Programming and Math
summary
Shows an algebra of functions with concrete Haskell code: purity forces IO types, composition and associativity hold, identity and constant functions become useful via foldr and flatMap id, length is implemented with foldl plus const and successor, enums are transformed as isomorphisms, products and coproducts use tuples and control.arrow, and many equational proofs are worked out (paper cited is by Jose Aliveria; examples compile and the laws check out).
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chapters (9)
- 0:00Start
- 2:48function application
- 3:26function composition (2/3)
- 10:01composition is associative
- 11:12identity function(s) (1/2)
- 18:41constant function()
- 24:47isomorphisms
- 45:45+ of two functions
- 48:57summary
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