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A Syntactic Approach to Type Soundness
 Information and Computation
, 1992
"... We present a new approach to proving type soundness for Hindley/Milnerstyle polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the la ..."
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Cited by 538 (21 self)
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We present a new approach to proving type soundness for Hindley/Milnerstyle polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the language semantics. The approach easily extends from polymorphic functional languages to imperative languages that provide references, exceptions, continuations, and similar features. We illustrate the technique with a type soundness theorem for the core of Standard ML, which includes the first type soundness proof for polymorphic exceptions and continuations. 1 Type Soundness Static type systems for programming languages attempt to prevent the occurrence of type errors during execution. A definition of type error depends on a specific language and type system, but always includes the use of a function on arguments for which it is not defined, and the attempted application of a nonfunction. ...
Reflections on Standard ML
 FUNCTIONAL PROGRAMMING, CONCURRENCY, SIMULATION AND AUTOMATED REASONING, VOLUME 693 OF LNCS
, 1992
"... Standard ML is one of a number of new programming languages developed in the 1980s that are seen as suitable vehicles for serious systems and applications programming. It offers an excellent ratio of expressiveness to language complexity, and provides competitive efficiency. Because of its type an ..."
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Cited by 198 (4 self)
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Standard ML is one of a number of new programming languages developed in the 1980s that are seen as suitable vehicles for serious systems and applications programming. It offers an excellent ratio of expressiveness to language complexity, and provides competitive efficiency. Because of its type and module system, Standard ML manages to combine safety, security, and robustness with much of the flexibility of dynamically typed languages like Lisp. It is also has the most welldeveloped scientific foundation of any major language. Here I review the strengths and weaknesses of Standard ML and describe some of what we have learned through the design, implementation, and use of the language.
Representing control: a study of the CPS transformation
, 1992
"... This paper investigates the transformation of v terms into continuationpassing style (CPS). We show that by appropriate jexpansion of Fischer and Plotkin's twopass equational specification of the CPS transform, we can obtain a static and contextfree separation of the result terms into "esse ..."
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Cited by 81 (7 self)
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This paper investigates the transformation of v terms into continuationpassing style (CPS). We show that by appropriate jexpansion of Fischer and Plotkin's twopass equational specification of the CPS transform, we can obtain a static and contextfree separation of the result terms into "essential" and "administrative" constructs. Interpreting the former as syntax builders and the latter as directly executable code, we obtain a simple and efficient onepass transformation algorithm, easily extended to conditional expressions, recursive definitions, and similar constructs. This new transformation algorithm leads to a simpler proof of Plotkin's simulation and indifference results. Further we show how CPSbased control operators similar to but more general than Scheme's call/cc can be naturally accommodated by the new transformation algorithm. To demonstrate the expressive power of these operators, we use them to present an equivalent but even more concise formulation of t...
Concurrent ML: Design, Application and Semantics
, 1993
"... Machine" [BB90], except that there are no "cooling" and "heating" transitions (the process sets of this semantics can be thought of as perpetually "hot" solutions). The concurrent evaluation relation extends "7\Gamma!" to finite sets of terms (i.e., processes) and adds additional rules for process c ..."
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Cited by 33 (0 self)
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Machine" [BB90], except that there are no "cooling" and "heating" transitions (the process sets of this semantics can be thought of as perpetually "hot" solutions). The concurrent evaluation relation extends "7\Gamma!" to finite sets of terms (i.e., processes) and adds additional rules for process creation, channel creation, and communication. We assume a set of process identifiers, and define the set of processes and process sets as: ß 2 ProcId process IDs p = hß; ei 2 Proc = (ProcId \Theta Exp) processes P 2 Fin(Proc) process sets We often write a process as hß; E[e]i, where the evaluation context serves the role of the program counter, marking the current state of evaluation. Definition4. A process set P is wellformed if for all hß; ei 2 P the following hold:  FV(e) = ; (e is closed), and  there is no e 0 6= e, such that hß; e 0 i 2 P. It is occasionally useful to view wellformed process sets as finite maps from ProcId to Exp. If P is a finite set of process state...
Asynchronous Signals in Standard ML
, 1990
"... We describe the design, implementation and use of a mechanism for handling asynchronous signals, such as user interrupts, in the New Jersey implementation of Standard ML. Providing this kind of mechanism is a necessary requirement for the development of realworld application programs. Our mechanism ..."
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Cited by 31 (1 self)
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We describe the design, implementation and use of a mechanism for handling asynchronous signals, such as user interrupts, in the New Jersey implementation of Standard ML. Providing this kind of mechanism is a necessary requirement for the development of realworld application programs. Our mechanism uses firstclass continuations to represent the execution state at the time at which a signal occurs. It has been used to support preemptive scheduling in concurrency packages and for forcing breakpoints in debuggers, as well as for handling user interrupts in the SML/NJ interactive environment. 1 Introduction Programs normally receive communication from the outside world via input operations. This method of communication is inherently synchronous: there is no way for the outside world to force the program to accept communication. But sometimes it is necessary to communicate asynchronously; for example, if the user wants to interrupt execution, or if the operating system needs to inform a...
A Typetheoretic Study on Partial Continuations
 Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics, volume 1872 of Lecture Notes in Computer Science
, 2000
"... . Partial continuations are control operators in functional programming such that a functionlike object is abstracted from a part of the rest of computation, rather than the whole rest of computation. Several dierent formulations of partial continuations have been proposed by Felleisen, Danvy&F ..."
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Cited by 12 (4 self)
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. Partial continuations are control operators in functional programming such that a functionlike object is abstracted from a part of the rest of computation, rather than the whole rest of computation. Several dierent formulations of partial continuations have been proposed by Felleisen, Danvy&Filinski, Hieb et al, and others, but as far as we know, no one ever studied logic for partial continuations, nor proposed a typed calculus of partial continuations which corresponds to a logical system through the CurryHoward isomorphism. This paper gives a simple typetheoretic formulation of a form of partial continuations (which we call delimited continuations), and study its properties. Our calculus does reect the intended operational semantics, and enjoys nice properties such as subject reduction and conuence. By restricting the type of delimiters to be atomic, we obtain the normal form property. We also show a few examples. 1 Introduction The mechanism of rstclass cont...
Search algorithms in type theory
, 2000
"... In this paper, we take an abstract view of search by describing search procedures via particular kinds of proofs in type theory. We rely on the proofsasprograms interpretation to extract programs from our proofs. Using these techniques we explore, in depth, a large family of search problems by par ..."
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Cited by 8 (2 self)
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In this paper, we take an abstract view of search by describing search procedures via particular kinds of proofs in type theory. We rely on the proofsasprograms interpretation to extract programs from our proofs. Using these techniques we explore, in depth, a large family of search problems by parameterizing the speci cation of the problem. A constructive proof is presented which has as its computational content a correct search procedure for these problems. We show how a classical extension to an otherwise constructive system can be used to describe a typical use of the nonlocal control operator call/cc. Using the classical typing of nonlocal control we extend our purely constructive proof to incorporate a sophisticated backtracking technique known as ‘con ictdirected backjumping’ (CBJ). A variant of this proof is formalized in Nuprl yielding a correctbyconstruction implementation of CBJ. The extracted program has been translated into Scheme and serves as the basis for an implementation of a new solution to the Hamiltonian circuit problem. This paper demonstrates a nontrivial application of the proofsasprograms paradigm by applying the technique to the derivation of a sophisticated search algorithm; also, it shows the generality of the resulting implementation by demonstrating its application in a new problem
Combining algebraic effects with continuations
, 2007
"... We consider the natural combinations of algebraic computational effects such as sideeffects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor ext ..."
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Cited by 8 (3 self)
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We consider the natural combinations of algebraic computational effects such as sideeffects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor extend, with effort, to include commonly used combinations of the various algebraic effects with continuations. Continuations also give rise to a third sort of combination, that given by applying the continuations monad transformer to an algebraic effect. We investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads, and the extent to which Felleisen et al.’s C operator extends from continuations to its combination with algebraic effects. To do all this, we use Dubuc’s characterisation of strong monads in terms of enriched large Lawvere theories.
On the callbyvalue CPS transform and its semantics
, 2004
"... We investigate continuations in the context of idealized callbyvalue programming languages. On the semantic side, we analyze the categorical structures that arise from continuation models of callbyvalue languages. On the syntactic side, we study the callbyvalue continuationpassing transformat ..."
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Cited by 5 (0 self)
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We investigate continuations in the context of idealized callbyvalue programming languages. On the semantic side, we analyze the categorical structures that arise from continuation models of callbyvalue languages. On the syntactic side, we study the callbyvalue continuationpassing transformation as a translation between equational theories. Among the novelties are an unusually simple axiomatization of control operators and a strengthened completeness result with a proof based on a delaying transform.