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lambda calculus

A collection of 8 posts

functional programming

Functional Basics: Expressions

The journey to master functional programming involves shifting one's approach of even the simplest problems. It is a different paradigm after all. But don't be intimidated, because this journey is best travelled by embracing small shifts in thinking. Unlearning small things and learning other (perhaps smaller) things. Previously we looked

functional programming

Functional Basics: Identity Function

The identity function is an unassuming little function with a signature of 'a -> 'a. It returns the value of the argument it's given. At first glance it can seem rather pointless but it serves a purpose in both practical and theoretical contexts. The identity function is probably the first

Abstraction

💡My thinking around this topic is influenced by Eric Normand's Lispcast episode on abstraction. Check it out, and his podcast. Abstraction is a common topic in programming discussions. You hear a lot about the right abstraction, the wrong abstraction; this level of abstraction or that level; leaky ones, bad ones,

functional programming

Lambda Calculus and Arguments

Functions in the lambda calculus are always unary - they only take one argument. Functional programming is based on the lambda calculus, and it is useful to learn to appreciate unary functions. One useful way to train your brain to think functionally is, when you find yourself writing an n-ary

lambda calculus

Argument Selection Function

The argument selection function λfirst.λsecond.first accepts a function as an argument and returns a function which, when given an argument, returns the first argument. // λfirst.λsecond.first const selectFirst = x => y => x const double = a => a * 2 const triple = a => a * 3 const applyDouble = selectFirst(double) const applyTriple

lambda calculus

Application Function

Function application function is represented by the term λf.λx.f x. It accepts a function as an argument and applies it to the argument of the function it returns. // λf.λx.f x let apply f x = f x let addOne c = c + 1 let applyAddOne = addOne |> apply |> (fun

lambda calculus

Self Application Function

The function λx.x x is the self application function. It applies its argument to its argument. // λx.x x const sa = x => x(x) Like the identity function, it doesn't seem helpful at first glance but it has some interesting applications. Consider the twice function λf.λx.f (f

lambda calculus

Identity Function

Identity function is the simplest of the lambda calculus functions, represented by λa.a. It simply returns the argument that it was given. // F# fun a -> a // JS a => a # Python lambda a: a While it is a simple function, it still has significance in composing functions in that