1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
|
let iterate
= λ(n : Natural)
→ λ(a : Type)
→ λ(f : a → a)
→ λ(x : a)
→ List/build
a
( λ(list : Type)
→ λ(cons : a → list → list)
→ List/fold
{ index : Natural, value : {} }
( List/indexed
{}
( List/build
{}
( λ(list : Type)
→ λ(cons : {} → list → list)
→ Natural/fold n list (cons {=})
)
)
)
list
( λ(y : { index : Natural, value : {} })
→ cons (Natural/fold y.index a f x)
)
)
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
: ∀(a : Type) → ∀(b : Type) → (a → b) → List a → List b
= λ(a : Type)
→ λ(b : Type)
→ λ(f : a → b)
→ λ(xs : List a)
→ List/build
b
( λ(list : Type)
→ λ(cons : b → list → list)
→ List/fold a xs list (λ(x : a) → cons (f x))
)
let any
: ∀(a : Type) → (a → Bool) → List a → Bool
= 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
: ∀(a : Type) → (a → Bool) → List a → List a
= λ(a : Type)
→ λ(f : a → Bool)
→ λ(xs : List a)
→ List/build
a
( λ(list : Type)
→ λ(cons : a → list → list)
→ List/fold
a
xs
list
(λ(x : a) → λ(xs : list) → if f x then cons x xs else xs)
)
in sum (filter Natural Natural/even
(map Natural Natural (λ(x:Natural) → x + 10) (countTo 1000)))
|
