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12
A Compositional Logic for Polymorphic HigherOrder Functions
 PPDP'04
, 2004
"... This paper introduces a compositional program logic for higherorder polymorphic functions and standard data types. The logic enables us to reason about observable properties of polymorphic programs starting from those of their constituents. Just as types attached to programs offer information on the ..."
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Cited by 27 (11 self)
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This paper introduces a compositional program logic for higherorder polymorphic functions and standard data types. The logic enables us to reason about observable properties of polymorphic programs starting from those of their constituents. Just as types attached to programs offer information on their composability so as to guarantee basic safety of composite programs, formulae of the proposed logic attached to programs offer information on their composability so as to guarantee finegrained behavioural properties of polymorphic programs. The central feature of the logic is a systematic usage of names and operations on them, whose origin is in the logics for typed πcalculi. The paper introduces the program logic and its proof rules and illustrates their usage by nontrivial reasoning examples, taking a prototypical callbyvalue functional language with impredicative polymorphism and recursive types as a target language.
Logical equivalence for subtyping object and recursive types
"... Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalised through an assignment system. It is shown that equality in the full first order ςcalculus is modelled by this notion, which i ..."
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Cited by 9 (8 self)
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Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalised through an assignment system. It is shown that equality in the full first order ςcalculus is modelled by this notion, which in turn is included in a Morrisstyle contextual equivalence.
Subtyping in Logical Form
, 2003
"... By using intersection types and filter models we formulate a theory of types for a λcalculus with record subtyping via a finitary programming logic. Types are interpreted as spaces of filters over a subset of the language of properties (the intersection types) which describes the underlying type fr ..."
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Cited by 8 (3 self)
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By using intersection types and filter models we formulate a theory of types for a λcalculus with record subtyping via a finitary programming logic. Types are interpreted as spaces of filters over a subset of the language of properties (the intersection types) which describes the underlying type free realizability structure. We show that such an interpretation is a PER semantics, proving that the quotient space arising from “logical” PERs taken with the intrinsic ordering is isomorphic to the filter semantics of types.
Restricted intersection type assignment systems and object properties
, 2002
"... In this note we consider a restricted version of the intersection types for a #calculus with records as presented in [5, 6] w.r.t. principal typing property and expressivity. We sketch how the classical approach to principal typing for intersection type assignment system can be adapted to cope with ..."
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Cited by 2 (0 self)
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In this note we consider a restricted version of the intersection types for a #calculus with records as presented in [5, 6] w.r.t. principal typing property and expressivity. We sketch how the classical approach to principal typing for intersection type assignment system can be adapted to cope with record types. We then exemplify typings in our system of selfapplication and recursive record interpretations of objects. 1
On Normalization by Evaluation for Object Calculi
"... We present a procedure for computing normal forms of terms in Abadi and Cardelli’s functional object calculus. Even when equipped with simple types, terms of this calculus are not terminating in general, and we draw on recent ideas about the normalization by evaluation paradigm for the untyped lambd ..."
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We present a procedure for computing normal forms of terms in Abadi and Cardelli’s functional object calculus. Even when equipped with simple types, terms of this calculus are not terminating in general, and we draw on recent ideas about the normalization by evaluation paradigm for the untyped lambda calculus. Technically, we work in the framework of Shinwell and Pitts ’ FMdomain theory, which leads to a normalization procedure for the object calculus that is directly implementable in a language like Fresh O’Caml.
Subtyping in logical form
"... Abstract By using intersection types and filter models we formulate a theory of types for a *calculus with record subtyping via a finitary programming logic. Types are interpreted as spaces of filters over a subset of the language of properties (the intersection types) which describes the underlyin ..."
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Abstract By using intersection types and filter models we formulate a theory of types for a *calculus with record subtyping via a finitary programming logic. Types are interpreted as spaces of filters over a subset of the language of properties (the intersection types) which describes the underlying type free realizability structure. We show that such an interpretation is a PER semantics, proving that the quotient space arising from &quot;logical &quot; PERs taken with the intrinsic ordering is isomorphic to the filter semantics of types. 1 Introduction Subtyping is a form of polymorphism which is based on the intuition that any term of type A might safely occur in a context of type B whenever A is a subtype of B. The basic approach to the theory of subtyping is syntactic in nature: looking for semantic investigations of this relation one is led to the successful approach which has been proposed in [6]. This is based on the same interpretation of types than second order types, namely PERs over the Kleene partial combinatory algebra (!; f g); in this framework the subtyping relation is modeled simply by subset inclusion of PERs.
Subtyping Object and Recursive Types Logically (Extended Abstract)
"... Abstract. Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalized through an assignment system. It is shown that equality in the full first order ςcalculus is modelled by this notio ..."
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Abstract. Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalized through an assignment system. It is shown that equality in the full first order ςcalculus is modelled by this notion, which on turn is included in a Morris style contextual equivalence. 1
Project funded by the European Community under the ‘Information Society Technologies’
"... this paper we show how they can be recast into algorithmic inference rules by applying a combination of standard techniques, among which constraint handling plays a central role. We then analyse the generated constraint sets and show that they share a common structure which can be simplified with a ..."
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this paper we show how they can be recast into algorithmic inference rules by applying a combination of standard techniques, among which constraint handling plays a central role. We then analyse the generated constraint sets and show that they share a common structure which can be simplified with a specialised algorithm we present. As the constraint simplification procedure is mainly based on unification, we implemented the whole inference algorithm in a Prolog program which we will comment upon
Logical Semantics for the First Order ζCalculus
 LNCS
, 2003
"... We investigate logical semantics of the first order #calculus. An assignment system of predicates to first order typed terms of the OB1 calculus is introduced. We define retraction models for that calculus and an interpretation of terms, types and predicates into such models. The assignment system ..."
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We investigate logical semantics of the first order #calculus. An assignment system of predicates to first order typed terms of the OB1 calculus is introduced. We define retraction models for that calculus and an interpretation of terms, types and predicates into such models. The assignment system is then proved to be sound and complete w.r.t. retraction models. 1
Subtyping object and recursive types logically (Draft)
, 2005
"... Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalized through an assignment system. It is shown that equality in the full first order ςcalculus is modelled by this notion, which o ..."
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Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalized through an assignment system. It is shown that equality in the full first order ςcalculus is modelled by this notion, which on turn is included in a Morris style contextual equivalence. 1