Last active
December 12, 2016 19:24
-
-
Save mxswd/9fc8d19f6cc235c23158 to your computer and use it in GitHub Desktop.
Thanks @robrix and CodaFi_ for the discussion :D
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
// this is a playground | |
protocol Nat { | |
class func construct() -> Self | |
class func value() -> Int | |
} | |
struct Z : Nat { | |
static func construct() -> Z { | |
return Z() | |
} | |
static func value() -> Int { | |
return 0 | |
} | |
} | |
struct S<N: Nat> : Nat { | |
static func construct() -> S<N> { | |
return S() | |
} | |
static func value() -> Int { | |
return 1 + N.value() | |
} | |
} | |
// how about type level bools | |
protocol BOOL { | |
class func value() -> Bool | |
} | |
struct TRUE : BOOL { | |
static func value() -> Bool { | |
return true | |
} | |
} | |
struct FALSE : BOOL { | |
static func value() -> Bool { | |
return false | |
} | |
} | |
// you saw identity before | |
func refl<N: Nat>(n: N) -> N { | |
return n | |
} | |
let twoEqualsTwo: S<S<Z>> = refl(S<S<Z>>()) | |
// now succ, given X, give me S<X> | |
func succ<N: Nat>(n: N) -> S<N> { | |
return S<N>() | |
} | |
let twoSuccThree: S<S<S<Z>>> = succ(S<S<Z>>()) | |
// cool, what about less than or equal? | |
func sub1<N: Nat, X: Nat>(proof: N -> S<X>)(n: N) -> X { | |
return X.construct() | |
} | |
// try to type it another way. you can't | |
let twoSubOne: S<Z> = sub1(refl)(n: S<S<Z>>()) | |
twoSubOne // not a lie | |
// x less than y, needs some more type constraints... but compiler bugs exist. | |
// im cheating here a little. | |
func lessThan<N: Nat, M: Nat>(proof: M -> N)(n: N)(m: M) -> TRUE { | |
return TRUE() | |
} | |
// is 2 less than 1? | |
let onelessthantwo = lessThan(sub1(refl))(n: S<Z>())(m: S<S<Z>>()) | |
let zerolessthantwo = lessThan(sub1(sub1(refl)))(n: Z())(m: S<S<Z>>()) | |
// now something useful | |
struct MVec<A, L: Nat> { | |
let vec: Array<A> | |
func index<I: Nat>(i: I, n: S<I> -> L -> TRUE) -> A { | |
return vec[I.value()] | |
} | |
} | |
// you must provide a proof that an index is inside the bounds of the array | |
let v1: MVec<String, S<S<S<Z>>>> = MVec(vec: ["hello", "rob", "rix"]) | |
v1.index(Z(), lessThan(sub1(sub1(refl)))) | |
v1.index(S<Z>(), lessThan(sub1(refl))) | |
v1.index(S<S<Z>>(), lessThan(refl)) | |
//v1.index(S<S<S<Z>>>(), lessThan(refl)) // type error, 3 > 2 | |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
What is a Nat? What is a Z?