• Jun 13 2008

## How to create "recursive" functions in λ-calculus

As you probably already now, recursive function are those that call them self. For instance, you can define the factorial function as: fact(0) = 1 fact(n) = n*fact(n-1) This doesn't look like something you can say with the small syntaxis of the λ-calculus...

• May 2 2008

## Arithmetic with Lambda Calculus

One simple way to make arithmetic expressions in lambda calculus, is just to extend the calculus with the arithmetic rules: (λx.(λy. x+y)) 2 3 → (λy. 2+y) 3 → 2+3 = 5 But that's pretty easy for us, and (as you problably have already noticed) we like...

• Mar 28 2008

## Lambda Calculus

From the Wikipedia: "calculus can refer to any method or system of calculation", and that's not an exception for the Lambda Calculus. First of all, lets define the terms of this calculus: A Lambda Term is something with the form x where x is in...

• Mar 15 2008

## Basis of Term Rewriting Systems

A Term Rewriting System (TRS) is a very powerful yet simple math tool used, for instance, for the creation of computational models. Given a set of function symbols S, and an (uncountable) set of variables V, I will define rewriting rule by example...