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16
Continuations: A Mathematical Semantics for Handling Full Jumps
, 1974
"... Abstract. This paper describes a method of giving the mathematical semantics of programming languages which include the most general form of jumps. 1. ..."
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Abstract. This paper describes a method of giving the mathematical semantics of programming languages which include the most general form of jumps. 1.
The Discoveries of Continuations
, 1993
"... We give a brief account of the discoveries of continuations and related concepts by, A. Van Wijngaarden , A. W. Mazurkiewicz , F. L. Morris , C. P. Wadsworth , J. H. Morris , M. J. Fischer , and S. K. Abdali. ..."
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Cited by 110 (2 self)
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We give a brief account of the discoveries of continuations and related concepts by, A. Van Wijngaarden , A. W. Mazurkiewicz , F. L. Morris , C. P. Wadsworth , J. H. Morris , M. J. Fischer , and S. K. Abdali.
LambdaCalculus Schemata
, 1993
"... A lambdacalculus schema is an expression of the lambda calculus augmented by uninterpreted constant and operator symbols. It is an abstraction of programming languages such as LISP which permit functions to be passed to and returned from other functions. When given an interpretation for its constan ..."
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Cited by 100 (1 self)
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A lambdacalculus schema is an expression of the lambda calculus augmented by uninterpreted constant and operator symbols. It is an abstraction of programming languages such as LISP which permit functions to be passed to and returned from other functions. When given an interpretation for its constant and operator symbols, certain schemata, called lambda abstractions, naturally define partial functions over the domain of interpretation. Two implementation strategies are considered: the retention strategy in which all variable bindings are retained until no longer needed (implying the use of some sort of garbagecollected store) and the deletion strategy, modeled after the usual stack implementation of ALGOL 60, in which variable bindings are destroyed when control leaves the procedure (or block) in which they were created. Not all lambda abstractions evaluate correctly under the deletion strategy. Nevertheless, both strategies are equally powerful in the sense that any lambda abstraction can be mechanically translated into another that evaluates correctly under the deletion strategy and defines the same partial function over the domain of interpretation as the original. Proof is by translation into continuationpassing style.
Abstracting Control
 In Proceedings of the 1990 ACM Conference on LISP and Functional Programming
, 1990
"... The last few years have seen a renewed interest in continuations for expressing advanced control structures in programming languages, and new models such as Abstract Continuations have been proposed to capture these dimensions. This article investigates an alternative formulation, exploiting the lat ..."
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Cited by 95 (6 self)
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The last few years have seen a renewed interest in continuations for expressing advanced control structures in programming languages, and new models such as Abstract Continuations have been proposed to capture these dimensions. This article investigates an alternative formulation, exploiting the latent expressive power of the standard continuationpassing style (CPS) instead of introducing yet other new concepts. We build on a single foundation: abstracting control as a hierarchy of continuations, each one modeling a specific language feature as acting on nested evaluation contexts. We show how iterating the continuationpassing conversion allows us to specify a wide range of control behavior. For example, two conversions yield an abstraction of Prologstyle backtracking. A number of other constructs can likewise be expressed i...
A Functional Abstraction of Typed Contexts
, 1989
"... ion of Typed Contexts Olivier Danvy & Andrzej Filinski DIKU  Computer Science Department, University of Copenhagen Universitetsparken 1, 2100 Copenhagen , Denmark uucp: danvy@diku.dk & andrzej@diku.dk Abstract This report investigates abstracting control with functions. This is achieved b ..."
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Cited by 65 (8 self)
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ion of Typed Contexts Olivier Danvy & Andrzej Filinski DIKU  Computer Science Department, University of Copenhagen Universitetsparken 1, 2100 Copenhagen , Denmark uucp: danvy@diku.dk & andrzej@diku.dk Abstract This report investigates abstracting control with functions. This is achieved by defining continuations as functions abstracting lexically a delimited context [C[ ]] rather than dynamically an unlimited one C[ ], as it is usually the case. Because their codomain is distinguished from the final domain of Answers, such continuations can be composed, and this contrasts with the simple exceptions of ML and Lisp and the unlimited firstclass continuations of Scheme. Making these functional control abstractions firstclass o#ers a new area in programming which this paper explores. The key points obtained here are: a denotational semantics for a simple, callbyvalue, strongly typed expression language with higherorder functions and firstclass continuations; its congruence with a ...
A ControlFlow Normalization Algorithm and Its Complexity
 IEEE Transactions on Software Engineering
, 1992
"... We present a simple method for normalizing the controlflow of programs to facilitate program transformations, program analysis, and automatic parallelization. While previous methods result in programs whose control flowgraphs are reducible, programs normalized by this technique satisfy a stronger c ..."
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We present a simple method for normalizing the controlflow of programs to facilitate program transformations, program analysis, and automatic parallelization. While previous methods result in programs whose control flowgraphs are reducible, programs normalized by this technique satisfy a stronger condition than reducibility and are therefore simpler in their syntax and structure than with previous methods. In particular, all controlflow cycles are normalized into singleentry, singleexit while loops, and all goto's are eliminated. Furthermore, the method avoids problems of code replication that are characteristic of nodesplitting techniques. This restructuring obviates the control dependence graph, since afterwards control dependence relations are manifest in the syntax tree of the program. In this paper we present transformations that effect this normalization, and study the complexity of the method. Index Terms: Continuations, controlflow, elimination algorithms, normalization,...
The Formal Relationship Between Direct and ContinuationPassing Style Optimizing Compilers: A Synthesis of Two Paradigms
, 1994
"... Compilers for higherorder programming languages like Scheme, ML, and Lisp can be broadly characterized as either "direct compilers" or "continuationpassing style (CPS) compilers", depending on their main intermediate representation. Our central result is a precise correspondenc ..."
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Compilers for higherorder programming languages like Scheme, ML, and Lisp can be broadly characterized as either "direct compilers" or "continuationpassing style (CPS) compilers", depending on their main intermediate representation. Our central result is a precise correspondence between the two compilation strategies. Starting from
Continuations for Parallel Logic Programming
 In Proc. of 2nd International ACMSIGPLAN Conference on Principles and practice of Declarative Programming (PPDP’00
, 2000
"... This paper gives denotational models for three logic programming languages of progressive complexity, adopting the \logic programming without logic" approach. The rst language is the control ow kernel of sequential Prolog, featuring sequential composition and backtracking. A committedchoice con ..."
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Cited by 4 (3 self)
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This paper gives denotational models for three logic programming languages of progressive complexity, adopting the \logic programming without logic" approach. The rst language is the control ow kernel of sequential Prolog, featuring sequential composition and backtracking. A committedchoice concurrent logic language with parallel composition (parallel AND) and don't care nondeterminism is studied next. The third language is the core of Warren's basic Andorra model, combining parallel composition and don't care nondeterminism with two forms of don't know nondeterminism (interpreted as sequential and parallel OR) and favoring deterministic over nondeterministic computation. We show that continuations are a valuable tool in the analysis and design of semantic models for both sequential and parallel logic programming. Instead of using mathematical notation, we use the functional programming language Haskell as a metalanguage for our denotational semantics, and employ monads in order to facilitate the transition from one language under study to another. Keywords Parallel logic programming, basic Andorra model, denotational semantics, continuations, monads, Haskell. 1.
Conservation and Uniform Normalization in Lambda Calculi With Erasing Reductions
, 2002
"... For a notion of reduction in a #calculus one can ask whether a term satises conservation and uniform normalization. Conservation means that singlestep reductions of the term preserve innite reduction paths from the term. Uniform normalization means that either the term will have no reduction path ..."
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For a notion of reduction in a #calculus one can ask whether a term satises conservation and uniform normalization. Conservation means that singlestep reductions of the term preserve innite reduction paths from the term. Uniform normalization means that either the term will have no reduction paths leading to a normal form, or all reduction paths will lead to a normal form.