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 ...

This paper describes the transformation of lambda-terms from continuation-passing style (CPS) to direct style. This transformation is the left inverse of Plotkin's left-to-right call-by-value CPS encoding for the pure lambda-calculus. Not all -terms are CPS terms, and not all CPS terms encode a left-to-right call-by-value evaluation. These CPS terms are characterized here; they can be mapped back to direct style. In addition, the two transformations -- to continuation-passing style and to direct style -- are factored using a language where all intermediate values are named and their computation is sequentialized. The issue of proper tail-recursion is also addressed.

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

The continuation-passing style (CPS) transformation is powerful but complex. Our thesis is that this transformation is in fact compound, and we set out to stage it. We factor the CPS transformation into several steps, separating aspects in each step: 1. Intermediate values are named. 2. Continuations are introduced. 3. Sequencing order is decided and administrative reductions are performed. Step 1 determines the evaluation order (e.g., call-by-name or call-by-value). Step 2 isolates the introduction of continuations and is expressed with local, structure-preserving rewrite rules --- a novel aspect standing in sharp contrast with the usual CPS transformations. Step 3 determines the ordering of continuations (e.g., left-to-right or right-to-left evaluation) and leads to the familiar-looking continuationpassing terms. Step 2 is completely reversible and Steps 1 and 3 form Galois connections. Together they leading to the direct style (DS) transformation of our earlier work (including first...

Compilers for higher-order programming languages like Scheme, ML, and Lisp can be broadly characterized as either "direct compilers" or "continuation-passing style (CPS) compilers", depending on their main intermediate representation. Our central result is a precise correspondence between the two compilation strategies. Starting from

In this paper, we study the formalization of one-pass call-by-value CPS compilation using higher-order abstract syntax. In particular, we verify mechanically that the source program and the CPS-transformed program have the same observable behavior. A key advantage of this approach is that it avoids any administrative redexes thereby simplifying the proofs about CPS-translations. The CPS translation together with its correctness proof is implemented and mechanically verified in the logical framework Twelf. Keywords: Program transformation, correctness proofs, higher-order abstract syntax, logical framework 1