quox/examples/list.quox

load "nat.quox";

namespace list {

def0 Vec : ℕ → ★ → ★ =
  λ n A ⇒
  caseω n return ★ of {
    zero           ⇒ {nil};
    succ _, 0.Tail ⇒ A × Tail
  };

def0 List : ★ → ★ =
  λ A ⇒ (len : ℕ) × Vec len A;

def nil : 0.(A : ★) → List A =
  λ A ⇒ (0, 'nil);

def cons : 0.(A : ★) → A → List A → List A =
  λ A x xs ⇒ case xs return List A of { (len, elems) ⇒ (succ len, x, elems) };

def foldr' : 0.(A B : ★) →
             B → ω.(A → B → B) → (n : ℕ) → Vec n A → B =
  λ A B z c n ⇒
  case n return n' ⇒ Vec n' A → B of {
    zero ⇒
      λ nil ⇒ case nil return B of { 'nil ⇒ z };
    succ n, 1.ih ⇒
      λ cons ⇒ case cons return B of { (first, rest) ⇒ c first (ih rest) }
  };

def foldr : 0.(A B : ★) → B → ω.(A → B → B) → List A → B =
  λ A B z c xs ⇒
  case xs return B of { (len, elems) ⇒ foldr' A B z c len elems };

def sum : List ℕ → ℕ = foldr ℕ ℕ 0 nat.plus;

def numbers : List ℕ = (5, (0, 1, 2, 3, 4, 'nil));

def number-sum : sum numbers ≡ 10 : ℕ = δ _ ⇒ 10;

}