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47 lines
1.4 KiB
Agda
47 lines
1.4 KiB
Agda
module Setoids where
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open import Level
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record _×_ {a b} (A : Set a) (B : Set b) : Set (a ⊔ b) where
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constructor _,_
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field
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fst : A
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snd : B
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open _×_
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<_,_> : ∀ {a b c} {A : Set a} {B : Set b} {C : Set c}
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→ (A → B) → (A → C) → A → (B × C)
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< f , g > x = (f x , g x)
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record ⊤ {l} : Set l where
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constructor tt
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! : ∀ {l} {X : Set l} → X → ⊤ {l}
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! _ = tt
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data _+_ {a b} (A : Set a) (B : Set b) : Set (a ⊔ b) where
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i₁ : A → A + B
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i₂ : B → A + B
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[_,_] : ∀ {a b c} {A : Set a} {B : Set b} {C : Set c}
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→ (A → C) → (B → C) → (A + B) → C
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[ f , g ] (i₁ x) = f x
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[ f , g ] (i₂ x) = g x
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data ⊥ {l} : Set l where
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¡ : ∀ {l} {X : Set l} → ⊥ {l} → X
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¡ ()
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distributeˡ⁻¹ : ∀ {a b c} {A : Set a} {B : Set b} {C : Set c} → (A × B) + (A × C) → A × (B + C)
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distributeˡ⁻¹ (i₁ (x , y)) = (x , i₁ y)
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distributeˡ⁻¹ (i₂ (x , y)) = (x , i₂ y)
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distributeˡ : ∀ {a b c} {A : Set a} {B : Set b} {C : Set c} → A × (B + C) → (A × B) + (A × C)
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distributeˡ (x , i₁ y) = i₁ (x , y)
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distributeˡ (x , i₂ y) = i₂ (x , y)
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curry : ∀ {a b c} {A : Set a} {B : Set b} {C : Set c} → (C × A → B) → C → A → B
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curry f x y = f (x , y)
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eval : ∀ {a b} {A : Set a} {B : Set b} → ((A → B) × A) → B
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eval (f , x) = f x
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