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equational-reasoning: Proof assistant for Haskell using DataKinds & PolyKinds

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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 (info)
Change log Changelog.md
Dependencies base (>=4 && <5), containers (>=0.5 && <0.8), template-haskell (>=2.11 && <2.23), th-desugar (>=1.8 && <1.18), void (>=0.6 && <0.8) [details]
Tested with ghc ==9.0.2 || ==9.2.8 || ==9.4.8 || ==9.6.5 || ==9.8.2
License BSD-3-Clause
Copyright (c) Hiromi ISHII 2013-2020
Author Hiromi ISHII
Maintainer konn.jinro_at_gmail.com
Revised Revision 1 made by HiromiIshii at 2024-05-17T12:07:27Z
Category Math
Source repo head: git clone git://github.com/konn/equational-reasoning-in-haskell.git
Uploaded by HiromiIshii at 2024-05-17T11:59:59Z
Distributions LTSHaskell:0.7.0.3, NixOS:0.7.0.3, Stackage:0.7.0.3
Reverse Dependencies 9 direct, 14 indirect [details]
Downloads 19511 total (112 in the last 30 days)
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Status Docs available [build log]
Last success reported on 2024-05-17 [all 1 reports]

Readme for equational-reasoning-0.7.0.3

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Agda-style Equational Reasoning in Haskell by Data Kinds

Build Status Hackage

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.