t((int(1) * int(2)) / int(3), "1 * 2 / 3");
t((int(1) / int(2)) * int(3), "1 / 2 * 3");
t((int(1) / int(2)) / int(3), "1 / 2 / 3");
t(int(1) * (int(2) * int(3)), "1 * 2 * 3");
t(int(1) * (int(2) / int(3)), "1 * 2 / 3");
t(int(1) / (int(2) * int(3)), "1 / (2 * 3)");
t(int(1) / (int(2) / int(3)), "1 / (2 / 3)");
t((int(1) + int(2)) / int(3), "(1 + 2) / 3");
t((int(1) / int(2)) + int(3), "1 / 2 + 3");
t(int(1) + (int(2) / int(3)), "1 + 2 / 3");
t(int(1) / (int(2) + int(3)), "1 / (2 + 3)");
t(pow(int(1) * int(2), int(3)), "(1 * 2) ^ 3");
t(pow(int(1), int(2)) * int(3), "1 ^ 2 * 3");
t(int(1) * pow(int(2), int(3)), "1 * 2 ^ 3");
t(pow(int(1), int(2) * int(3)), "1 ^ (2 * 3)");
t(pow(pow(int(1), int(2)), int(3)), "(1 ^ 2) ^ 3");
t(pow(int(1), pow(int(2), int(3))), "1 ^ 2 ^ 3");
t(pow(int(1), int(2)), "1 ^ 2");
t(pow(int(-1), int(2)), "(-1) ^ 2");
t(pow(rat(1, 2), int(3)), "(1/2) ^ 3");
t(pow(ratd(1, 2), int(3)), "0.5 ^ 3");
t(pow(com(0, 1, -1, 1), int(2)), "(-i) ^ 2");
t(com(1, 1, 1, 1) * int(2), "(1 + i) * 2");
t(com(1, 1, -1, 1) - int(2), "1 - i - 2");
t(int(2) - com(1, 1, -1, 1), "2 - (1 - i)");
// TODO: Comparison operators!
t(and(and(var("A"), var("B")), var("C")), "A && B && C");
t(or(and(var("A"), var("B")), var("C")), "A && B || C");
t(and(or(var("A"), var("B")), var("C")), "(A || B) && C");
t(or(or(var("A"), var("B")), var("C")), "A || B || C");
t(and(var("A"), and(var("B"), var("C"))), "A && B && C");
t(and(var("A"), or(var("B"), var("C"))), "A && (B || C)");
t(or(var("A"), and(var("B"), var("C"))), "A || B && C");
t(or(var("A"), or(var("B"), var("C"))), "A || B || C");
}
}
================================================
FILE: savage_core/src/simplify.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use crate::{expression::Expression, helpers::*};
impl Expression {
/// Applies standard algebraic simplification rules to the expression,
/// and returns the result.
///
/// Note that this function does not itself recurse into sub-expressions;
/// but since it is called from `evaluate_step`, which *does* recurse,
/// simplifications are applied to the entire expression tree during evaluation.
pub(crate) fn simplify(&self) -> Self {
use crate::expression::Expression::*;
match self {
Negation(a) => {
if let Negation(a) = &**a {
*a.clone()
} else {
self.clone()
}
}
Not(a) => {
if let Not(a) = &**a {
*a.clone()
} else {
self.clone()
}
}
Sum(a, b) => {
let a = *a.clone();
let b = *b.clone();
if a == int(0) {
b
} else if b == int(0) {
a
} else if a == b {
int(2) * a
} else if a == -b.clone() || b == -a {
int(0)
} else {
self.clone()
}
}
Difference(a, b) => {
let a = *a.clone();
let b = *b.clone();
if a == int(0) {
-b
} else if b == int(0) {
a
} else if a == b {
int(0)
} else if a == -b.clone() || b == -a.clone() {
int(2) * a
} else {
self.clone()
}
}
Product(a, b) => {
let a = *a.clone();
let b = *b.clone();
if a == int(1) {
b
} else if b == int(1) {
a
} else if a == int(0) || b == int(0) {
int(0)
} else if a == b {
pow(a, int(2))
} else if a == int(1) / b.clone() || b == int(1) / a {
int(1)
} else {
self.clone()
}
}
Quotient(a, b) => {
let a = *a.clone();
let b = *b.clone();
if b == int(1) {
a
} else if a == int(0) {
// FIXME: This is incorrect if `b` evaluates to zero!
int(0)
} else if a == b {
// FIXME: This is incorrect if `b` evaluates to zero!
int(1)
} else {
self.clone()
}
}
Remainder(a, b) => {
let a = *a.clone();
let b = *b.clone();
if a == int(0) || a == b {
// FIXME: This is incorrect if `b` evaluates to zero!
int(0)
} else {
self.clone()
}
}
Power(a, b) => {
let a = *a.clone();
let b = *b.clone();
if a == int(1) {
int(1)
} else if b == int(1) {
a
} else if a == int(0) {
// FIXME: This is incorrect if `b` evaluates to zero!
int(0)
} else if b == int(0) {
// FIXME: This is incorrect if `a` evaluates to zero!
int(1)
} else {
self.clone()
}
}
Equal(a, b) | LessThanOrEqual(a, b) | GreaterThanOrEqual(a, b) => {
if a == b {
Boolean(true)
} else {
self.clone()
}
}
NotEqual(a, b) | LessThan(a, b) | GreaterThan(a, b) => {
if a == b {
Boolean(false)
} else {
self.clone()
}
}
And(a, b) => {
let a = *a.clone();
let b = *b.clone();
if a == Boolean(true) {
b
} else if b == Boolean(true) {
a
} else if a == Boolean(false) || b == Boolean(false) {
Boolean(false)
} else if a == b {
a
} else if a == !b.clone() || b == !a {
Boolean(false)
} else {
self.clone()
}
}
Or(a, b) => {
let a = *a.clone();
let b = *b.clone();
if a == Boolean(false) {
b
} else if b == Boolean(false) {
a
} else if a == Boolean(true) || b == Boolean(true) {
Boolean(true)
} else if a == b {
a
} else if a == !b.clone() || b == !a {
Boolean(true)
} else {
self.clone()
}
}
_ => self.clone(),
}
}
}
#[cfg(test)]
mod tests {
use crate::expression::Expression;
#[track_caller]
fn t(expression: &str, result: &str) {
assert_eq!(
expression
.parse::<Expression>()
.unwrap()
.simplify()
.to_string(),
result,
);
}
#[test]
fn arithmetic() {
t("-(-a)", "a");
t("0 + a", "a");
t("a + 0", "a");
t("a + a", "2 * a");
t("(-a) + a", "0");
t("a + (-a)", "0");
t("0 - a", "-a");
t("a - 0", "a");
t("a - a", "0");
t("(-a) - a", "2 * -a");
t("a - (-a)", "2 * a");
t("1 * a", "a");
t("a * 1", "a");
t("0 * a", "0");
t("a * 0", "0");
t("a * a", "a ^ 2");
t("(1 / a) * a", "1");
t("a * (1 / a)", "1");
t("a / 1", "a");
t("0 / a", "0");
t("a / a", "1");
t("0 % a", "0");
t("a % a", "0");
t("1 ^ a", "1");
t("a ^ 1", "a");
t("0 ^ a", "0");
t("a ^ 0", "1");
}
#[test]
fn logic() {
t("!(!a)", "a");
t("true && a", "a");
t("a && true", "a");
t("false && a", "false");
t("a && false", "false");
t("a && a", "a");
t("(!a) && a", "false");
t("a && (!a)", "false");
t("false || a", "a");
t("a || false", "a");
t("true || a", "true");
t("a || true", "true");
t("a || a", "a");
t("(!a) || a", "true");
t("a || (!a)", "true");
}
#[test]
fn comparisons() {
t("a == a", "true");
t("a != a", "false");
t("a < a", "false");
t("a <= a", "true");
t("a > a", "false");
t("a >= a", "true");
}
}
================================================
FILE: savage_macros/Cargo.toml
================================================
[package]
name = "savage_macros"
version = "0.1.0"
authors = ["Philipp Emanuel Weidmann <pew@worldwidemann.com>"]
description = "A primitive computer algebra system (macro helper crate, NOT INTENDED FOR USE BY THIRD-PARTY CRATES)"
repository = "https://github.com/p-e-w/savage"
readme = "README.md"
license = "AGPL-3.0-or-later"
edition = "2021"
[lib]
proc-macro = true
[dependencies]
syn = "1.0.85"
quote = "1.0.14"
darling = "0.14.1"
================================================
FILE: savage_macros/src/lib.rs
================================================
// SPDX-License-Identifier: AGPL-3.0-or-later
// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.com>
use darling::FromMeta;
use proc_macro::TokenStream;
use quote::{format_ident, quote};
use syn::{
parse_macro_input, punctuated::Punctuated, token::Comma, AttributeArgs, ExprArray, FnArg,
ItemFn, Path, Type,
};
#[derive(FromMeta)]
struct Arguments {
name: String,
description: String,
examples: ExprArray,
categories: ExprArray,
}
/// Generates code required for the marked function to be usable in a function expression.
/// Function metadata is generated from the provided attribute arguments.
#[proc_macro_attribute]
pub fn function(attr: TokenStream, item: TokenStream) -> TokenStream {
let arguments = match Arguments::from_list(&parse_macro_input!(attr as AttributeArgs)) {
Ok(arguments) => arguments,
Err(error) => return TokenStream::from(error.write_errors()),
};
let name_argument = arguments.name;
let description_argument = arguments.description;
let examples_argument = arguments.examples;
let categories_argument = arguments.categories;
let item_fn = parse_macro_input!(item as ItemFn);
let name = &item_fn.sig.ident;
let metadata_name = format_ident!("{}_METADATA", name.to_string().to_uppercase());
let proxy_name = format_ident!("{}_proxy", name);
let parameters = item_fn.sig.inputs.iter().map(|fn_arg| {
if let FnArg::Typed(pat_type) = fn_arg {
if let Type::Path(type_path) = &*pat_type.ty {
match type_path.path.get_ident().unwrap().to_string().as_str() {
"Expression" => quote! { crate::functions::Parameter::Expression },
"Integer" => quote! { crate::functions::Parameter::Integer },
"NonNegativeInteger" => {
quote! { crate::functions::Parameter::NonNegativeInteger }
}
"PositiveInteger" => {
quote! { crate::functions::Parameter::PositiveInteger }
}
"Rational" => quote! { crate::functions::Parameter::Rational },
"Complex" => quote! { crate::functions::Parameter::Complex },
"Vector" => quote! { crate::functions::Parameter::Vector },
"Matrix" => quote! { crate::functions::Parameter::Matrix },
"SquareMatrix" => quote! { crate::functions::Parameter::SquareMatrix },
"bool" => quote! { crate::functions::Parameter::Boolean },
_ => unimplemented!(),
}
} else {
unreachable!();
}
} else {
unreachable!();
}
});
let arguments =
(0..item_fn.sig.inputs.len()).map(|i| quote! { arguments[#i].clone().try_into()? });
let tokens = quote! {
#item_fn
pub(crate) const #metadata_name: crate::functions::Metadata = crate::functions::Metadata {
name: #name_argument,
description: #description_argument,
parameters: &[#(#parameters),*],
examples: &#examples_argument,
categories: &#categories_argument,
};
pub(crate) fn #proxy_name(arguments: &[crate::expression::Expression]) ->
::std::result::Result<crate::expression::Expression, crate::expression::Expression> {
::std::result::Result::Ok(#name(#(#arguments),*).into())
}
};
tokens.into()
}
/// Returns a vector of function definitions generated from the base function paths provided as arguments.
#[proc_macro]
pub fn functions(input: TokenStream) -> TokenStream {
let mut statements = Vec::new();
for path in parse_macro_input!(input with Punctuated::<Path, Comma>::parse_terminated) {
let name = &path.segments.last().unwrap().ident;
let mut metadata_path = path.clone();
metadata_path.segments.last_mut().unwrap().ident =
format_ident!("{}_METADATA", name.to_string().to_uppercase());
let mut proxy_path = path.clone();
proxy_path.segments.last_mut().unwrap().ident = format_ident!("{}_proxy", name);
statements.push(quote! {
functions.push(Function {
metadata: #metadata_path,
implementation: wrap_proxy(#metadata_path.parameters, #proxy_path),
});
});
}
let tokens = quote! {{
let mut functions = Vec::new();
#(#statements)*
functions
}};
tokens.into()
}
gitextract_86suw3hs/
├── .github/
│ ├── dependabot.yml
│ └── workflows/
│ └── continuous_integration.yml
├── .gitignore
├── CHANGELOG.md
├── Cargo.toml
├── LICENSE
├── README.md
├── savage/
│ ├── Cargo.toml
│ ├── help/
│ │ ├── footer.md
│ │ └── header.md
│ └── src/
│ ├── command.rs
│ ├── help.rs
│ ├── input.rs
│ └── main.rs
├── savage_core/
│ ├── Cargo.toml
│ └── src/
│ ├── evaluate.rs
│ ├── expression.rs
│ ├── functions/
│ │ ├── combinatorics.rs
│ │ ├── linear_algebra.rs
│ │ ├── logic.rs
│ │ ├── mod.rs
│ │ └── number_theory.rs
│ ├── helpers.rs
│ ├── lib.rs
│ ├── parse.rs
│ ├── print.rs
│ └── simplify.rs
└── savage_macros/
├── Cargo.toml
└── src/
└── lib.rs
SYMBOL INDEX (156 symbols across 16 files)
FILE: savage/src/command.rs
type Command (line 13) | pub enum Command {
function parser (line 20) | fn parser() -> impl Parser<char, Command, Error = Error> {
type Err (line 49) | type Err = Vec<Error>;
method from_str (line 51) | fn from_str(string: &str) -> Result<Self, Self::Err> {
function t (line 63) | fn t(string: &str, command: Command) {
function parse (line 68) | fn parse() {
FILE: savage/src/help.rs
constant HELP_HEADER (line 23) | const HELP_HEADER: &str = include_str!("../help/header.md");
constant HELP_FOOTER (line 24) | const HELP_FOOTER: &str = include_str!("../help/footer.md");
function view_area (line 76) | fn view_area() -> Area {
function show_help (line 87) | pub fn show_help(text: String) -> Result<(), Error> {
FILE: savage/src/input.rs
type TokenType (line 17) | enum TokenType {
function tokenize (line 27) | fn tokenize(input: &str) -> Vec<(String, TokenType)> {
type InputHelper (line 85) | pub struct InputHelper {}
method highlight_prompt (line 88) | fn highlight_prompt<'b, 's: 'b, 'p: 'b>(
method highlight (line 96) | fn highlight<'l>(&self, line: &'l str, pos: usize) -> Cow<'l, str> {
method highlight_char (line 165) | fn highlight_char(&self, _line: &str, _pos: usize) -> bool {
method validate (line 171) | fn validate(&self, ctx: &mut ValidationContext) -> Result<ValidationResu...
FILE: savage/src/main.rs
function format_parse_error (line 37) | fn format_parse_error(error: ParseError) -> Report {
function main (line 97) | fn main() {
FILE: savage_core/src/evaluate.rs
type Error (line 15) | pub enum Error {
function default_context (line 64) | pub fn default_context() -> HashMap<String, Expression> {
method evaluate_step_unary (line 87) | fn evaluate_step_unary(
method evaluate_step_binary (line 151) | fn evaluate_step_binary(
method evaluate_step (line 403) | fn evaluate_step(&self, context: &HashMap<String, Self>) -> Result<Self,...
method evaluate (line 608) | pub fn evaluate(&self, context: &HashMap<String, Self>) -> Result<Self, ...
function t (line 629) | fn t(expression: &str, result: &str) {
function arithmetic (line 642) | fn arithmetic() {
function linear_algebra (line 704) | fn linear_algebra() {
function indices (line 725) | fn indices() {
function logic (line 736) | fn logic() {
function comparisons (line 752) | fn comparisons() {
FILE: savage_core/src/expression.rs
type Function (line 15) | pub type Function =
type Integer (line 19) | pub type Integer = num::bigint::BigInt;
type Rational (line 22) | pub type Rational = num::rational::Ratio<Integer>;
type Complex (line 25) | pub type Complex = num::complex::Complex<Rational>;
type Vector (line 28) | pub type Vector = nalgebra::DVector<Expression>;
type Matrix (line 31) | pub type Matrix = nalgebra::DMatrix<Expression>;
type RationalRepresentation (line 35) | pub enum RationalRepresentation {
method merge (line 46) | pub(crate) fn merge(self, other: Self) -> Self {
type Expression (line 60) | pub enum Expression {
method typ (line 155) | pub(crate) fn typ(&self) -> Type {
method precedence_and_associativity (line 197) | pub(crate) fn precedence_and_associativity(&self) -> (isize, Associati...
method precedence (line 261) | pub(crate) fn precedence(&self) -> isize {
method associativity (line 268) | pub(crate) fn associativity(&self) -> Associativity {
method parts (line 275) | pub(crate) fn parts(&self) -> Vec<Self> {
method variables (line 339) | pub fn variables(&self) -> HashSet<String> {
type Type (line 123) | pub(crate) enum Type {
type Associativity (line 144) | pub(crate) enum Associativity {
FILE: savage_core/src/functions/combinatorics.rs
function factorial (line 22) | fn factorial(n: NonNegativeInteger) -> Integer {
FILE: savage_core/src/functions/linear_algebra.rs
function determinant (line 21) | fn determinant(matrix: SquareMatrix) -> Expression {
FILE: savage_core/src/functions/logic.rs
function and (line 20) | fn and(a: bool, b: bool) -> bool {
FILE: savage_core/src/functions/mod.rs
type NonNegativeInteger (line 19) | pub(crate) type NonNegativeInteger = Integer;
type PositiveInteger (line 24) | pub(crate) type PositiveInteger = Integer;
type SquareMatrix (line 29) | pub(crate) type SquareMatrix = Matrix;
type Parameter (line 33) | pub enum Parameter {
type Metadata (line 58) | pub struct Metadata {
type Function (line 72) | pub struct Function {
function wrap_proxy (line 81) | fn wrap_proxy(
function functions (line 143) | pub fn functions() -> Vec<Function> {
function function_expression (line 156) | pub fn function_expression(name: &str) -> Option<Expression> {
function t (line 176) | fn t(expression: &str, result: &str) {
function examples (line 189) | fn examples() {
FILE: savage_core/src/functions/number_theory.rs
function is_prime (line 30) | fn is_prime(n: NonNegativeInteger) -> Expression {
function nth_prime (line 52) | fn nth_prime(n: PositiveInteger) -> Expression {
function prime_pi (line 75) | fn prime_pi(n: NonNegativeInteger) -> Expression {
FILE: savage_core/src/helpers.rs
type Output (line 17) | type Output = Self;
method neg (line 19) | fn neg(self) -> Self {
type Output (line 25) | type Output = Self;
method not (line 27) | fn not(self) -> Self {
type Output (line 33) | type Output = Self;
method add (line 35) | fn add(self, other: Self) -> Self {
method add_assign (line 41) | fn add_assign(&mut self, other: Self) {
type Output (line 47) | type Output = Self;
method sub (line 49) | fn sub(self, other: Self) -> Self {
method sub_assign (line 55) | fn sub_assign(&mut self, other: Self) {
type Output (line 61) | type Output = Self;
method mul (line 63) | fn mul(self, other: Self) -> Self {
method mul_assign (line 69) | fn mul_assign(&mut self, other: Self) {
type Output (line 75) | type Output = Self;
method div (line 77) | fn div(self, other: Self) -> Self {
method div_assign (line 83) | fn div_assign(&mut self, other: Self) {
type Output (line 89) | type Output = Self;
method rem (line 91) | fn rem(self, other: Self) -> Self {
method rem_assign (line 97) | fn rem_assign(&mut self, other: Self) {
method from (line 103) | fn from(expression: &Self) -> Self {
method from (line 109) | fn from(integer: Integer) -> Self {
type Error (line 115) | type Error = Expression;
method try_from (line 117) | fn try_from(expression: Expression) -> Result<Self, Self::Error> {
method from (line 131) | fn from(rational: Rational) -> Self {
type Error (line 137) | type Error = Expression;
method try_from (line 139) | fn try_from(expression: Expression) -> Result<Self, Self::Error> {
method from (line 153) | fn from(complex: Complex) -> Self {
type Error (line 159) | type Error = Expression;
method try_from (line 161) | fn try_from(expression: Expression) -> Result<Self, Self::Error> {
method from (line 171) | fn from(vector: Vector) -> Self {
type Error (line 177) | type Error = Expression;
method try_from (line 179) | fn try_from(expression: Expression) -> Result<Self, Self::Error> {
method from (line 193) | fn from(matrix: Matrix) -> Self {
type Error (line 199) | type Error = Expression;
method try_from (line 201) | fn try_from(expression: Expression) -> Result<Self, Self::Error> {
method from (line 211) | fn from(boolean: bool) -> Self {
type Error (line 217) | type Error = Expression;
function try_from (line 219) | fn try_from(expression: Expression) -> Result<Self, Self::Error> {
function var (line 229) | pub fn var(identifier: impl Into<String>) -> Expression {
function fun (line 234) | pub fn fun(function: impl Into<Expression>, arguments: impl Into<Vec<Exp...
function int (line 239) | pub fn int(integer: impl Into<Integer>) -> Expression {
function rat (line 245) | pub fn rat(numerator: impl Into<Integer>, denominator: impl Into<Integer...
function ratd (line 256) | pub fn ratd(numerator: impl Into<Integer>, denominator: impl Into<Intege...
function com (line 266) | pub fn com(
function comd (line 286) | pub fn comd(
function pow (line 302) | pub fn pow(base: impl Into<Expression>, exponent: impl Into<Expression>)...
function eq (line 307) | pub fn eq(left: impl Into<Expression>, right: impl Into<Expression>) -> ...
function ne (line 312) | pub fn ne(left: impl Into<Expression>, right: impl Into<Expression>) -> ...
function lt (line 317) | pub fn lt(left: impl Into<Expression>, right: impl Into<Expression>) -> ...
function le (line 322) | pub fn le(left: impl Into<Expression>, right: impl Into<Expression>) -> ...
function gt (line 327) | pub fn gt(left: impl Into<Expression>, right: impl Into<Expression>) -> ...
function ge (line 332) | pub fn ge(left: impl Into<Expression>, right: impl Into<Expression>) -> ...
function and (line 337) | pub fn and(a: impl Into<Expression>, b: impl Into<Expression>) -> Expres...
function or (line 342) | pub fn or(a: impl Into<Expression>, b: impl Into<Expression>) -> Express...
FILE: savage_core/src/parse.rs
type Error (line 14) | pub type Error = chumsky::error::Simple<char, Range<usize>>;
type ErrorReason (line 17) | pub type ErrorReason = chumsky::error::SimpleReason<char, Range<usize>>;
function parser (line 25) | pub fn parser() -> impl Parser<char, Expression, Error = Error> {
type Err (line 241) | type Err = Vec<Error>;
method from_str (line 243) | fn from_str(string: &str) -> Result<Self, Self::Err> {
function t (line 256) | fn t(string: &str, expression: Expression) {
function variables (line 261) | fn variables() {
function functions (line 268) | fn functions() {
function integers (line 287) | fn integers() {
function rational_numbers (line 295) | fn rational_numbers() {
function vectors (line 303) | fn vectors() {
function matrices (line 318) | fn matrices() {
function booleans (line 338) | fn booleans() {
function operators (line 344) | fn operators() {
function benchmark (line 389) | fn benchmark() {
FILE: savage_core/src/print.rs
function decimal_representation (line 13) | fn decimal_representation(x: &Rational) -> Option<(Integer, usize)> {
method fmt_prefix (line 43) | fn fmt_prefix(&self, f: &mut Formatter<'_>, symbol: &str, a: &Self) -> R...
method fmt_infix (line 57) | fn fmt_infix(&self, f: &mut Formatter<'_>, symbol: &str, a: &Self, b: &S...
method fmt (line 82) | fn fmt(&self, f: &mut Formatter<'_>) -> Result {
function t (line 247) | fn t(expression: Expression, string: &str) {
function variables (line 252) | fn variables() {
function functions (line 259) | fn functions() {
function integers (line 275) | fn integers() {
function rational_numbers (line 286) | fn rational_numbers() {
function complex_numbers (line 310) | fn complex_numbers() {
function vectors (line 336) | fn vectors() {
function matrices (line 351) | fn matrices() {
function booleans (line 372) | fn booleans() {
function operators (line 378) | fn operators() {
FILE: savage_core/src/simplify.rs
method simplify (line 13) | pub(crate) fn simplify(&self) -> Self {
function t (line 186) | fn t(expression: &str, result: &str) {
function arithmetic (line 198) | fn arithmetic() {
function logic (line 235) | fn logic() {
function comparisons (line 256) | fn comparisons() {
FILE: savage_macros/src/lib.rs
type Arguments (line 13) | struct Arguments {
function function (line 23) | pub fn function(attr: TokenStream, item: TokenStream) -> TokenStream {
function functions (line 93) | pub fn functions(input: TokenStream) -> TokenStream {
Condensed preview — 29 files, each showing path, character count, and a content snippet. Download the .json file or copy for the full structured content (193K chars).
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{
"path": ".github/dependabot.yml",
"chars": 278,
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"chars": 1829,
"preview": "# Based on https://github.com/actions-rs/meta/blob/master/recipes/msrv.md\n\non: [push, pull_request]\n\nname: Continuous in"
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"path": ".gitignore",
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"path": "CHANGELOG.md",
"chars": 1322,
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"preview": " GNU AFFERO GENERAL PUBLIC LICENSE\n Version 3, 19 November 2007\n\n Copyright (C)"
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"preview": "// SPDX-License-Identifier: AGPL-3.0-or-later\n// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.co"
},
{
"path": "savage_core/src/lib.rs",
"chars": 238,
"preview": "// SPDX-License-Identifier: AGPL-3.0-or-later\n// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.co"
},
{
"path": "savage_core/src/parse.rs",
"chars": 13179,
"preview": "// SPDX-License-Identifier: AGPL-3.0-or-later\n// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.co"
},
{
"path": "savage_core/src/print.rs",
"chars": 15729,
"preview": "// SPDX-License-Identifier: AGPL-3.0-or-later\n// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.co"
},
{
"path": "savage_core/src/simplify.rs",
"chars": 7443,
"preview": "// SPDX-License-Identifier: AGPL-3.0-or-later\n// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.co"
},
{
"path": "savage_macros/Cargo.toml",
"chars": 438,
"preview": "[package]\nname = \"savage_macros\"\nversion = \"0.1.0\"\nauthors = [\"Philipp Emanuel Weidmann <pew@worldwidemann.com>\"]\ndescri"
},
{
"path": "savage_macros/src/lib.rs",
"chars": 4604,
"preview": "// SPDX-License-Identifier: AGPL-3.0-or-later\n// Copyright (C) 2021-2022 Philipp Emanuel Weidmann <pew@worldwidemann.co"
}
]
About this extraction
This page contains the full source code of the p-e-w/savage GitHub repository, extracted and formatted as plain text for AI agents and large language models (LLMs). The extraction includes 29 files (179.6 KB), approximately 42.8k tokens, and a symbol index with 156 extracted functions, classes, methods, constants, and types. Use this with OpenClaw, Claude, ChatGPT, Cursor, Windsurf, or any other AI tool that accepts text input. You can copy the full output to your clipboard or download it as a .txt file.
Extracted by GitExtract — free GitHub repo to text converter for AI. Built by Nikandr Surkov.