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22
Proving congruence of bisimulation in functional programming languages
 Information and Computation
, 1996
"... Email: howe research.att.com We give a method for proving congruence of bisimulationlike equivalences in functional programming languages. The method applies to languages that can be presented as a set of expressions together with an evaluation relation. We use this method to show that some genera ..."
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Cited by 113 (1 self)
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Email: howe research.att.com We give a method for proving congruence of bisimulationlike equivalences in functional programming languages. The method applies to languages that can be presented as a set of expressions together with an evaluation relation. We use this method to show that some generalizations of Abramsky's applicative bisimulation are congruences whenever evaluation can be specified by a certain natural form of structured operational semantics. One of the generalizations handles nondeterminism and diverging computations.] 1996 Academic Press, Inc. 1.
Improvement in a Lazy Context: An Operational Theory for CallByNeed
 Proc. POPL'99, ACM
, 1999
"... Machine The semantics presented in this section is essentially Sestoft's \mark 1" abstract machine for laziness [Sestoft 1997]. In that paper, he proves his abstract machine 6 A. K. Moran and D. Sands h fx = Mg; x; S i ! h ; M; #x : S i (Lookup) h ; V; #x : S i ! h fx = V g; V; S i (Up ..."
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Cited by 43 (8 self)
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Machine The semantics presented in this section is essentially Sestoft's \mark 1" abstract machine for laziness [Sestoft 1997]. In that paper, he proves his abstract machine 6 A. K. Moran and D. Sands h fx = Mg; x; S i ! h ; M; #x : S i (Lookup) h ; V; #x : S i ! h fx = V g; V; S i (Update) h ; M x; S i ! h ; M; x : S i (Unwind) h ; x:M; y : S i ! h ; M [ y = x ]; S i (Subst) h ; case M of alts ; S i ! h ; M; alts : S i (Case) h ; c j ~y; fc i ~x i N i g : S i ! h ; N j [ ~y = ~x j ]; S i (Branch) h ; let f~x = ~ Mg in N; S i ! h f~x = ~ Mg; N; S i ~x dom(;S) (Letrec) Fig. 1. The abstract machine semantics for callbyneed. semantics sound and complete with respect to Launchbury's natural semantics, and we will not repeat those proofs here. Transitions are over congurations consisting of a heap, containing bindings, the expression currently being evaluated, and a stack. The heap is a partial function from variables to terms, and denoted in an identical manner to a coll...
A Naïve Time Analysis and its Theory of Cost Equivalence
 Journal of Logic and Computation
, 1995
"... Techniques for reasoning about extensional properties of functional programs are well understood, but methods for analysing the underlying intensional or operational properties have been much neglected. This paper begins with the development of a simple but useful calculus for time analysis of nons ..."
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Cited by 39 (7 self)
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Techniques for reasoning about extensional properties of functional programs are well understood, but methods for analysing the underlying intensional or operational properties have been much neglected. This paper begins with the development of a simple but useful calculus for time analysis of nonstrict functional programs with lazy lists. One limitation of this basic calculus is that the ordinary equational reasoning on functional programs is not valid. In order to buy back some of these equational properties we develop a nonstandard operational equivalence relation called cost equivalence, by considering the number of computation steps as an `observable' component of the evaluation process. We define this relation by analogy with Park's definition of bisimulation in CCS. This formulation allows us to show that cost equivalence is a contextual congruence (and thus is substitutive with respect to the basic calculus) and provides useful proof techniques for establishing costequivalen...
Proving the Correctness of RecursionBased Automatic Program Transformations
 Theoretical Computer Science
, 1996
"... This paper shows how the Improvement Theorema semantic condition ..."
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Cited by 32 (4 self)
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This paper shows how the Improvement Theorema semantic condition
A Tutorial on Coinduction and Functional Programming
 IN GLASGOW FUNCTIONAL PROGRAMMING WORKSHOP
, 1994
"... Coinduction is an important tool for reasoning about unbounded structures. This tutorial explains the foundations of coinduction, and shows how it justifies intuitive arguments about lazy streams, of central importance to lazy functional programmers. We explain from first principles a theory based ..."
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Cited by 27 (1 self)
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Coinduction is an important tool for reasoning about unbounded structures. This tutorial explains the foundations of coinduction, and shows how it justifies intuitive arguments about lazy streams, of central importance to lazy functional programmers. We explain from first principles a theory based on a new formulation of bisimilarity for functional programs, which coincides exactly with Morrisstyle contextual equivalence. We show how to prove properties of lazy streams by coinduction and derive Bird and Wadler's Take Lemma, a wellknown proof technique for lazy streams.
Relational Reasoning about Contexts
 HIGHER ORDER OPERATIONAL TECHNIQUES IN SEMANTICS, PUBLICATIONS OF THE NEWTON INSTITUTE
, 1998
"... ..."
Total Correctness by Local Improvement in Program Transformation
 In Proceedings of the 22nd Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages (POPL
, 1995
"... The goal of program transformation is to improve efficiency while preserving meaning. One of the best known transformation techniques is Burstall and Darlington's unfoldfold method. Unfortunately the unfoldfold method itself guarantees neither improvement in efficiency nor totalcorrectness. ..."
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Cited by 20 (3 self)
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The goal of program transformation is to improve efficiency while preserving meaning. One of the best known transformation techniques is Burstall and Darlington's unfoldfold method. Unfortunately the unfoldfold method itself guarantees neither improvement in efficiency nor totalcorrectness. The correctness problem for unfoldfold is an instance of a strictly more general problem: transformation by locally equivalencepreserving steps does not necessarily preserve (global) equivalence. This paper presents a condition for the total correctness of transformations on recursive programs, which, for the first time, deals with higherorder functional languages (both strict and nonstrict) including lazy data structures. The main technical result is an improvement theorem which says that if the local transformation steps are guided by certain optimisation concerns (a fairly natural condition for a transformation), then correctness of the transformation follows. The improvement theorem make...
From SOS Rules to Proof Principles: An Operational Metatheory for Functional Languages
 In Proc. POPL'97, the 24 th ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 1997
"... Structural Operational Semantics (SOS) is a widely used formalism for specifying the computational meaning of programs, and is commonly used in specifying the semantics of functional languages. Despite this widespread use there has been relatively little work on the imetatheoryj for such semantics. ..."
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Cited by 18 (1 self)
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Structural Operational Semantics (SOS) is a widely used formalism for specifying the computational meaning of programs, and is commonly used in specifying the semantics of functional languages. Despite this widespread use there has been relatively little work on the imetatheoryj for such semantics. As a consequence the operational approach to reasoning is considered ad hoc since the same basic proof techniques and reasoning tools are reestablished over and over, once for each operational semantics speciøcation. This paper develops some metatheory for a certain class of SOS language speciøcations for functional languages. We deøne a rule format, Globally Deterministic SOS (gdsos), and establish some proof principles for reasoning about equivalence which are sound for all languages which can be expressed in this format. More speciøcally, if the SOS rules for the operators of a language conform to the syntax of the gdsos format, then ffl a syntactic analogy of continuity holds, which rel...
The geometry of linear higherorder recursion
 In Logic in Computer Science, 20th International Symposium, Proceedings
, 2005
"... Linearity and ramification constraints have been widely used to weaken higherorder (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions, as the works by Leivant, Hofmann and others show. This paper shows that finetuning these two cons ..."
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Cited by 12 (5 self)
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Linearity and ramification constraints have been widely used to weaken higherorder (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions, as the works by Leivant, Hofmann and others show. This paper shows that finetuning these two constraints leads to different expressive strengths, some of them lying well beyond polynomial time. This is done by introducing a new semantics, called algebraic context semantics. The framework stems from Gonthier’s original work and turns out to be a versatile and powerful tool for the quantitative analysis of normalization in the lambdacalculus with constants and higherorder recursion. 1