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 ...

We formalize a partial evaluator for Eugenio Moggi's computational metalanguage. This formalization gives an evaluation-order independent view of binding-time analysis and program specialization, including a proper treatment of call unfolding, and enables us to express the essence of "control-based binding-time improvements" for let expressions. Specifically,

Block structure is a fundamental mechanism for expressing the scope of variables in a computation. Scope can be expressed either explicitly with formal parameters or implicitly with free variables. We discuss the transformations between explicit and implicit scope. Making scope explicit is current practice in functional programming: it is called "lambdalifting. " Our thesis addresses the transformations between explicit and implicit scope. We show lambda-dropping to be a useful transformation that can be applied to clarify the structure of programs and to increase the efficiency of recursive functions. In addition, we demonstrate that lambda-dropping is of practical use as a back-end in a partial evaluator. 1 Preface This document describes most of the work that was done in conjunction with the author's "speciale" (master's thesis). One of the primary subjects of this work is a program transformation called "lambda-dropping." It was first conceived by my thesis advisor, Olivier Dan...

ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, NY 10036 USA, fax +1 (212) 869-0481, or permissions@acm.org. 2 \Delta J. Hatcliff e 2 Terms[ ml ] e ::= x j pnq j tick j x : e j @ e0 e1 j unit e j let x ( e1 in e2 2 Types[ ml ] ::= nat j 1 ! e 2 j e \Gamma 2 Assumptions[ ml ] \Gamma ::= \Delta j \Gamma; x : \Gamma ` ml x : \Gamma(x) \Gamma ` ml pnq : nat \Gamma ` ml tick : f nat \Gamma; x : 1 ` ml e : e 2 \Gamma ` ml x : e : 1 ! e 2 \Gamma ` ml e0 : 1 ! e 2 \Gamma ` ml e1 : 1 \Gamma ` ml @ e0 e1 : e 2 monadic constructs: \Gamma ` ml e : \Gamma ` ml unit e : e \Gamma ` ml e 1 : e 1 \Gamma; x : 1 ` ml e 2 : e 2 \Gamma ` ml let x ( e1 in e2 : e 2 Fig. 1. The computational meta-language ml input/output, and robust...

Research on partial evaluation has flourished in the context of pure functional languages, yet modern functional languages include many notions of computation that partial evaluation technology has only recently been able to handle. We summarize how using Moggi's computational metalanguage as intermediate language provides a foundation for this recent advance in technology. 1 Partial Evaluation of Programs with Computational Effects Partial evaluation is a highly useful program specialization technique that can be applied to programs from any language paradigm. Yet, it is in the paradigm of pure functional languages that partial evaluation technology grew to maturity. The simple semantics of pure functional programs (which do not include computational effects such as state modification, input/output, and first-class exceptions) makes it easier to perform the basic actions of partial evaluation such as static analysis, function unfolding (inlining), and symbolic execution. Clearly, t...