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