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let iterate =
λ(n : Natural)
→ λ(a : Type)
→ λ(f : a → a)
→ λ(x : a)
→ (Natural/fold n
(a → List a → {fst:a, snd:List a})
(λ (hyp : a → List a → {fst:a, snd:List a}) →
λ (x : a) → λ (xs : List a)
→ let tup = hyp x xs
in {fst = f (tup.fst), snd = tup.snd # [tup.fst]})
(λ (x : a) → λ (xs : List a) → {fst=x, snd=xs})
x ([] : List a)).snd
let countTo =
λ (x : Natural)
→ iterate x Natural (λ (x : Natural) → x + 1) 0
let sum =
λ (xs : List Natural)
→ List/fold Natural xs Natural (λ (x : Natural) → λ (acc : Natural) → x + acc) 0
let map
= λ(a : Type)
→ λ(b : Type)
→ λ(f : a → b)
→ λ(xs : List a)
→ List/fold a xs (List b) (λ (x : a) → λ (xs : List b) → [f x] # xs) ([] : List b)
let any
= λ(a : Type)
→ λ(f : a → Bool)
→ λ(xs : List a)
→ List/fold a xs Bool (λ(x : a) → λ(r : Bool) → f x || r) False
let filter
= λ(a : Type)
→ λ(f : a → Bool)
→ λ(xs : List a)
→ List/fold a xs (List a)
(λ (x : a) → λ (xs : List a) → if f x then [x] # xs else xs) ([] : List a)
in sum (filter Natural Natural/even
(map Natural Natural (λ(x:Natural) → x + 10) (countTo 1000)))
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