Claus Reinke wrote:
there is usually a way to interpret monadic structures built in this way (a 'run' operation of some kind).
The "run" operation of type (m a -> a) is the (comonadic) coreturn. Many monads are almost comonads too, for a meaning of "almost" to be made precise. Claus Reinke wrote:
- i/o: primitive monadic things are basic i/o operations, the 'run' operation is outside the language, applied to 'Main.main', and interprets (abstract) IO monad structures sequentially, starting with the leftmost innermost i/o operation in the structure and applying the second argument of (>>=) to the result of executing the first.
"Run" for IO monad is obviously unsafePerformIO :: IO a -> a. Claus Reinke wrote:
- []: primitive monadic things are lists, the 'run' operation is the identity, ie, the lists are directly exposed as data structures, return creates a singleton list, (>>=) applies its second argument to each element of its first argument and concatenates the results (concatMap).
"Run" for [] is almost head :: [a] -> a. For the type of infinite streams, the research community's comonad de rigeur, coreturn _is_ h(ea)d. Claus Reinke wrote:
- State: primitive monadic things are operations on a state type, returning a result and a state; return returns its parameter, passing its input state unchanged, (>>=) applies its first parameter to the input state, applies its second parameter to the result value and result state of the first. 'run' is runState and applies a (possibly) complex monadic thing to an input state, returning a result and a (modified) state.
The State monad is almost (there's that word again!) like the Context comonad. And the Context comonad is a comonadification of the suboptimally named Reader monad, a comonadification that wants to be made precise. In fact, there's another comonad that solves the analogical equation: comonad x is to monad State as comonad Context is to monad Reader. Any takers on calling x the Costate comonad and Reader the Ntext monad? -- View this message in context: http://www.nabble.com/FW%3A-RE-Monad-Description-For-Imperative-Programmer-t... Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.