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23
Parametric Polymorphism and Operational Equivalence
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
"... Studies of the mathematical properties of impredicative polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard–Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where ..."
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Cited by 75 (2 self)
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Studies of the mathematical properties of impredicative polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard–Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where the partialness arising from the presence of fixpoint recursion complicates the nature of potentially infinite (‘lazy’) data types. An approach to Reynolds' notion of relational parametricity is developed that works directly on the syntax of a programming language, using a novel closure operator to relate operational behaviour to parametricity properties of types. Working with an extension of Plotkin's PCF with ∀types, lazy lists and existential types, we show by example how the resulting logical relation can be used to prove properties of polymorphic types up to operational equivalence.
A bisimulation for type abstraction and recursion
 SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 2005
"... We present a bisimulation method for proving the contextual equivalence of packages in λcalculus with full existential and recursive types. Unlike traditional logical relations (either semantic or syntactic), our development is “elementary, ” using only sets and relations and avoiding advanced mach ..."
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Cited by 46 (4 self)
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We present a bisimulation method for proving the contextual equivalence of packages in λcalculus with full existential and recursive types. Unlike traditional logical relations (either semantic or syntactic), our development is “elementary, ” using only sets and relations and avoiding advanced machinery such as domain theory, admissibility, and ⊤⊤closure. Unlike other bisimulations, ours is complete even for existential types. The key idea is to consider sets of relations—instead of just relations—as bisimulations.
Compilation and Equivalence of Imperative Objects
, 1998
"... We adopt the untyped imperative object calculus of Abadi and Cardelli as a minimal setting in which to study problems of compilation and program equivalence that arise when compiling objectoriented languages. We present both a bigstep and a smallstep substitutionbased operational semantics fo ..."
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Cited by 32 (4 self)
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We adopt the untyped imperative object calculus of Abadi and Cardelli as a minimal setting in which to study problems of compilation and program equivalence that arise when compiling objectoriented languages. We present both a bigstep and a smallstep substitutionbased operational semantics for the calculus. Our rst two results are theorems asserting the equivalence of our substitutionbased semantics with a closurebased semantics like that given by Abadi and Cardelli. Our third result is a direct proof of the correctness of compilation to a stackbased abstract machine via a smallstep decompilation algorithm. Our fourth result is that contextual equivalence of objects coincides with a form of Mason and Talcott's CIU equivalence; the latter provides a tractable means of establishing operational equivalences. Finally, we prove correct an algorithm, used in our prototype compiler, for statically resolving method osets. This is the rst study of correctness of an objectoriented abstract machine, and of operational equivalence for the imperative object calculus.
Relational Reasoning about Contexts
 HIGHER ORDER OPERATIONAL TECHNIQUES IN SEMANTICS, PUBLICATIONS OF THE NEWTON INSTITUTE
, 1998
"... ..."
Normal form bisimulation for parametric polymorphism
 In LICS
, 2008
"... This paper presents a new bisimulation theory for parametric polymorphism which enables straightforward coinductive proofs of program equivalences involving existential types. The theory is an instance of typed normal form bisimulation and demonstrates the power of this recent framework for modeling ..."
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Cited by 10 (2 self)
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This paper presents a new bisimulation theory for parametric polymorphism which enables straightforward coinductive proofs of program equivalences involving existential types. The theory is an instance of typed normal form bisimulation and demonstrates the power of this recent framework for modeling typed lambda calculi as labelled transition systems. We develop our theory for a continuationpassing style calculus, JumpWithArgument, where normal form bisimulation takes a simple form. We equip the calculus with both existential and recursive types. An “ultimate pattern matching theorem ” enables us to define bisimilarity and we show it to be a congruence. We apply our theory to proving program equivalences, type isomorphisms and genericity. 1
Bisimilarity for the region calculus
 HigherOrder and Symbolic Computation
"... Abstract. A region calculus is a programming language calculus with explicit instrumentation for memory management. Every value is annotated with a region in which it is stored and regions are allocated and deallocated in a stacklike fashion. The annotations can be statically inferred by a type and ..."
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Cited by 2 (1 self)
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Abstract. A region calculus is a programming language calculus with explicit instrumentation for memory management. Every value is annotated with a region in which it is stored and regions are allocated and deallocated in a stacklike fashion. The annotations can be statically inferred by a type and effect system, making a region calculus suitable as an intermediate language for a compiler of statically typed programming languages. Although a lot of attention has been paid to type soundness properties of different flavors of region calculi, it seems that little effort has been made to develop a semantic framework. In this paper, we present a theory based on bisimulation, which serves as a coinductive proof principle for showing equivalences of polymorphically regionannotated terms. Our notion of bisimilarity is reminiscent of open bisimilarity for the πcalculus and we prove it sound and complete with respect to Morrisstyle contextual equivalence. As an application, we formulate a syntactic equational theory, which is used elsewhere to prove the soundness of a specializer based on region inference. We use our bisimulation framework to show that the equational theory is sound with respect to contextual equivalence.
An Equational Theory for a Region Calculus
, 2002
"... A region calculus is a polymorphically typed lambda calculus with explicit memory management primitives. Every value is annotated with a region in which it is stored. Regions are allocated and deallocated in a stacklike fashion. The annotations can be statically inferred by a type and eect syst ..."
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Cited by 1 (1 self)
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A region calculus is a polymorphically typed lambda calculus with explicit memory management primitives. Every value is annotated with a region in which it is stored. Regions are allocated and deallocated in a stacklike fashion. The annotations can be statically inferred by a type and eect system, making a region calculus suitable as an intermediate language for a compiler of statically typed programming languages.
Resolving Inductive Definitions with Binders in HigherOrder Typed Functional Programming
, 2009
"... This paper studies inductive definitions involving binders, in which aliasing between free and bound names is permitted. Such aliasing occurs in informal specifications of operational semantics, but is excluded by the common representation of binding as metalevel λabstraction. Drawing upon ideas f ..."
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Cited by 1 (0 self)
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This paper studies inductive definitions involving binders, in which aliasing between free and bound names is permitted. Such aliasing occurs in informal specifications of operational semantics, but is excluded by the common representation of binding as metalevel λabstraction. Drawing upon ideas from functional logic programming, we represent such definitions with aliasing as recursively defined functions in a higherorder typed functional programming language that extends core ML with types for namebinding, a type of “semidecidable propositions” and existential quantification for types with decidable equality. We show that the representation is sound and complete with respect to the language’s operational semantics, which combines the use of evaluation contexts with constraint programming. We also give a new and simple proof that the associated constraint problem is NPcomplete.
Theories of Information Hiding in LambdaCalculus: Logical Relations and Bisimulations for Encryption and Type Abstraction
"... Two methods are studied for proving equivalence of programs involving two forms of information hiding. The proof methods are logical relations and bisimulations; the forms of information hiding are type abstraction and perfect encryption (also known as dynamic sealing). Our thesis is that these theo ..."
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Two methods are studied for proving equivalence of programs involving two forms of information hiding. The proof methods are logical relations and bisimulations; the forms of information hiding are type abstraction and perfect encryption (also known as dynamic sealing). Our thesis is that these theories are useful for reasoning about programs involving information hiding. We prove it through soundness and completeness theorems as well as examples including abstract data structures and cryptographic protocols. Type abstraction is the most foundational form of information hiding in programming languages. Logical relations are the primary method for reasoning about type abstraction, which is often called relational parametricity or representation independence. Encryption is another foundational form of information hiding that is predominant in communication systems. In fact, an encryptionlike primitive is useful for abstraction in programming languages as well, where it is called dynamic sealing. Given this intuitive connection between two forms of information hiding in computer software, it is natural to wonder whether we can establish more formal connections between them and transfer reasoning techniques from one to the other. We give affirmative answers