------------------------------------------------------------------------
-- The Agda standard library
--
-- Automatic solvers for equations over integers
------------------------------------------------------------------------
-- See README.Tactic.RingSolver for examples of how to use this solver
{-# OPTIONS --cubical-compatible --safe #-}
module Data.Integer.Tactic.RingSolver where
open import Agda.Builtin.Reflection
open import Data.Maybe.Base using (just; nothing)
open import Data.Integer.Base using (+0)
open import Data.Integer.Properties using (+-*-commutativeRing)
open import Level using (0ℓ)
open import Data.Unit.Base using (⊤)
open import Relation.Binary.PropositionalEquality.Core using (refl)
import Tactic.RingSolver as Solver using (solve-∀-macro; solve-macro)
import Tactic.RingSolver.Core.AlmostCommutativeRing as ACR
using (AlmostCommutativeRing; fromCommutativeRing)
------------------------------------------------------------------------
-- A module for automatically solving propositional equivalences
-- containing _+_ and _*_
ring : ACR.AlmostCommutativeRing 0ℓ 0ℓ
ring = ACR.fromCommutativeRing +-*-commutativeRing
λ { +0 → just refl; _ → nothing }
macro
solve-∀ : Term → TC ⊤
solve-∀ = Solver.solve-∀-macro (quote ring)
macro
solve : Term → Term → TC ⊤
solve n = Solver.solve-macro n (quote ring)
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