An introduction to Lambda Calculus
summary
Step-by-step conversion of programming primitives into pure lambda calculus implemented in JavaScript: defines Church booleans as two-argument selectors and builds NOT/AND/OR, encodes numbers as Church numerals with successor, predecessor via pairs, then implements addition, subtraction, multiplication, exponentiation and numeric comparisons, all shown with console outputs proving they work. Then reduces functions to combinators, ending with S and K combinators (and the Y combinator for recursion), demonstrating that every example compiles to these primitives and the live examples produce the claimed numeric and boolean results.
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chapters (14)
- 0:00Intro
- 0:50What is lambda calculus
- 6:15Replacing booleans
- 8:46Replacing numbers
- 10:30Sum function
- 12:22Sum successor
- 14:50Wrapper
- 16:00Pair
- 17:24Subtraction
- 21:50Replace exponentiation
- 22:48Replace boolean operators
- 26:42Replace lesser equals
- 28:23Replace with functions
- 30:38Replace with combinators
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