30 lines
790 B
Agda
30 lines
790 B
Agda
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module hwk2 where
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open import Data.Nat
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open import Data.Sum
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open import Data.Unit
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open import Data.Empty
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open import Relation.Binary.PropositionalEquality as Eq hiding (subst)
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open Eq.≡-Reasoning
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J : {A : Set}
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→ (C : (x y : A) → x ≡ y → Set)
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→ (c : (x : A) → C x x refl)
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→ (x y : A) → (p : x ≡ y) → C x y p
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J C c x x refl = c x
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subst : {A : Set} {a b : A}
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→ (P : A → Set)
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→ (c : a ≡ b)
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→ (p : P a)
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→ P b
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subst {A} {a} {b} P c = J (λ x y p → (P x → P y)) (λ x → (λ a → a)) a b c
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discriminate : {A : Set} {B : Set} → (s : A ⊎ B) → Set
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discriminate (inj₁ x) = ⊤
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discriminate (inj₂ y) = ⊥
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problem2 : {A : Set} {B : Set}
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→ (a : A) → (b : B)
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→ inj₁ a ≢ inj₂ b
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problem2 a b p = subst discriminate p tt
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