Fun with the Lambda Calculus
summary
Live codes a tiny lambda calculus in Ruby using single-argument Ruby lambdas and the CLI, defines true/false as chooser functions, builds an if that executes choices and an assert/refute test harness, implements pairs as pair-as-function to carry the predecessor, defines successor and predecessor so numbers behave like 0, 1, 2, proves successor is never zero, converts between Ruby ints and these naturals and demos running a 10-times loop printing ten.
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chapters (11)
- 0:00Start
- 0:12The Lambda Calculus
- 2:26Piano's Axioms
- 2:43Equality Axioms
- 3:14Axiom about Being Closed under Equality
- 3:31Successor Function
- 6:15Zeros of Natural Number
- 10:07The Single Responsibility Principle
- 14:53If Statement
- 28:07Nonzero Numbers
- 40:46Programming by Wishful Thinking
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