Abstract

. Moggi proposed a monadic account of computational e#ects. He also presented the computational #-calculus, #c , a core call-by-value functional programming language for e#ects; the e#ects are obtained by adding appropriate operations. The question arises as to whether one can give a corresponding treatment of operational semantics. We do this in the case of algebraic e#ects where the operations are given by a single-sorted algebraic signature, and their semantics is supported by the monad, in a certain sense. We consider call-by-value PCF with--- and without---recursion, an extension of #c with arithmetic. We prove general adequacy theorems, and illustrate these with two examples: nondeterminism and probabilistic nondeterminism. 1 Introduction Moggi introduced the idea of a general account of computational e#ects, proposing encapsulating them via monads T : C # C; the main idea is that T (x) is the type of computations of elements of x. He also presented the computational #-calcul...

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