38 lines
1.2 KiB
Text
38 lines
1.2 KiB
Text
def0 Vec : 0.ℕ → 0.★₀ → ★₀ =
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λ n A ⇒
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caseω n return ★₀ of {
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zero ⇒ {nil};
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succ _, 0.Tail ⇒ A × Tail
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};
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def0 List : 0.★₀ → ★₀ =
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λ A ⇒ (len : ℕ) × Vec len A;
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def nil : 0.(A : ★₀) → List A =
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λ A ⇒ (0, 'nil);
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def cons : 0.(A : ★₀) → 1.A → 1.(List A) → List A =
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λ A x xs ⇒ case1 xs return List A of { (len, elems) ⇒ (succ len, x, elems) };
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def foldr' : 0.(A : ★₀) → 0.(B : ★₀) →
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1.B → ω.(1.A → 1.B → B) → 1.(n : ℕ) → 1.(Vec n A) → B =
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λ A B z c n ⇒
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case1 n return n' ⇒ 1.(Vec n' A) → B of {
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zero ⇒
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λ nil ⇒ case1 nil return B of { 'nil ⇒ z };
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succ n, 1.ih ⇒
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λ cons ⇒ case1 cons return B of { (first, rest) ⇒ c first (ih rest) }
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};
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def foldr : 0.(A : ★₀) → 0.(B : ★₀) →
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1.B → ω.(1.A → 1.B → B) → 1.(List A) → B =
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λ A B z c xs ⇒
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case1 xs return B of { (len, elems) ⇒ foldr' A B z c len elems };
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load "nat.quox";
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def sum : 1.(List ℕ) → ℕ = foldr ℕ ℕ 0 plus;
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def numbers : List ℕ = (5, (0, 1, 2, 3, 4, 5, 'nil));
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def number-sum : sum numbers ≡ 10 : ℕ = δ _ ⇒ 10;
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