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Adequacy of compositional translations for observational semantics
 INTERNATIONAL CONFERENCE ON THEORETICAL COMPUTER SCIENCE
, 2008
"... We investigate methods and tools for analyzing translations between programming languages with respect to observational semantics. The behavior of programs is observed in terms of may and mustconvergence in arbitrary contexts, and adequacy of translations, i.e., the reflection of program equivalenc ..."
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Cited by 9 (7 self)
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We investigate methods and tools for analyzing translations between programming languages with respect to observational semantics. The behavior of programs is observed in terms of may and mustconvergence in arbitrary contexts, and adequacy of translations, i.e., the reflection of program equivalence, is taken to be the fundamental correctness condition. For compositional translations we propose a notion of convergence equivalence as a means for proving adequacy. This technique avoids explicit reasoning about contexts, and is able to deal with the subtle role of typing in implementations of language extensions.
On generic context lemmas for lambda calculi with sharing
, 2008
"... This paper proves several generic variants of context lemmas and thus contributes to improving the tools for observational semantics of deterministic and nondeterministic higherorder calculi that use a smallstep reduction semantics. The generic (sharing) context lemmas are provided for may as we ..."
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Cited by 5 (3 self)
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This paper proves several generic variants of context lemmas and thus contributes to improving the tools for observational semantics of deterministic and nondeterministic higherorder calculi that use a smallstep reduction semantics. The generic (sharing) context lemmas are provided for may as well as two variants of mustconvergence, which hold in a broad class of extended process and extended lambda calculi, if the calculi satisfy certain natural conditions. As a guideline, the proofs of the context lemmas are valid in callbyneed calculi, in callbyvalue calculi if substitution is restricted to variablebyvariable and in process calculi like variants of the πcalculus. For calculi employing betareduction using a callbyname or callbyvalue strategy or similar reduction rules, some iuvariants of ciutheorems are obtained from our context lemmas. Our results reestablish several context lemmas already proved in the literature, and also provide some new context lemmas as well as some new variants of the ciutheorem. To make the results widely applicable, we use a higherorder abstract syntax that allows untyped calculi as well as certain simple typing schemes. The approach may lead to a unifying view of higherorder calculi, reduction, and observational equality.
Correctness of Copy in Calculi with Letrec,
, 2007
"... Abstract. This paper extends the internal frank report 28 as follows: It is shown that for a callbyneed lambda calculus LRCCPλ extending the calculus LRCCλ by por, i.e in a lambdacalculus with letrec, case, constructors, seq and por, copying can be done without restrictions, and also that callby ..."
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Cited by 5 (3 self)
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Abstract. This paper extends the internal frank report 28 as follows: It is shown that for a callbyneed lambda calculus LRCCPλ extending the calculus LRCCλ by por, i.e in a lambdacalculus with letrec, case, constructors, seq and por, copying can be done without restrictions, and also that callbyneed and callbyname strategies are equivalent w.r.t. contextual equivalence. 1
Equivalence of callbyname and callbyneed for lambdacalculi with letrec. Frank report 25
 Inst. f. Informatik
, 2006
"... Abstract. We develop a proof method to show that in a (deterministic) lambda calculus with letrec and equipped with contextual equivalence the callbyname and the callbyneed evaluation are equivalent, and also that the unrestricted copyoperation is correct. Given a letbinding x = t, the copyop ..."
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Cited by 3 (1 self)
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Abstract. We develop a proof method to show that in a (deterministic) lambda calculus with letrec and equipped with contextual equivalence the callbyname and the callbyneed evaluation are equivalent, and also that the unrestricted copyoperation is correct. Given a letbinding x = t, the copyoperation replaces an occurrence of the variable x by the expression t, regardless of the form of t. This gives an answer to unresolved problems in several papers, it adds a strong method to the tool set for reasoning about contextual equivalence in higherorder calculi with letrec, and it enables a class of transformations that can be used as optimizations. The method can be used in different kind of lambda calculi with cyclic sharing. Probably it can also be used in nondeterministic lambda calculi if the variable x is “deterministic”, i.e., has no interference with nondeterministic executions. The main technical idea is to use a restricted variant of the infinitary lambdacalculus, whose objects are the expressions that are unrolled w.r.t. let, to define the infinite developments as a reduction calculus on the infinite trees and showing a standardization theorem. 1
Correctness of copy in calculi with letrec, case and constructors
, 2007
"... Callbyneed lambda calculi with letrec provide a rewritingbased operational semantics for (lazy) callbyname functional languages. These calculi model the sharing behavior during evaluation more closely than letbased calculi that use a fixpoint combinator. In a previous paper we showed that the ..."
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Cited by 3 (0 self)
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Callbyneed lambda calculi with letrec provide a rewritingbased operational semantics for (lazy) callbyname functional languages. These calculi model the sharing behavior during evaluation more closely than letbased calculi that use a fixpoint combinator. In a previous paper we showed that the copytransformation is correct for the small calculus LRλ. In this paper we demonstrate that the proof method based on a calculus on infinite trees for showing correctness of instantiation operations can be extended to the calculus LRCCλ with case and constructors, and show that copying at compiletime can be done without restrictions. We also show that the callbyneed and callbyname strategies are equivalent w.r.t. contextual equivalence. A consequence is correctness of all the transformations like instantiation, inlining, specialization and common subexpression elimination in LRCCλ. We are confident that the method scales up for proving correctness of copyrelated transformations in nondeterministic lambda calculi if restricted to “deterministic” subterms.
On Conservativity of Concurrent Haskell
, 2011
"... Abstract. The calculus CHF models Concurrent Haskell extended by concurrent, implicit futures. It is a process calculus with concurrent threads, monadic concurrent evaluation, and includes a pure functional lambdacalculus which comprises data constructors, caseexpressions, letrecexpressions, and ..."
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Abstract. The calculus CHF models Concurrent Haskell extended by concurrent, implicit futures. It is a process calculus with concurrent threads, monadic concurrent evaluation, and includes a pure functional lambdacalculus which comprises data constructors, caseexpressions, letrecexpressions, and Haskell’s seq. Futures can be implemented in Concurrent Haskell using the primitive unsafeInterleaveIO, which is available in most implementations of Haskell. Our main result is conservativity of CHF, that is, all equivalences of pure functional expressions are also valid in CHF. This implies that compiler optimizations and transformations from pure Haskell remain valid in Concurrent Haskell even if it is extended by futures. We also show that this is no longer valid if Concurrent Haskell is extended by the arbitrary use of unsafeInterleaveIO. 1
StepIndexed Relational Reasoning for Countable Nondeterminism
"... Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces noncontinuous behaviour, it is wellknown that developing semantic models for program ..."
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Cited by 2 (2 self)
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Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces noncontinuous behaviour, it is wellknown that developing semantic models for programming languages with countable nondeterminism is challenging. We present a stepindexed logical relations model of a higherorder functional programming language with countable nondeterminism and demonstrate how it can be used to reason about contextually defined may and mustequivalence. In earlier stepindexed models, the indices have been drawn from ω. Here the stepindexed relations for mustequivalence are indexed over an ordinal greater than ω.
Contextual Equivalence in LambdaCalculi extended with letrec and with a Parametric Polymorphic Type System
, 2009
"... This paper describes a method to treat contextual equivalence in polymorphically typed lambdacalculi, and also how to transfer equivalences from the untyped versions of lambdacalculi to their typed variant, where our specific calculus has letrec, recursive types and is nondeterministic. An additio ..."
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Cited by 1 (1 self)
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This paper describes a method to treat contextual equivalence in polymorphically typed lambdacalculi, and also how to transfer equivalences from the untyped versions of lambdacalculi to their typed variant, where our specific calculus has letrec, recursive types and is nondeterministic. An addition of a type label to every subexpression is all that is needed, together with some natural constraints for the consistency of the type labels and wellscopedness of expressions. One result is that an elementary but typed notion of program transformation is obtained and that untyped contextual equivalences also hold in the typed calculus as long as the expressions are welltyped. In order to have a nice interaction between reduction and typing, some reduction rules have to be accompanied with a type modification by generalizing or instantiating types.
On Correctness of Buffer Implementations in a Concurrent Lambda Calculus with Futures
, 2009
"... Abstract. Motivated by the question of correctness of a specific implementation of concurrent buffers in the lambda calculus with futures underlying Alice ML, we prove that concurrent buffers and handled futures can correctly encode each other. Correctness means that our encodings preserve and refle ..."
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Abstract. Motivated by the question of correctness of a specific implementation of concurrent buffers in the lambda calculus with futures underlying Alice ML, we prove that concurrent buffers and handled futures can correctly encode each other. Correctness means that our encodings preserve and reflect the observations of may and mustconvergence. This also shows correctness wrt. program semantics, since the encodings are adequate translations wrt. contextual semantics. While these translations encode blocking into queuing and waiting, we also provide an adequate encoding of buffers in a calculus without handles, which is more lowlevel and uses busywaiting instead of blocking. Furthermore we demonstrate that our correctness concept applies to the whole compilation process from highlevel to lowlevel concurrent languages, by translating the calculus with buffers, handled futures and data constructors into a small core language without those constructs. 1
Program Equivalence for a Concurrent Lambda Calculus with Futures
, 2006
"... Abstract. Reasoning about the correctness of program transformations requires a notion of program equivalence. We present an observational semantics for the concurrent lambda calculus with futures λ(fut), which formalizes the operational semantics of the programming language Alice ML. We show that n ..."
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Abstract. Reasoning about the correctness of program transformations requires a notion of program equivalence. We present an observational semantics for the concurrent lambda calculus with futures λ(fut), which formalizes the operational semantics of the programming language Alice ML. We show that natural program optimizations, as well as partial evaluation with respect to deterministic rules, are correct for λ(fut). This relies on a number of fundamental properties that we establish for our observational semantics. 1