1234567891011121314151617181920212223242526272829303132333435363738-------------------------------------------------------------------------- The Agda standard library---- Indexed binary relations------------------------------------------------------------------------ -- The contents of this module should be accessed via-- `Relation.Binary.Indexed.Heterogeneous`. {-# OPTIONS --cubical-compatible --safe #-} module Relation.Binary.Indexed.Heterogeneous.Core where open import Level using (Level)import Relation.Binary.Core as B using (Rel; REL; _⇒_) -------------------------------------------------------------------------- Indexed binary relations -- Heterogeneous types IREL : ∀ {i₁ i₂ a₁ a₂} {I₁ : Set i₁} {I₂ : Set i₂} → (I₁ → Set a₁) → (I₂ → Set a₂) → (ℓ : Level) → Set _IREL A₁ A₂ ℓ = ∀ {i₁ i₂} → A₁ i₁ → A₂ i₂ → Set ℓ -- Homogeneous types IRel : ∀ {i a} {I : Set i} → (I → Set a) → (ℓ : Level) → Set _IRel A ℓ = IREL A A ℓ -------------------------------------------------------------------------- Generalised implication. infixr 4 _=[_]⇒_ _=[_]⇒_ : ∀ {a b ℓ₁ ℓ₂} {A : Set a} {B : A → Set b} → B.Rel A ℓ₁ → ((x : A) → B x) → IRel B ℓ₂ → Set _P =[ f ]⇒ Q = ∀ {i j} → P i j → Q (f i) (f j)