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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 (Update) h ; ..."
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Cited by 38 (7 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...
Process Semantics of Graph Reduction
 Proc. CONCUR '95, volume 962 of Lecture Notes in Computer Science
, 1995
"... This paper introduces an operational semantics for callbyneed reduction in terms of Milner's ßcalculus. The functional programming interest lies in the use of ßcalculus as an abstract yet realistic target language. The practical value of the encoding is demonstrated with an outline for a paralle ..."
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Cited by 6 (1 self)
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This paper introduces an operational semantics for callbyneed reduction in terms of Milner's ßcalculus. The functional programming interest lies in the use of ßcalculus as an abstract yet realistic target language. The practical value of the encoding is demonstrated with an outline for a parallel code generator. From a theoretical perspective, the ßcalculus representation of computational strategies with shared reductions is novel and solves a problem posed by Milner [13]. The compactness of the process calculus presentation makes it interesting as an alternative definition of callbyneed. Correctness of the encoding is proved with respect to the callbyneed calculus of Ariola et al. [3]. 1 Introduction Graph reduction of extended calculi has become a mature field of applied research. The efficiency of the implementations is due in great measure to a technique known as `sharing', whereby argument values are computed (at most) once and then memoized for future reference. Both...
Interpreting functions as πcalculus processes: a tutorial
, 1999
"... This paper is concerned with the relationship betweencalculus and ��calculus. Thecalculus talks about functions and their applicative behaviour. This contrasts with the ��calculus, that talks about processes and their interactive behaviour. Application is a special form of interaction, and there ..."
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Cited by 1 (0 self)
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This paper is concerned with the relationship betweencalculus and ��calculus. Thecalculus talks about functions and their applicative behaviour. This contrasts with the ��calculus, that talks about processes and their interactive behaviour. Application is a special form of interaction, and therefore functions can be seen as a special form of processes. We study how the functions of thecalculus (the computable functions) can be represented as ��calculus processes. The ��calculus semantics of a language induces a notion of equality on the terms of that language. We therefore also analyse the equality among functions that is induced by their representation as ��calculus processes. This paper is intended as a tutorial. It however contains some original contributions. The main ones are: the use of wellknown Continuation Passing Style transforms to derive the encodings into ��calculus and prove their correctness; the encoding of typedcalculi.
Reasoning about Selective Strictness  Operational Equivalence, Heaps and CallbyNeed Evaluation, New Inductive Principles
, 2009
"... Many predominantly lazy languages now incorporate strictness enforcing primitives, for example a strict let or sequential composition seq. Reasons for doing this include gains in time or space efficiencies, or control of parallel evaluation. This thesis studies how to prove equivalences between pro ..."
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Cited by 1 (0 self)
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Many predominantly lazy languages now incorporate strictness enforcing primitives, for example a strict let or sequential composition seq. Reasons for doing this include gains in time or space efficiencies, or control of parallel evaluation. This thesis studies how to prove equivalences between programs in languages with selective strictness, specifically, we use a restricted core lazy functional language with a selective strictness operator seq whose operational semantics is a variant of one considered by van Eckelen and de Mol, which itself was derived from Launchbury’s natural semantics for lazy evaluation. The main research contributions are as follows: We establish some of the first ever equivalences between programs with selective strictness. We do this by manipulating operational semantics derivations, in
Closed Reductions in the λcalculus (Extended Abstract)
, 1999
"... Closed reductions in the lamdacalculus is a strategy for a calculus of explicit substitutions which overcomes many of the usual syntactical problems of substitution. This is achieved by only moving closed substitutions through certain constructs, which gives a weak form of reduction, but is rich en ..."
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Closed reductions in the lamdacalculus is a strategy for a calculus of explicit substitutions which overcomes many of the usual syntactical problems of substitution. This is achieved by only moving closed substitutions through certain constructs, which gives a weak form of reduction, but is rich enough to capture the usual strategies in the lambdacalculus (callbyvalue, callbyneed, etc.) and is adequate for the evaluation of programs. An interesting point is that the calculus permits substitutions to move through abstractions, and reductions are allowed under abstractions, if certain conditions hold. The calculus naturally provides an efficient notion of reduction (with a high degree of sharing), which can easily be implemented....
Reasoning about Selective Strictness  Operational Equivalence, Heaps and CallbyNeed Evaluation, New Inductive Principles
, 2009
"... This thesis studies how to prove equivalences between programs in languages with selective strictness, specifically, we use a restricted core lazy functional language with a selective strictness operator seq. We establish some of the first ever equivalences between lazy programs with selective str ..."
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This thesis studies how to prove equivalences between programs in languages with selective strictness, specifically, we use a restricted core lazy functional language with a selective strictness operator seq. We establish some of the first ever equivalences between lazy programs with selective strictness by manipulating operational semantics derivations. Our operational semantics is similar to that used by van Eekelen and De Mol, though we introduce a ‘garbagecollecting’ rule for (let) which turns out to cause expressiveness restrictions. For example, arguably reasonable lazy programs such as let y = λz.z in λx.y do not reduce in our operational semantics. We prove some properties of seq, including associativity, idempotence, and leftcommutativity. The proofs use our three notions of program equivalence defined