oisdk / agda-ring-solver Goto Github PK

View Code? Open in Web Editor NEW

38.0 4.0 4.0 6.21 MB

A fast, easy-to-use ring solver for agda with step-by-step solutions

Home Page: https://oisdk.github.io/agda-ring-solver/README.html

License: MIT License

Agda 94.18% Python 4.66% CSS 0.95% Shell 0.21%

agda agda-library interactive-theorem-proving

agda-ring-solver's People

Contributors

Stargazers

Watchers

Forkers

silky aljce strangeglyph citrusmunch

agda-ring-solver's Issues

Solve doesn't seem to support suc

lemma : ∀ n → suc n ≡ suc n * 1
lemma n = solveOver (n ∷ []) Nat.ring

The code above fails with:

/home/amckean/repos/thesis/proofs/Prelude/Nat.agda:123,11-38
n * 1 != n of type ℕ
when checking that the expression
Polynomial.Simple.Solver.Ops.correct {_} {_} Nat.ring {_}
(Polynomial.Expr.Expr._⊗_ {_}
 {AlmostCommutativeRing.Carrier {_} {_} Nat.ring} {1}
 (Polynomial.Expr.Expr.Κ {_}
  {AlmostCommutativeRing.Carrier {_} {_} Nat.ring} {1} (suc n))
 (Polynomial.Expr.Expr.Κ {_}
  {AlmostCommutativeRing.Carrier {_} {_} Nat.ring} {1} 1))
(Data.Vec.Base.Vec._∷_ {_} {_} {_} n
 (Data.Vec.Base.Vec.[] {_} {_}))
has type
(Nat.ring AlmostCommutativeRing.≈
 Polynomial.Simple.Solver.Ops.⟦ Nat.ring ⇓⟧
 (Polynomial.Expr.Expr.Κ (suc n))
 (n Data.Vec.Base.Vec.∷ Data.Vec.Base.Vec.[]))
_k_414

while the following type checks:

lemma : ∀ n → n ≡ n * 1
lemma n = solveOver (n ∷ []) Nat.ring

Is there a way to teach the solver about suc? All my proofs that include suc fail in a similar way.

Solving generic rings

open import Level using (_⊔_)
open import Algebra using (CommutativeRing)

open import Data.Maybe using (nothing)
open import Data.List using (List)
open List

module Prelude.Modular {c ℓ} (R : CommutativeRing c ℓ) where

open CommutativeRing R using (_≈_; setoid; 0#; 1#; _+_; _*_; _-_)
  renaming (Carrier to C)

open import Polynomial.Simple.AlmostCommutativeRing using (AlmostCommutativeRing; fromCommutativeRing)
open import Polynomial.Simple.Reflection using (solveOver)

ACR : AlmostCommutativeRing c ℓ
ACR = fromCommutativeRing R λ _ → nothing

record _≈_[mod_] (x : C) (y : C) (n : C) : Set (c ⊔ ℓ) where
  constructor modulo
  field
    k : C
    x-y≈k*n : x - y ≈ k * n

refl : ∀ {x} {n} → x ≈ x [mod n ]
refl {x} {n} = modulo 0# (solveOver (x ∷ n ∷ []) ACR)

Errors with

CommutativeRing._*_ /= CommutativeRing._+_
when checking that the expression
Polynomial.Simple.Solver.Ops.correct {_} {_} ACR {_}
(Polynomial.Expr.Expr._⊗_ {_}
 {AlmostCommutativeRing.Carrier {_} {_} ACR} {2}
 (Polynomial.Expr.Expr.Κ {_}
  {AlmostCommutativeRing.Carrier {_} {_} ACR} {2}
  (CommutativeRing.0# {_} {_} R))
 (Polynomial.Expr.Expr.Ι {_}
  {AlmostCommutativeRing.Carrier {_} {_} ACR} {2}
  (Data.Fin.Base.Fin.zero {_})))
(Data.Vec.Base.Vec._∷_ {_} {_} {_} n
 (Data.Vec.Base.Vec._∷_ {_} {_} {_} x
  (Data.Vec.Base.Vec.[] {_} {_})))
has type
(ACR AlmostCommutativeRing.≈
 Polynomial.Simple.Solver.Ops.⟦ ACR ⇓⟧
 (Polynomial.Expr.Expr.Κ (x - x))
 (n Data.Vec.Base.Vec.∷ x Data.Vec.Base.Vec.∷ Data.Vec.Base.Vec.[]))

Is it possible to solve rings that aren't currently instantiated

Issues regarding the compiler pragmas? (safe, without-K, etc.)

Hi! First of all, thanks and congrats on completing what seems to be the most advanced solver for Agda, at least as far as reflection is involved (and probably in general).

I'm trying to use it and the code is failing to check, because it seems that a lot of modules in this project use various compiler options such as --safe, which only allow importing other modules that are also safe. Unfortunately, many modules in the Agda standard library are currently not safe, indeed [1] states that

virtually any project relying on the standard library will not be successfully typechecked with the --safe option

When I try to type-check e.g. Polynomial.Simple.Reflection, indeed I get many errors regarding this:

/home/osense/dev/agda-libs/agda-ring-solver/src/Polynomial/Simple/Reflection.agda:5,1-23
Importing module Reflection not using the --safe flag from a module
which does.
when scope checking the declaration
  open import Reflection
/home/osense/dev/agda-libs/agda-ring-solver/src/Polynomial/Simple/Reflection.agda:5,1-23
Importing module Reflection not using the --without-K flag from a
module which does.
when scope checking the declaration
  open import Reflection
/home/osense/dev/agda-libs/agda-ring-solver/src/Polynomial/Simple/Reflection.agda:5,1-23
Importing module Reflection not using the --no-sized-types flag
from a module which does.
when scope checking the declaration
  open import Reflection
/home/osense/dev/agda-libs/agda-ring-solver/src/Polynomial/Simple/Reflection.agda:5,1-23
Importing module Reflection not using the --no-guardedness flag
from a module which does.
when scope checking the declaration
  open import Reflection

How do you manage to use the library in the current state? The above is using Agda 2.6.0 and version 0.17 of the standard library, but I have also tried the latest stdlib.

[1] https://agda.readthedocs.io/en/v2.5.4.1/language/safe-agda.html#standard-library

Does not type check with recent Agda.

This project does not type check with the recent Agda, looks like Agda's internal types from Agda.Builtin.Reflection have been pulled out from under it.

This is the error:

/home/kindaro/code/agda/agda-ring-solver/src/Reflection/Helpers.agda:60,17-38
Relevance !=< Modality
when checking that the expression relevant has type Modality

This is the code:

infixr 5 _⋯⟅∷⟆_
_⋯⟅∷⟆_ : ℕ → List (Arg Term) → List (Arg Term)
zero  ⋯⟅∷⟆ xs = xs
suc i ⋯⟅∷⟆ xs = unknown ⟅∷⟆ i ⋯⟅∷⟆ xs
{-# INLINE _⋯⟅∷⟆_ #-}

I am trying to build the project with the latest Agda, built from source code today.

oisdk / agda-ring-solver Goto Github PK

agda-ring-solver's People

Contributors

Stargazers

Watchers

Forkers

agda-ring-solver's Issues

Solve doesn't seem to support suc

Solving generic rings

Issues regarding the compiler pragmas? (safe, without-K, etc.)

Does not type check with recent Agda.

Recommend Projects

React

Vue.js

Typescript

TensorFlow

Django

Laravel

D3

Recommend Topics

javascript

web

server

Machine learning

Visualization

Game

Recommend Org

Facebook

Microsoft

Google

Alibaba

D3

Tencent