Date of Original Version

1974

Type

Conference Proceeding

Abstract or Description

The use of continuations in the definition of programming languages has gained considerable currency recently, particularly in conjunction with the lattice-theoretic methods of D. Scott. Although continuations are apparently needed to provide a mathematical semantics for non-applicative control features, they are unnecessary for the definition of a purely applicative language, even when call-by-value occurs. This raises the question of the relationship between the direct and the continuation semantic functions for a purely applicative language. We give two theorems which specify this relationship and show that, in a precise sense, direct semantics are included in continuation semantics. The heart of the problem is the construction of a relation which must be a fixed-point of a non-monotonic "relational functor." A general method is given for the construction of such relations between recursively defined domains.

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