# Category: Lambda Calculus

• ## Lambda Calculus in OCaml: “fun” and “function”

Lambda is fun! Lambda is certainly fun, but what I mean here is that the λ in lambda calculus is similar to the expression fun in OCaml. Recall that in lambda calculus, we have function expressions and function applications: λx.λy.x+y (*A function expression*) λx.λy.x+y 3 4 (*A function application*) In OCaml, you can express the same…

• ## Lazy or Eager? Order of Evaluation in Lambda Calculus and OCaml

Recall in lambda calculus, two items side by side is an application.  One applies the left item (the function) to the right item (the input).  E.g.: f x is read as “apply f to x”, in which f and x can be any lambda expressions.  Therefore, f and/or x may be expressions that can be evaluated…

• ## Currying in Lambda Calculus and OCaml

Currying Recall that in lambda calculus, a function can have more than one input, each preceded by a λ symbol.  Another way of thinking about more than one input is currying.  Currying a function of two inputs turns that function into a function with one input by passing one of the inputs into it.  In other…

• ## Encoding Recursion with the Y Combinator

In this post I’ll go through some exercises and encode some recursive functions with the Y combinator. Encoding with rec Continuing on from my last post, Professor Hutton gave us two exercises in the Y combinator video: Encode loop (the function that just calls itself) with rec.  I.e., loop = rec (?) Encode the factorial function…

• ## Recursion in Lambda Calculus: The Y Combinator

In the last post I talked about how powerful lambda calculus is.  In this post I further proves the point by encoding recursion in it.  This enables you to do recursion in any languages! If you haven’t read my last post already, please do so!  It’d be easier for you to follow this post, especially…

• ## Simple Yet Powerful: Lambda Calculus

I’ve long since heard of “Lambda Calculus” but I didn’t really know what it is about until I saw this video.  It got me super excited!  What I love about it is that it’s built on almost nothing!  Only the concept of functions.  It’s so simple and elegant!  Professor Graham Hutton also listed good reasons to…