Recap In the last post not dealing with the internals of the Lambda Calculator, we introduced Church Numerals and some basic operations. There are actually only two operations that are needed and these are: isZero which is true if the number is zero and false otherwisesucc which gives us the successor of any Church numeral … Continue reading Lambda Calculus: More Numbers

# Category: Lambda Calculus

## Protocol OrientedProgramming part 2

This post is all about how I achieved stage 1 of the conversion of the Lambda Calculator. It follows on from Protocol Oriented Programming. I have commented out all of the code in Expression.swift and added a protocol Expressible. All the functions that were "abstract" in Expression become protocol requirements and all of the functions … Continue reading Protocol OrientedProgramming part 2

## Protocol Oriented Programming

This is technically a post in the Lambda Calculus series but I am concerned with the implementation of my Lambda calculator today. Anybody who has looked at the code will see I have used a class hierarchy to represent Lambda expressions. I use classes because I want my objects to be of reference types so … Continue reading Protocol Oriented Programming

## Numbers in The Lambda Calculus

God created the natural numbers. All else is the work of man.Leopold Kronecker We've got lists and with lists we can do pretty much any data structure we like. However, in computing, we also need numbers. Usually, numbers are thought of as fairly basic entities with respect to computing, but, in the Lambda Calculus they … Continue reading Numbers in The Lambda Calculus

## Lambda Calculus: Recursion

"When preceded by its quotation yields falsehood" when preceded by its quotation yields falsehood.Willard Van Orman Quine Before we start, recursion is a tricky subject. I suggest you read this article before continuing. Also, you're going to need at least version 1.3.1 of the lambda calculator to try out the examples. This version allows variable … Continue reading Lambda Calculus: Recursion

## Lists in the Lambda Calculus

Some Lambda Calculator Enhancements In version 1.2.1 of the Lambda Calculator, I have added the concept of a meta command. A meta command starts with a / (forward slash) and is used for doing things outside of the Lambda Calculus (forward slash is sort of the opposite of backslash, which is my alternate way of … Continue reading Lists in the Lambda Calculus

## Higher Level Concepts In The Lambda Calculus

Some Syntactic Sugar We are going to be talking about some pretty high level concepts in this post, like true and false and maybe even the natural numbers (although that might be too high level and need to be left to the next post). You've probably realised that the Lambda Calculus has no means of … Continue reading Higher Level Concepts In The Lambda Calculus

## Computation With The World’s Smallest Programming Language

Update: The latest version of the lambda calculator has line editing and a command history. It's more convenient than the version linked in the blog and is tagged 0.1.0. Note to the reader: much of this post is based on an article I found on the web called Lambda Calculus (part I). That article covers … Continue reading Computation With The World’s Smallest Programming Language

## The World’s Smallest Programming Language

Update: The latest version of the lambda calculator has line editing and a command history. It's more convenient than the version linked in the blog and is tagged 0.1.0. Introduction The world's smallest programming language is probably the Lambda Calculus. The Lambda Calculus was invented by Alonzo Church in the 1930's as a means of … Continue reading The World’s Smallest Programming Language