57 lines
1.4 KiB
Text
57 lines
1.4 KiB
Text
import data.vector
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open nat vector
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definition fib : nat → nat,
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fib 0 := 1,
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fib 1 := 1,
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fib (a+2) := (fib a ↓ lt.step (lt.base a)) + (fib (a+1) ↓ lt.base (a+1))
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[wf] lt.wf
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definition gcd : nat → nat → nat,
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gcd 0 x := x,
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gcd x 0 := x,
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gcd (succ x) (succ y) := if y ≤ x
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then gcd (x - y) (succ y) ↓ !sigma.lex.left (lt_succ_of_le (sub_le x y))
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else gcd (succ x) (y - x) ↓ !sigma.lex.right (lt_succ_of_le (sub_le y x))
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[wf] sigma.lex.wf lt.wf (λ x, lt.wf)
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definition add : nat → nat → nat,
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add zero b := b,
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add (succ a) b := succ (add a b)
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definition map {A B C : Type} (f : A → B → C) : Π {n}, vector A n → vector B n → vector C n,
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map nil nil := nil,
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map (a :: va) (b :: vb) := f a b :: map va vb
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definition half : nat → nat,
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half 0 := 0,
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half 1 := 0,
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half (x+2) := half x + 1
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variables {A B : Type}
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inductive image_of (f : A → B) : B → Type :=
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mk : Π a, image_of f (f a)
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definition inv {f : A → B} : Π b, image_of f b → A,
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inv ⌞f a⌟ (image_of.mk f a) := a
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namespace tst
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definition fib : nat → nat,
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fib 0 := 1,
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fib 1 := 1,
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fib (a+2) := fib a + fib (a+1)
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end tst
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definition simple : nat → nat → nat,
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simple x y := x + y
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definition simple2 : nat → nat → nat,
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simple2 (x+1) y := x + y,
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simple2 ⌞y+1⌟ y := y
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check @vector.brec_on
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check @vector.cases_on
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