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29
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 34 (15 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.
Relational parametricity for references and recursive types
 In Proceedings Fourth ACM Workshop on Types in Language Design and Implementation, TLDI’09
, 2009
"... We present a possible world semantics for a callbyvalue higherorder programming language with impredicative polymorphism, general references, and recursive types. The model is one of the first relationally parametric models of a programming language with all these features. To model impredicative ..."
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Cited by 13 (5 self)
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We present a possible world semantics for a callbyvalue higherorder programming language with impredicative polymorphism, general references, and recursive types. The model is one of the first relationally parametric models of a programming language with all these features. To model impredicative polymorphism we define the semantics of types via parameterized (worldindexed) logical relations over a universal domain. It is wellknown that it is nontrivial to show the existence of logical relations in the presence of recursive types. Here the problems are exacerbated because of general references. We explain what the problems are and present our solution, which makes use of a novel approach to modeling references. We prove that the resulting semantics is adequate with respect to a standard operational semantics and include simple examples of reasoning about contextual equivalence via parametricity.
Categorical and domain theoretic models of parametric polymorphism
, 2005
"... We present a domaintheoretic model of parametric polymorphism based on admissible per’s over a domaintheoretic model of the untyped lambda calculus. The model is shown to be a model of Abadi & Plotkin’s logic for parametricity, by the construction of an LAPLstructure as defined by the authors ..."
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Cited by 9 (6 self)
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We present a domaintheoretic model of parametric polymorphism based on admissible per’s over a domaintheoretic model of the untyped lambda calculus. The model is shown to be a model of Abadi & Plotkin’s logic for parametricity, by the construction of an LAPLstructure as defined by the authors in [7, 5]. This construction gives formal proof of solutions to a large class of recursive domain equations, which we explicate. As an example of a computation in the model, we explicitly describe the natural numbers object obtained using parametricity. The theory of admissible per’s can be considered a domain theory for (impredicative) polymorphism. By studying various categories of admissible and chain complete per’s and their relations, we discover a picture very similar to that of domain theory. 1
Synthetic domain theory and models of linear Abadi & Plotkin logic
, 2005
"... Plotkin suggested using a polymorphic dual intuitionistic / linear type theory (PILLY) as a metalanguage for parametric polymorphism and recursion. In recent work the first two authors and R.L. Petersen have defined a notion of parametric LAPLstructure, which are models of PILLY, in which one can r ..."
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Cited by 8 (7 self)
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Plotkin suggested using a polymorphic dual intuitionistic / linear type theory (PILLY) as a metalanguage for parametric polymorphism and recursion. In recent work the first two authors and R.L. Petersen have defined a notion of parametric LAPLstructure, which are models of PILLY, in which one can reason using parametricity and, for example, solve a large class of domain equations, as suggested by Plotkin. In this paper we show how an interpretation of a strict version of Bierman, Pitts and Russo’s language Lily into synthetic domain theory presented by Simpson and Rosolini gives rise to a parametric LAPLstructure. This adds to the evidence that the notion of LAPLstructure is a general notion suitable for treating many different parametric models, and it provides formal proofs of consequences of parametricity expected to hold for the interpretation. Finally, we show how these results in combination with Rosolini and Simpson’s computational adequacy result can be used to prove consequences of parametricity for Lily. In particular we show that one can solve domain equations in Lily up to ground contextual equivalence. 1
Relational Parametricity for Higher Kinds
"... Abstract. Reynolds ’ notion of relational parametricity has been extremely influential and well studied for polymorphic type theories such as System F. The extension of relational parametricity to higher kinded polymorphism, which allows quantification over type operators as well as types, has not b ..."
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Cited by 7 (0 self)
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Abstract. Reynolds ’ notion of relational parametricity has been extremely influential and well studied for polymorphic type theories such as System F. The extension of relational parametricity to higher kinded polymorphism, which allows quantification over type operators as well as types, has not been as well studied. In this paper we give a model of relational parametricity for System F ω and investigate some of its consequences. 1
HASCASL: Integrated HigherOrder Specification and Program Development
"... We lay out the design of HasCasl, a higher order extension of the algebraic specification language Casl that serves both as a widespectrum language for the rigorous specification and development of software, in particular but not exclusively in modern functional programming languages, and as an exp ..."
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We lay out the design of HasCasl, a higher order extension of the algebraic specification language Casl that serves both as a widespectrum language for the rigorous specification and development of software, in particular but not exclusively in modern functional programming languages, and as an expressive standard language for higherorder logic. Distinctive features of HasCasl include partial higher order functions, higher order subtyping, shallow polymorphism, and an extensive typeclass mechanism. Moreover, HasCasl provides dedicated specification support for monadbased functionalimperative programming with generic side effects, including a monadbased generic Hoare logic.
Interpreting polymorphic FPC into domain theoretic models of parametric polymorphism
 in: International Colloquium on Automata, Languages and Programming, Proceedings, Vol. 4052 of LNCS, SpringerVerlag
, 2006
"... Abstract. This paper shows how parametric PILLY (Polymorphic Intuitionistic / Linear Lambda calculus with a fixed point combinator Y) can be used as a metalanguage for domain theory, as originally suggested by Plotkin more than a decade ago. Using recent results about solutions to recursive domain e ..."
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Cited by 4 (1 self)
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Abstract. This paper shows how parametric PILLY (Polymorphic Intuitionistic / Linear Lambda calculus with a fixed point combinator Y) can be used as a metalanguage for domain theory, as originally suggested by Plotkin more than a decade ago. Using recent results about solutions to recursive domain equations in parametric models of PILLY, we show how to interpret FPC in these. Of particular interest is a model based on “admissible ” pers over a reflexive domain, the theory of which can be seen as a domain theory for (impredicative) polymorphism. We show how this model gives rise to a parametric and computationally adequate model of PolyFPC, an extension of FPC with impredicative polymorphism. This is the first model of a language with parametric polymorphism, recursive terms and recursive types in a nonlinear setting. 1
Relational parametricity for control considered as a computational effect
 Electr. Notes Theor. Comput. Sci
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 3 (2 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
CATEGORYTHEORETIC MODELS OF LINEAR ABADI & PLOTKIN LOGIC
, 2008
"... This paper presents a sound and complete categorytheoretic notion of models for Linear Abadi & Plotkin Logic [Birkedal et al., 2006], a logic suitable for reasoning about parametricity in combination with recursion. A subclass of these called parametric LAPL structures can be seen as an axioma ..."
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This paper presents a sound and complete categorytheoretic notion of models for Linear Abadi & Plotkin Logic [Birkedal et al., 2006], a logic suitable for reasoning about parametricity in combination with recursion. A subclass of these called parametric LAPL structures can be seen as an axiomatization of domain theoretic models of parametric polymorphism, and we show how to solve general (nested) recursive domain equations in these. Parametric LAPL structures constitute a general notion of model of parametricity in a setting with recursion. In future papers we will demonstrate this by showing how many different models of parametricity and recursion give rise to parametric LAPL structures, including Simpson and Rosolini’s set theoretic models [Rosolini and Simpson, 2004], a syntactic model based on Lily [Pitts, 2000, Bierman et al., 2000] and a model based on admissible pers over a reflexive domain [Birkedal et al., 2007].
A logic for parametric polymorphism with effects
"... Abstract. We present a logic for reasoning about parametric polymorphism in combination with arbitrary computational effects (nondeterminism, exceptions, continuations, sideeffects etc.). As examples of reasoning in the logic, we show how to verify correctness of polymorphic type encodings in the p ..."
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Abstract. We present a logic for reasoning about parametric polymorphism in combination with arbitrary computational effects (nondeterminism, exceptions, continuations, sideeffects etc.). As examples of reasoning in the logic, we show how to verify correctness of polymorphic type encodings in the presence of effects. 1