We unify previous work on the continuation-passing style (CPS) transformations in a generic framework based on Moggi's computational meta-language. This framework is used to obtain CPS transformations for a variety of evaluation strategies and to characterize the corresponding administrative reductions and inverse transformations. We establish generic formal connections between operational semantics and equational theories. Formal properties of transformations for specific evaluation orders follow as corollaries. Essentially, we factor transformations through Moggi's computational meta-language. Mapping -terms into the meta-language captures computational properties (e.g., partiality, strictness) and evaluation order explicitly in both the term and the type structure of the meta-language. The CPS transformation is then obtained by applying a generic transformation from terms and types in the meta-language to CPS terms and types, based on a typed term representation of the continuation ...

Abstract. Landin’s SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin’s J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continuation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke’s doublebarrelled continuations and to Felleisen’s encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions

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In the functional programming literature, compiling is often expressed as a translation between source and target program calculi. In recent work, Sabry and Wadler proposed the notion of a reflection as a basis for relating the source and target calculi. A reflection elegantly describes the situation where there is a kernel of the source language that is isomorphic to the target language. However, we believe that the reflection criteria is so strong that it often excludes the usual situation in compiling where one is compiling from a higher-level to a lower-level language. We give a detailed analysis of several translations commonly used in compiling that fail to be reflections. We conclude that, in addition to the notion of reflection, there are several relations weaker a reflection that are useful for characterizing translations. We show that several familiar translations (that are not naturally reflections) form what we call a reduction correspondence. We introduce the more genera...

Type-directed partial evaluation stems from the residualization of static values in dynamic contexts, given their type and the type of their free variables. Its algorithm coincides with the algorithm for coercing a subtype value into a supertype value, which itself coincides with Berger and Schwichtenberg's normalization algorithm for the simply typed -calculus. Type-directed partial evaluation thus can be used to specialize a compiled, closed program, given its type.

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The CPS (continuation-passing style) transformation on -terms has an interpretation both in programming languages, type theory, proof theory, and logic. Programming intuition suggests that it is idempotent, but this does not directly hold for all existing CPS transformations (Plotkin, Reynolds, Fischer, etc.). We rephrase it to make it syntactically idempotent, modulo j-reduction of the newly introduced continuation.