https://github.com/andrew-johnson-4/InPlace

An implementation of several strongly-normalizing string rewriting systems
https://github.com/andrew-johnson-4/InPlace

Last synced: 3 months ago
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An implementation of several strongly-normalizing string rewriting systems

• Host: GitHub
• URL: https://github.com/andrew-johnson-4/InPlace
• Owner: andrew-johnson-4
• License: mit
• Created: 2023-12-04T22:51:07.000Z (7 months ago)
• Default Branch: main
• Last Pushed: 2024-01-06T05:44:55.000Z (6 months ago)
• Last Synced: 2024-02-28T07:40:46.224Z (4 months ago)
• Language: Rust
• Size: 81.1 KB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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• awesome-rust-formalized-reasoning - Relog - implementation of several strongly-normalizing string rewriting systems. (Unclassified / Libraries)

README

        
# [Relog](https://github.com/andrew-johnson-4/InPlace/wiki)

An implementation of several strongly-normalizing string rewriting systems

# Relog (Reduction Logic) Flavor

```relog

a = Int;

List

---output----

List


A> = A>;

R

---output-------------------

R


A := R;

A

---output----------

R


Print<"hello world">

---output-----------

[stdout]hello world

0

For

>

---output------------------------------

[stdout]99 bottles of beer on the wall

...

0

```

## Relog Syntax

Relog is a type system, not a programming language. It is not Turing Complete, it is Strongly Normalizing.

The basic syntax of a Relog program is defined by unifications, followed by a result.

Unifications have a left-hand-side and a right-hand-side separated by an equal sign with a semicolon after each unification:

```

Pair = Pair;

```


Results are a single term and can reference unification variables bound by previous actions:

```

Pair

```


An example program might represent the application of a function `a -> Maybe` with argument `Int` which would look like below:


```

a = Int;

Maybe

```


when running this program the unification will bind `Int` to `a` and return the result `Maybe`.

## Relog Type System

![Reduction](https://github.com/andrew-johnson-4/InPlace/blob/main/unifyreify.png)

$$apply \ \ \frac{unify(f,fx)⊢r}{f⇻r⊢reify(apply(r))}$$