Viclib viclib

Simplifying division of church-numbers with church-fractions.

A church number n can be understood as the act of applying a function to a value n times. That is:

(λ f x . (f (f (f x))))

Can be understood as the church number 3, since it is an action that applies a function, f, to a value, x, 3 times. Here, I will be using "number" as a synonym for "church number" and, thus, a "natural number". Implementing addition, multiplication and exponentiation on church numbers is straightforward. Division is more awkward. Wikipedia, for instance, uses a recursive definition that doesn't have a normal form and is, thus, unsuited for strongly normalizing evaluators. This version is total, but has a huge normal form and works for integers, not naturals. There is a simpler way to define it, extending the same intuition to bu

	// This is a simple interpreter for the untyped lambda calculus
	// in JavaScript, used as an example of the possible benefits of
	// hash-consing. Skip to the end of the file to see the tests.
	// ~ SrPeixinho

	var i32size = Math.pow(2,32);
	var i32sizeInv = 1/i32size;
	var stats = {
	beta_reductions : 0,
	reductions : 0,

	var h$currentThread = null;
	var h$stack = null;
	var h$sp = 0;
	var h$initStatic = [];
	var h$staticThunks = {};
	var h$staticThunksArr = [];
	var h$regs = [];
	var h$r1 = 0;
	var h$r2 = 0;

	"perfis":{
	"conservador":{
	"renda_fixa":{
	"percentuais":[70,65,60,55,50,45,40,35,30,25],
	"divisao":{
	"Renda Fixa Referenciado":100,
	"Renda Fixa Índice":0
	}
	},
	"multimercado":{

	global.perfis = {}
	for p,perfil of data.perfis
	perfis[p] = {}
	for c,cat of perfil
	perfis[p][c] = {}
	for sc,parcela of cat.divisao
	categoria[sc] = c
	perfis[p][c][sc] = interpolated (map (->it*parcela/100), cat.percentuais), 0, 10

	testVec : Vect 5 Int
	testVec = 3 :: 4 :: 5 :: 6 :: 7 :: Nil
	aff : Int
	aff = index (2 + 2) testVec