Yoneda.swift

//
//  Yoneda.swift
//  Basis
//
//  Created by Robert Widmann on 12/11/14.
//  Copyright (c) 2014 Robert Widmann. All rights reserved.
//

import Basis

public struct Yoneda<F : Functor> {	
	let runYoneda : (F.A -> F.B) -> F.FB
}

public func liftYoneda<F : Functor>(a : F) -> Yoneda<F> {
	return Yoneda({ f in F.fmap(f)(a) })
}

public func lowerYoneda<F : Functor>(y : Yoneda<F>) -> F {
	return unsafeCoerce(y.runYoneda(unsafeCoerce)) as F
}

public struct Coyoneda<F : Contravariant> {
	let contraFun : (F.A -> F.B)
	let contra : F.FB
	
	init(_ contraFun : (F.A -> F.B), _ contra : F.FB) {
		self.contraFun = contraFun
		self.contra = contra
	}
}

public func liftCoyoneda<F : Contravariant>(a : F.FB) -> Coyoneda<F> {
	return Coyoneda(unsafeCoerce, a)
}

public func lowerCoyoneda<F : Contravariant>(c : Coyoneda<F>) -> F {
	return F.contramap(c.contraFun)(c.contra)
}