Applied category theory and abstract algebra
summary
Claim: category theory and abstract algebra give concrete, reusable Haskell interfaces that simplify code and proofs. Examples include explicit monoid laws verified for lists, unit, tuples, functions and IO; a running demo composes managed transactions (STM queues, forked threads, HTTP on port 8080), showing ticks, stdin and curl messages interleaved and plugins added or removed live; proofs scale by reusing smaller monoid proofs for nested tuples; and the talk shows type-level composition (applicative/monad lifting, DeriveFunctor/GHC8 features) that compiles and runs.
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chapters (18)
- 0:00Introduction
- 1:02Start with function composition
- 4:12Unix pipelines analogy
- 5:58Talk overview
- 6:19Monoid in Haskell
- 11:33Monoid interfaces
- 13:22Monoid implementations in Haskell
- 20:50Monad for IO
- 23:59Plugin composition
- 28:35Software transactional memory monoid
- 31:02Event streams example
- 36:40Configurable plugins
- 38:04Tracking plugins
- 41:15Monoid instances pattern
- 45:11Applicative interface
- 49:00Type-level composition
- 54:58Type vs value composition
- 56:01Summary
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