Monads.md

#Monads

1. Formal definition
   • M a
   • (M a) -> (a -> M b) -> (M b)
2. "Common" definition
   • A wrapped value - a value in a box This description seems conceptually easy, but
   • A hidden computation
3. The most basic Monad - Maybe
   • A box that can hold a value and can be empty
   • Box analogy is very limited
   • A computation that might produce a value - much better!
4. A bit of reasoning about functional purity before we proceed
   • The explicit function contract Function given the same input must always give the same output
   • We are "cheating" - HOFs are a way to "break" the purity Because a HOF seeing a (bound) function sees it for the first time, and thus is in practice unlimited as to what it might output).
   • Monads are a convenient way to encapsulate computations while still keeping functional purity. They essentially limit what we can do with the computations, and that's more explicit -> better (why is beyond the scope of this presentation, quick remark about The Pit of Success)
5. Examples of extended function contracts
   • Reader
   • Writer
   • State
6. Relations to Functors and Applicative Functors
7. Questions?