90 lines
2.1 KiB
Plaintext
90 lines
2.1 KiB
Plaintext
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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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defω nil : 0.(A : ★₀) → List A =
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λ A ⇒ (0, 'nil);
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defω S : 1.ℕ → ℕ = λ n ⇒ succ n;
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defω cons : 0.(A : ★₀) → 1.A → 1.(List A) → List A =
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λ A x xs ⇒
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case1 xs return List A of {
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(len, elems) ⇒ (succ len, x, elems)
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};
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{-
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-- needs coercions overall,
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-- and real w-types to be linear
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defω list-ind :
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0.(A : ★₀) →
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0.(P : ω.(List A) → ★₀) →
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1.(n : P (nil A)) →
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ω.(c : 1.(x : A) → 0.(xs : List A) → 1.(P xs) → P (cons A x xs)) →
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1.(lst : List A) → P lst =
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λ A P n c lst ⇒
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case1 lst return l ⇒ P l of {
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(len, elems) ⇒
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case1 len return len' ⇒ P (len', elems) of {
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zero ⇒ n;
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succ len', 1.ih ⇒
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case1 elems return P (succ len', elems) of {
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(first, rest) ⇒ c first rest ih
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}
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}
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};
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defω foldr :
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0.(A : ★₀) → 0.(B : ★₀) →
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1.(n : B) → ω.(c : 1.A → 1.B → B) →
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1.(List A) → B =
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λ A B n c lst ⇒ list-ind A (λ _ ⇒ B) n (λ a as b ⇒ c a b) lst;
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-- ...still does
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defω foldr :
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0.(A : ★₀) → 0.(B : ★₀) →
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ω.(n : B) → ω.(c : 1.A → 1.B → B) →
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ω.(List A) → B =
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λ A B n c lst ⇒
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caseω lst return B of {
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(len, elems) ⇒
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caseω len return B of {
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zero ⇒ caseω elems return B of { 'nil ⇒ n };
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succ _, ω.ih ⇒
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caseω elems return B of {
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(first, rest) ⇒ c first ih
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}
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}
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};
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-}
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defω plus : 1.ℕ → 1.ℕ → ℕ =
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λ m n ⇒
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case1 m return ℕ of {
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zero ⇒ n;
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succ _, 1.mn ⇒ succ mn
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};
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-- case-ℕ's qout needs to be Σz + ωΣs
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def0 plus-3-3 : plus 3 3 ≡ 6 : ℕ =
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δ 𝑖 ⇒ 6;
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{-
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defω sum : ω.(List ℕ) → ℕ = foldr ℕ ℕ 0 plus;
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defω numbers : List ℕ =
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(5, (0, 1, 2, 3, 4, 'nil));
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defω number-sum : sum numbers ≡ 10 : ℕ =
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δ _ ⇒ 10;
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-}
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