E-mail: howe research.att.com We give a method for proving congruence of bisimulation-like equivalences in functional programming languages. The method applies to languages that can be presented as a set of expressions together with an evaluation relation. We use this method to show that some generalizations of Abramsky's applicative bisimulation are congruences whenever evaluation can be specified by a certain natural form of structured operational semantics. One of the generalizations handles nondeterminism and diverging computations.] 1996 Academic Press, Inc. 1.

We introduce an untyped-calculus with input-output, based on Gordon's continuation-passing model of input-output. This calculus is intended to allow the classification of possibly infinite input-output behaviors. We introduce a property, called "losslessness," which is a natural property of any reasonable model of this calculus. We then characterize the largest lossless precongruence that refines simulation for this calculus.

We extend Plotkin's PCF by adding monadic-style input-output operations. This extension is intended to allow the classification of possibly infinite input-output behaviors, such as those required for servers or distributed This work is partly supported by NSF Grants CCR-9417382, CCR-9304144, and by Polish KBN Grant 2 P301 031 06. y Work supported by the National Science Foundation under grants number CCR9304144 and CCR-9404646. 1 systems. We define a notion of applicative approximation and show that it coincides with operational equivalence for these new behaviors. Last, we show that the new notion of operational equivalence is a conservative extension of the usual one. 1 Introduction In the study of languages such as PCF [12], the standard paradigm for studying equivalence of terms begins by setting up some relatively weak notion of behavior (or immediate observation). For PCF, this is generally taken to be convergence to an integer constant. Two terms are said to be operational...