Notions of computation determine monads

Gordon Plotkin and John Power

To appear at Foundations of Software Science and Computation Structures (FOSSACS02), Grenoble, France, 6-14 April, 2002


We give semantics for notions of computation, also called computational effects, by means of operations and equations. We show that these generate several of the monads of primary interest that have been used to model computational effects, with the striking omission of the continuations monad, demonstrating the latter to be of a different character, as is computationally true. We focus on semantics for global and local state, showing that taking operations and equations as primitive yields a mathematical relationship that reflects their computational relationship.

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