We revisit the connection between three notions of computation: Moggi’s monads, Hughes’s arrows and\ud McBride and Paterson’s idioms (also called applicative functors). We show that idioms are equivalent to\ud arrows that satisfy the type isomorphism A;B ' 1;(A ! B) and that monads are equivalent to arrows\ud that satisfy the type isomorphism A;B ' A ! (1;B). Further, idioms embed into arrows and arrows\ud embed into monads
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