Disappointment
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Date:  20080722 (15:17) 
From:  Andrej Bauer <Andrej.Bauer@a...> 
Subject:  Re: [Camllist] Disappointment 
Axel PoignÃ© wrote: > Maybe computer scientists obfuscate. The mathematical concept of monads > however is dead simple (at least if interpreted in a world of sets): > > Let X be a set of values and let TX denote a set of "simple terms" over > these values. A "simple term" may be thought of as either "an operator > applied to a tuple of values" or "a value", e.g. "values" are 1,2,3,... > and "simple terms" are 3, +(3,5), ... > > Additionally to the "operator" T on sets there are two functions: > >  \eta: X > TX that turns a value into a "simple term", e.g. \eta(3) = 3 >  \mu: TX > X that computes the value of a "simple term", hence > defines the semantics, e.g. \mu(+(3,5)) = 8. > > (T, \eta, and \mu) form a monad if This is incorrect. You are describing some sort of a mutant between a monad and an algebra for a functor T. A monad T has a different \mu, namely a family of maps (one for each set X) \mu_X : T (T X) > T X One such \mu takes a "simple term of simple terms over X" and flattens it to a "simple term over X". Andrej