------------------------------------------------------------------------
-- The Agda standard library
--
-- Automatic solvers for equations over naturals
------------------------------------------------------------------------
-- See README.Tactic.RingSolver for examples of how to use this solver
{-# OPTIONS --cubical-compatible --safe #-}
module Data.Nat.Tactic.RingSolver where
open import Agda.Builtin.Reflection using (Term; TC)
open import Data.Maybe.Base using (just; nothing)
open import Data.Nat.Base using (zero)
open import Data.Nat.Properties using (+-*-commutativeSemiring)
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
------------------------------------------------------------------------
-- A module for automatically solving propositional equivalences
-- containing _+_ and _*_
ring : ACR.AlmostCommutativeRing 0ℓ 0ℓ
ring = ACR.fromCommutativeSemiring +-*-commutativeSemiring
λ { zero → 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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