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IdempotentCommutativeMonoid Expand file tree Collapse file tree 9 files changed +29
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lines changed Original file line number Diff line number Diff line change @@ -13,14 +13,17 @@ open import Algebra.Bundles using (CommutativeMonoid)
1313module Algebra.Solver.CommutativeMonoid.Normal {c ℓ} (M : CommutativeMonoid c ℓ) where
1414
1515import Algebra.Properties.CommutativeSemigroup as CSProperties
16+ using (interchange)
1617import Algebra.Properties.Monoid.Mult as MultProperties
18+ using (_×_; ×-homo-1; ×-homo-+)
1719open import Data.Fin.Base using (Fin; zero; suc)
1820open import Data.Nat as ℕ using (ℕ; zero; suc; _+_)
1921open import Data.Vec.Base using (Vec; []; _∷_; lookup; replicate; zipWith)
2022import Data.Vec.Relation.Binary.Pointwise.Inductive as Pointwise
23+ using (Pointwise; _∷_; []; Pointwise-≡↔≡; decidable)
2124open import Relation.Binary.Definitions using (DecidableEquality)
2225import Relation.Binary.Reasoning.Setoid as ≈-Reasoning
23- import Relation.Nullary.Decidable as Dec
26+ import Relation.Nullary.Decidable as Dec using (map)
2427
2528open CommutativeMonoid M
2629open MultProperties monoid using (_×_; ×-homo-1; ×-homo-+)
Original file line number Diff line number Diff line change @@ -13,10 +13,8 @@ import Algebra.Solver.IdempotentCommutativeMonoid as ICM-Solver
1313
1414open import Data.Bool.Base using (_∨_)
1515open import Data.Bool.Properties using (∨-idempotentCommutativeMonoid)
16-
1716open import Data.Fin.Base using (zero; suc)
1817open import Data.Vec.Base using ([]; _∷_)
19-
2018open import Relation.Binary.PropositionalEquality.Core using (_≡_)
2119
2220open ICM-Solver ∨-idempotentCommutativeMonoid
Original file line number Diff line number Diff line change @@ -20,9 +20,10 @@ open import Data.Fin.Base using (Fin; zero; suc)
2020open import Data.Nat.Base using (ℕ)
2121open import Data.Vec.Base using (Vec; []; _∷_; lookup; replicate; zipWith)
2222import Data.Vec.Relation.Binary.Pointwise.Inductive as Pointwise
23+ using (Pointwise; _∷_; []; Pointwise-≡↔≡; decidable)
2324open import Relation.Binary.Definitions using (DecidableEquality)
2425import Relation.Binary.Reasoning.Setoid as ≈-Reasoning
25- import Relation.Nullary.Decidable as Dec
26+ import Relation.Nullary.Decidable as Dec using (map)
2627
2728open IdempotentCommutativeMonoid M
2829open CSProperties commutativeSemigroup using (x∙yz≈xy∙z; x∙yz≈y∙xz)
Original file line number Diff line number Diff line change @@ -19,7 +19,7 @@ open import Data.Vec.Base using (lookup)
1919open import Function.Base using (_∘_; _$_)
2020open import Relation.Binary.Definitions using (DecidableEquality)
2121import Relation.Binary.Reasoning.Setoid as ≈-Reasoning
22- import Relation.Nullary.Decidable as Dec
22+ import Relation.Nullary.Decidable as Dec using (map; map′)
2323
2424open Monoid M
2525open ≈-Reasoning setoid
Original file line number Diff line number Diff line change 99
1010module Algebra.Solver.Ring.AlmostCommutativeRing where
1111
12- open import Algebra
13- open import Algebra.Structures
14- open import Algebra.Definitions
15- import Algebra.Morphism as Morphism
16- import Algebra.Morphism.Definitions as MorphismDefinitions
12+ open import Algebra using
13+ (Op₁; Op₂; CommutativeSemiring; RawRing; CommutativeRing)
14+ open import Algebra.Structures using (IsCommutativeSemiring)
15+ open import Algebra.Definitions using (Congruent₁; Congruent₂)
16+ import Algebra.Morphism.Definitions as MorphismDefinitions using
17+ (Homomorphic₀; Homomorphic₁; Homomorphic₂; Morphism)
1718open import Function.Base using (id)
18- open import Level
19+ open import Level using (suc; _⊔_)
1920open import Relation.Binary.Core using (Rel)
2021
2122
Original file line number Diff line number Diff line change 88
99{-# OPTIONS --cubical-compatible --safe #-}
1010
11- open import Algebra
12- open import Algebra.Solver.Ring.AlmostCommutativeRing
11+ open import Algebra using (RawRing)
12+ open import Algebra.Solver.Ring.AlmostCommutativeRing using (AlmostCommutativeRing; _-Raw-AlmostCommutative⟶_)
1313
1414module Algebra.Solver.Ring.Lemmas
1515 {r₁ r₂ r₃ r₄}
Original file line number Diff line number Diff line change 77
88{-# OPTIONS --cubical-compatible --safe #-}
99
10- open import Algebra
10+ open import Algebra using (RawRing; CommutativeSemiring )
1111import Algebra.Properties.Semiring.Mult as SemiringMultiplication
1212open import Data.Maybe.Base using (Maybe; just; nothing; map)
13- open import Algebra.Solver.Ring.AlmostCommutativeRing
14- open import Data.Nat.Base as ℕ
15- open import Data.Product.Base using (module Σ )
16- open import Function.Base using (id)
17- open import Relation.Binary.PropositionalEquality.Core using (_≡_)
1813
1914module Algebra.Solver.Ring.NaturalCoefficients
2015 {r₁ r₂} (R : CommutativeSemiring r₁ r₂)
2116 (open CommutativeSemiring R)
2217 (open SemiringMultiplication semiring using () renaming (_×_ to _×ᵤ_))
2318 (dec : ∀ m n → Maybe (m ×ᵤ 1# ≈ n ×ᵤ 1#)) where
2419
25- open import Algebra.Properties.Semiring.Mult.TCOptimised semiring
20+ open import Algebra.Solver.Ring.AlmostCommutativeRing
21+ open import Data.Nat.Base as ℕ using (ℕ; _+_; _*_)
22+ open import Data.Product.Base using (module Σ )
23+ open import Function.Base using (id)
24+ open import Relation.Binary.PropositionalEquality.Core using (_≡_)
2625
26+ open import Algebra.Properties.Semiring.Mult.TCOptimised semiring
2727open import Relation.Binary.Reasoning.Setoid setoid
2828
2929private
Original file line number Diff line number Diff line change @@ -16,11 +16,11 @@ open import Algebra
1616module Algebra.Solver.Ring.NaturalCoefficients.Default
1717 {r₁ r₂} (R : CommutativeSemiring r₁ r₂) where
1818
19- import Algebra.Properties.Semiring.Mult as SemiringMultiplication
19+ import Algebra.Properties.Semiring.Mult as SemiringMultiplication using (_×_)
2020open import Data.Maybe.Base using (Maybe; map)
2121open import Data.Nat using (_≟_)
2222open import Relation.Binary.Consequences using (dec⇒weaklyDec)
23- import Relation.Binary.PropositionalEquality.Core as ≡
23+ import Relation.Binary.PropositionalEquality.Core as ≡ using (refl; cong)
2424
2525open CommutativeSemiring R
2626open SemiringMultiplication semiring
Original file line number Diff line number Diff line change 77
88{-# OPTIONS --cubical-compatible --safe #-}
99
10- open import Algebra.Solver.Ring.AlmostCommutativeRing
10+ open import Algebra.Solver.Ring.AlmostCommutativeRing using
11+ (AlmostCommutativeRing; -raw-almostCommutative⟶)
1112open import Relation.Binary.Definitions using (Decidable)
12- open import Relation.Binary.Consequences using (dec⇒weaklyDec)
1313
1414module Algebra.Solver.Ring.Simple
1515 {r₁ r₂} (R : AlmostCommutativeRing r₁ r₂)
1616 (_≟_ : Decidable (AlmostCommutativeRing._≈_ R))
1717 where
1818
19+ open import Relation.Binary.Consequences using (dec⇒weaklyDec)
20+
1921open AlmostCommutativeRing R
2022import Algebra.Solver.Ring as RS
2123open RS rawRing R (-raw-almostCommutative⟶ R) (dec⇒weaklyDec _≟_) public
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