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Semantics of separationlogic typing and higherorder frame rules
 In Symposium on Logic in Computer Science, LICS’05
, 2005
"... We show how to give a coherent semantics to programs that are wellspecified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables). In particular, we provide simple sound rules for deriving higherorder frame rules ..."
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Cited by 58 (17 self)
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We show how to give a coherent semantics to programs that are wellspecified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables). In particular, we provide simple sound rules for deriving higherorder frame rules, allowing for local reasoning.
From semantics to rules: A machine assisted analysis
 Proceedings of CSL '93, LNCS 832
, 1999
"... this paper is similar to the one in [2]. In this paper they define a normalization function for simply typed ..."
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Cited by 29 (0 self)
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this paper is similar to the one in [2]. In this paper they define a normalization function for simply typed
Prelogical Relations
, 1999
"... this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results ..."
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Cited by 26 (5 self)
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this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results
A New Characterization of Lambda Definability
, 1993
"... . We give a new characterization of lambda definability in Henkin models using logical relations defined over ordered sets with varying arity. The advantage of this over earlier approaches by Plotkin and Statman is its simplicity and universality. Yet, decidability of lambda definability for heredit ..."
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Cited by 26 (1 self)
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. We give a new characterization of lambda definability in Henkin models using logical relations defined over ordered sets with varying arity. The advantage of this over earlier approaches by Plotkin and Statman is its simplicity and universality. Yet, decidability of lambda definability for hereditarily finite Henkin models remains an open problem. But if the variable set allowed in terms is also restricted to be finite then our techniques lead to a decision procedure. 1 Introduction An applicative structure consists of a family (A oe ) oe2T of sets, one for each type oe, together with a family (app oe;ø ) oe;ø 2T of application functions, where app oe;ø maps A oe!ø \Theta A oe into A ø . For an applicative structure to be a model of the simply typed lambda calculus (in which case we call it a Henkin model, following [4]), one requires two more conditions to hold. It must be extensional which means that the elements of A oe!ø are uniquely determined by their behavior under app oe;ø...
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...
A Relevant Analysis of Natural Deduction
 Journal of Logic and Computation
, 1999
"... Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and ..."
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Cited by 23 (7 self)
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Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and Plotkin's LF, with a representation mechanism: the language of RLF is the lLcalculus; the representation mechanism is judgementsastypes, developed for relevant logics. The lLcalculus type theory is a firstorder dependent type theory with two kinds of dependent function spaces: a linear one and an intuitionistic one. We study a natural deduction presentation of the type theory and establish the required prooftheoretic metatheory. The RLF framework is a conservative extension of LF. We show that RLF uniformly encodes (fragments of) intuitionistic linear logic, Curry's l I calculus and ML with references. We describe the CurryHowardde Bruijn correspondence of the lLcalculus with a s...
Categorical Reconstruction of a Reduction Free Normalization Proof
, 1995
"... Introduction We present a categorical proof of the normalization theorem for simply typed calculus, i.e. we derive a computable function nf which assigns to every typed term a normal form, s.t. M ' N nf(M ) = nf(N ) nf(M ) ' M where ' is fij equality. Both the function nf and its correctness ..."
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Cited by 23 (5 self)
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Introduction We present a categorical proof of the normalization theorem for simply typed calculus, i.e. we derive a computable function nf which assigns to every typed term a normal form, s.t. M ' N nf(M ) = nf(N ) nf(M ) ' M where ' is fij equality. Both the function nf and its correctness properties can be deduced from the categorical construction. To substantiate this, we present an ML program in the appendix which can be extracted from our argument. We emphasize that this presentation of normalization is reduction free, i.e. we do not mention term rewriting or use properties of term rewriting systems such as the ChurchRosser property. An immediate consequence of normalization is the decidability of ' but there are other useful corollaries; for instance we can show that
A Proof Search Specification of the πCalculus
 IN 3RD WORKSHOP ON THE FOUNDATIONS OF GLOBAL UBIQUITOUS COMPUTING
, 2004
"... We present a metalogic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite πcalculus within this metalogic. Since we ..."
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Cited by 21 (11 self)
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We present a metalogic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite πcalculus within this metalogic. Since we
Fibrations, Logical Predicates and Indeterminates
, 1993
"... Within the framework of categorical logic or categorical type theory, predicate logics and type theories are understood asfibEE6D: with structure. Fibcture. orfibD] categories, provide anabE:J]S account of the notions of indexing andsub]:S]KE[: These notions are central to the interpretations of ..."
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Cited by 20 (1 self)
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Within the framework of categorical logic or categorical type theory, predicate logics and type theories are understood asfibEE6D: with structure. Fibcture. orfibD] categories, provide anabE:J]S account of the notions of indexing andsub]:S]KE[: These notions are central to the interpretations of predicate logics and type theories with dependent types or polymorphism. In these systems, predicates/dependent types are indexedb y the contexts which declare the types of their free v ariab[K and there is an operation of sub:]:KSRR of terms for free variab'K With this setting, it is natural to give a categorytheoretic account of certain logical issues in terms offib'RD]KS In this thesis we explore logical predicates for simply typed theories, induction principles for inductive data types, and indeterminate elements forfibS6[[J in relation to polymorphic #calculi. The notion of logical predicate is a useful tool in the study of type theories like simply typed #calculus. For a categorical account of this concept, we are led to study certain structure offibSR categories. In particular, the kind of structure involved in the interpretation of simply typed #calculus, namely cartesian closure, is expressed in terms of adjunctions. Hence we are led to consider adjunctionsb etweenfibE categories. We give a characterisation of these adjunctions which allows us to provide structure, givenb y adjunctions, to afibS] category in terms of appropriate structure on its bsand itsfibD6 By expressing theab ovementioned categorical structure logically, in the internal language of a fibS[:D' we can give an account of logical predicates for a cartesian closed category. By recourse to the internal language, we regard afib66 category as a category of predicates. With the same method, w...