------------------------------------------------------------------------ -- The Agda standard library -- -- A type for expressions over a raw ring. ------------------------------------------------------------------------ {-# OPTIONS --cubical-compatible --safe #-} module Tactic.RingSolver.Core.Expression where open import Data.Nat.Base using (ℕ) open import Data.Fin.Base using (Fin) open import Data.Vec.Base as Vec using (Vec) open import Algebra infixl 6 _⊕_ infixl 7 _⊗_ infixr 8 _⊛_ infix 8 ⊝_ data Expr {a} (A : Set a) (n : ℕ) : Set a where Κ : A → Expr A n -- Constant Ι : Fin n → Expr A n -- Variable _⊕_ : Expr A n → Expr A n → Expr A n -- Addition _⊗_ : Expr A n → Expr A n → Expr A n -- Multiplication _⊛_ : Expr A n → ℕ → Expr A n -- Exponentiation ⊝_ : Expr A n → Expr A n -- Negation module Eval {ℓ₁ ℓ₂} (rawRing : RawRing ℓ₁ ℓ₂) (open RawRing rawRing) {a} {A : Set a} (⟦_⟧ᵣ : A → Carrier) where open import Algebra.Definitions.RawSemiring rawSemiring using (_^′_) ⟦_⟧ : ∀ {n} → Expr A n → Vec Carrier n → Carrier ⟦ Κ x ⟧ ρ = ⟦ x ⟧ᵣ ⟦ Ι x ⟧ ρ = Vec.lookup ρ x ⟦ x ⊕ y ⟧ ρ = ⟦ x ⟧ ρ + ⟦ y ⟧ ρ ⟦ x ⊗ y ⟧ ρ = ⟦ x ⟧ ρ * ⟦ y ⟧ ρ ⟦ ⊝ x ⟧ ρ = - ⟦ x ⟧ ρ ⟦ x ⊛ i ⟧ ρ = ⟦ x ⟧ ρ ^′ i
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