Lambda Calculus

What is the simplest functional language that is still Turing complete?

Where do functional languages really come from?

Historical Context

Syntax of the Lambda Calculus

Examples

Alpha reduction, Beta reduction

Simulating multiple arguments: “Currying”

Combinators

True, False, and the IF-THEN-ELSE construct

Church numerals

Church’s Y combinator; recursion; Factorial

Church’s Thesis

Next slide

Back to first slide

View graphic version