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Syntactic Type Abstraction
 ACM TOPLAS
, 2000
"... data types; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming LanguagesOperational Semantics; F.3.3 [Logics and Meanings of Programs]: Studies of Program ConstructsType Structure General Terms: Languages, Security, Theory, Verification Additional Key Words and Phrases: Opera ..."
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Cited by 52 (1 self)
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data types; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming LanguagesOperational Semantics; F.3.3 [Logics and Meanings of Programs]: Studies of Program ConstructsType Structure General Terms: Languages, Security, Theory, Verification Additional Key Words and Phrases: Operational semantics, parametricity, proof techniques, syntactic proofs, type abstraction 1.
Dynamic Opacity for Abstract Types
"... Existential types are the standard formalisation of abstract types. While this formulation is sufficient in entirely statically typed languages, it proves to be too weak for languages enriched with forms of dynamic typing: in the presence of operations performing type analysis, the abstraction barri ..."
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Cited by 44 (11 self)
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Existential types are the standard formalisation of abstract types. While this formulation is sufficient in entirely statically typed languages, it proves to be too weak for languages enriched with forms of dynamic typing: in the presence of operations performing type analysis, the abstraction barrier erected by the static typing rules for existential types is no longer impassable, because parametricity is violated. We present a lightweight calculus for polymorphic languages with abstract types that addresses this shortcoming. It features a variation of existential types that retains most of the simplicity of standard existentials. It relies on modified scoping rules and explicit coercions between the quantified variable and its witness type.
Categorical Models for Local Names
 LISP AND SYMBOLIC COMPUTATION
, 1996
"... This paper describes the construction of categorical models for the nucalculus, a language that combines higherorder functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. T ..."
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Cited by 39 (2 self)
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This paper describes the construction of categorical models for the nucalculus, a language that combines higherorder functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. The intent behind this language is to examine one aspect of the imperative character of Standard ML: the use of local state by dynamic creation of references. The nucalculus is equivalent to a certain fragment of ML, omitting side effects, exceptions, datatypes and recursion. Even without all these features, the interaction of name creation with higherorder functions can be complex and subtle; it is particularly difficult to characterise the observable behaviour of expressions. Categorical monads, in the style of Moggi, are used to build denotational models for the nucalculus. An intermediate stage is the use of a computational metalanguage, which distinguishes in the type system between values and computations. The general requirements for a categorical model are presented, and two specific examples described in detail. These provide a sound denotational semantics for the nucalculus, and can be used to reason about observable equivalence in the language. In particular a model using logical relations is fully abstract for firstorder expressions.
An observationally complete program logic for imperative higherorder functions
 In Proc. LICS’05
, 2005
"... Abstract. We propose a simple compositional program logic for an imperative extension of callbyvalue PCF, built on Hoare logic and our preceding work on program logics for pure higherorder functions. A systematic use of names and operations on them allows precise and general description of comple ..."
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Cited by 39 (11 self)
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Abstract. We propose a simple compositional program logic for an imperative extension of callbyvalue PCF, built on Hoare logic and our preceding work on program logics for pure higherorder functions. A systematic use of names and operations on them allows precise and general description of complex higherorder imperative behaviour. The proof rules of the logic exactly follow the syntax of the language and can cleanly embed, justify and extend the standard proof rules for total correctness of Hoare logic. The logic offers a foundation for general treatment of aliasing and local state on its basis, with minimal extensions. After establishing soundness, we prove that valid assertions for programs completely characterise their behaviour up to observational congruence, which is proved using a variant of finite canonical forms. The use of the logic is illustrated through reasoning examples which are hard to assert and infer using existing program logics.
A Semantics of Object Types
 Proc. IEEE Symposium on Logic in Computer Science
, 1994
"... : We give a semantics for a typed object calculus, an extension of System F with object subsumption and method override. We interpret the calculus in a per model, proving the soundness of both typing and equational rules. This semantics suggests a syntactic translation from our calculus into a simpl ..."
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Cited by 35 (7 self)
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: We give a semantics for a typed object calculus, an extension of System F with object subsumption and method override. We interpret the calculus in a per model, proving the soundness of both typing and equational rules. This semantics suggests a syntactic translation from our calculus into a simpler calculus with neither subtyping nor objects. 1. Objects, Records, and Functions Despite the many formal accounts of objectoriented languages, the meaning and the properties of object types remain unclear. In particular, the soundness of object subtyping depends on invariants difficult to capture with standard type constructions; attempts based on record types have been inspiring but not compelling. In order to study object types in a clear setting, we give semantics to an extension of Girard's System F [Girard, Lafont, Taylor 1989] with subtyping, recursion, and some basic object constructs. Like all common objectoriented languages, this calculus supports object subsumption and metho...
Existential Types: Logical Relations and Operational Equivalence
 In Proceedings of the 25th International Colloquium on Automata, Languages and Programming
, 1998
"... . Existential types have proved useful for classifying various kinds of information hiding in programming languages, such as occurs in abstract datatypes and objects. In this paper we address the question of when two elements of an existential type are semantically equivalent. Of course, it depends ..."
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Cited by 31 (2 self)
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. Existential types have proved useful for classifying various kinds of information hiding in programming languages, such as occurs in abstract datatypes and objects. In this paper we address the question of when two elements of an existential type are semantically equivalent. Of course, it depends what one means by `semantic equivalence'. Here we take a syntactic approachso semantic equivalence will mean some kind of operational equivalence. The paper begins by surveying some of the literature on this topic involving `logical relations'. Matters become quite complicated if the programming language mixes existential types with function types and features involving nontermination (such as recursive definitions). We give an example (suggested by Ian Stark) to show that in this case the existence of suitable relations is sufficient, but not necessary for proving operational equivalences at existential types. Properties of this and other examples are proved using a new form of operatio...
Relational parametricity and separation logic
 In 10th FOSSACS, LNCS 4423
, 2007
"... Abstract. Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types. Our interpretation is based on Reynolds’s relation ..."
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Cited by 31 (14 self)
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Abstract. Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types. Our interpretation is based on Reynolds’s relational parametricity, and it provides a formal connection between separation logic and data abstraction.
Sequentiality and the πCalculus
, 2001
"... We present a simple type discipline for the πcalculus which precisely captures the notion of sequential functional computation as a specific class of name passing interactive behaviour. The typed calculus allows direct interpretation of both callbyname and callbyvalue sequential functions. T ..."
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Cited by 29 (15 self)
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We present a simple type discipline for the πcalculus which precisely captures the notion of sequential functional computation as a specific class of name passing interactive behaviour. The typed calculus allows direct interpretation of both callbyname and callbyvalue sequential functions. The precision of the representation is demonstrated by way of a fully abstract encoding of PCF.
Notes on Sconing and Relators
, 1993
"... This paper describes a semantics of typed lambda calculi based on relations. The main mathematical tool is a categorytheoretic method of sconing, also called glueing or Freyd covers. Its correspondence to logical relations is also examined. 1 Introduction Many modern programming languages feature ..."
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Cited by 24 (0 self)
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This paper describes a semantics of typed lambda calculi based on relations. The main mathematical tool is a categorytheoretic method of sconing, also called glueing or Freyd covers. Its correspondence to logical relations is also examined. 1 Introduction Many modern programming languages feature rather sophisticated typing mechanisms. In particular, languages such as ML include polymorphic data types, which allow considerable programming flexibility. Several notions of polymorphism were introduced into computer science by Strachey [Str67], among them the important notion of parametric polymorphism. Strachey's intuitive definition is that a polymorphic function is parametric if it has a uniformly given algorithm in all types, that is, if the function's behavior is independent of the type at which the function is instantiated. Reynolds [Rey83] proposed a mathematical definition of parametric polymorphic functions by means of invariance with respect to certain relations induced by typ...