equational-reasoning: Proof assistant for Haskell using DataKinds & PolyKinds
A simple convenient library to write equational / preorder proof as in Agda.
Since 0.6.0.0, this no longer depends on singletons package, and the Proof.Induction module goes to equational-reasoning-induction package.
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| Versions [RSS] | 0.0.1.0, 0.0.3.0, 0.0.4.0, 0.0.4.1, 0.1.0.0, 0.2.0.0, 0.2.0.1, 0.2.0.2, 0.2.0.3, 0.2.0.4, 0.2.0.5, 0.2.0.6, 0.2.0.7, 0.3.0.0, 0.4.0.0, 0.4.1.0, 0.4.1.1, 0.5.0.0, 0.5.1.0, 0.5.1.1, 0.6.0.0, 0.6.0.1, 0.6.0.2, 0.6.0.3, 0.6.0.4, 0.7.0.0, 0.7.0.1, 0.7.0.2, 0.7.0.3, 0.7.1.0 (info) |
|---|---|
| Change log | Changelog.md |
| Dependencies | base (>=4.13 && <5), containers (>=0.5 && <0.9), template-haskell (>=2.11 && <2.25), th-desugar (>=1.13 && <1.20), void (>=0.6 && <0.8) [details] |
| Tested with | ghc ==9.2.8 || ==9.4.8 || ==9.6.5 || ==9.8.4 || ==9.10.1 || ==9.12.2 || ==9.14.1 |
| License | BSD-3-Clause |
| Copyright | (c) Hiromi ISHII 2013-2020 |
| Author | Hiromi ISHII |
| Maintainer | konn.jinro_at_gmail.com |
| Uploaded | by HiromiIshii at 2025-01-02T06:49:25Z |
| Revised | Revision 1 made by HiromiIshii at 2026-01-18T03:41:01Z |
| Category | Math |
| Source repo | head: git clone https://github.com/konn/equational-reasoning-in-haskell |
| Distributions | LTSHaskell:0.7.1.0, NixOS:0.7.1.0, Stackage:0.7.1.0 |
| Reverse Dependencies | 9 direct, 14 indirect [details] |
| Downloads | 20216 total (115 in the last 30 days) |
| Rating | (no votes yet) [estimated by Bayesian average] |
| Your Rating | |
| Status | Docs available [build log] Last success reported on 2025-01-02 [all 1 reports] |
Readme for equational-reasoning-0.7.1.0
[back to package description]Agda-style Equational Reasoning in Haskell by Data Kinds
What is this?
This library provides means to prove equations in Haskell. You can prove equations in Agda's EqReasoning like style.
See blow for an example:
plusZeroL :: SNat m -> Zero :+: m :=: m
plusZeroL SZero = Refl
plusZeroL (SSucc m) =
start (SZero %+ (SSucc m))
=== SSucc (SZero %+ m) `because` plusSuccR SZero m
=== SSucc m `because` succCongEq (plusZeroL m)
It also provides some utility functions to use an induction.
For more detail, please read source codes!
TODOs
- Automatic generation for induction schema for any inductive types.