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Programming with Intersection Types and Bounded Polymorphism
, 1991
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representing the official policies, either expressed or implied, of the U.S. Government.
On Asynchronous Communication Semantics
, 1992
"... This paper presents some results concerning equational theories for an elementary calculus based on a fragment of Milner's ßcalculus. The system is interesting because it realises asynchronous message passing not by extending but reducing the original fragment, while preserving the computation ..."
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Cited by 74 (3 self)
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This paper presents some results concerning equational theories for an elementary calculus based on a fragment of Milner's ßcalculus. The system is interesting because it realises asynchronous message passing not by extending but reducing the original fragment, while preserving the computational power. The bisimulation based on a novel asynchronous transition system is introduced and studied. Presented results include congruence of the bisimilarity for the calculus, its relationship with two other asynchronous theories based on traces and failures, strict inclusion of its synchronous counterpart in the asynchronous theory, and the method called the I completion that transforms two asynchronously bisimilar terms into synchronously bisimilar ones. 1 Introduction This paper presents some results concerning equational theories for an elementary calculus based on a fragment of Milner's ßcalculus [22]. The calculus, which first appeared in its present form in [12], expresses asynchronous...
The Grammar and Processing of Order and Dependency: a Categorial Approach
, 1990
"... This thesis presents accounts of a range of linguistic phenomena in an extended categorial framework, and develops proposals for processing grammars set within this framework. Linguistic phenomena whose treatment we address include word order, grammatical relations and obliqueness, extraction and is ..."
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Cited by 70 (6 self)
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This thesis presents accounts of a range of linguistic phenomena in an extended categorial framework, and develops proposals for processing grammars set within this framework. Linguistic phenomena whose treatment we address include word order, grammatical relations and obliqueness, extraction and island constraints, and binding. The work is set within a flexible categorial framework which is a version of the Lambek calculus (Lambek, 1958) extended by the inclusion of additional typeforming operators whose logical behaviour allows for the characterization of some aspect of linguistic phenomena. We begin with the treatment of extraction phenomena and island constraints. An account is developed in which there are many interrelated notions of boundary, and where the sensitivity of any syntactic process to a particular class of boundaries can be addressed within the grammar. We next present a new categorial treatment of word order which factors apart the specification of the order of a h...
Five axioms of alphaconversion
 Ninth international Conference on Theorem Proving in Higher Order Logics TPHOL
, 1996
"... Abstract. We present five axioms of namecarrying lambdaterms identified up to alphaconversion—that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambdaabstraction. Other constants represent a function Fv that returns the set of free variab ..."
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Cited by 56 (0 self)
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Abstract. We present five axioms of namecarrying lambdaterms identified up to alphaconversion—that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambdaabstraction. Other constants represent a function Fv that returns the set of free variables in a term and a function that substitutes a term for a variable free in another term. Our axioms are (1) equations relating Fv and each constructor, (2) equations relating substitution and each constructor, (3) alphaconversion itself, (4) unique existence of functions on lambdaterms defined by structural iteration, and (5) construction of lambdaabstractions given certain functions from variables to terms. By building a model from de Bruijn’s nameless lambdaterms, we show that our five axioms are a conservative extension of HOL. Theorems provable from the axioms include distinctness, injectivity and an exhaustion principle for the constructors, principles of structural induction and primitive recursion on lambdaterms, Hindley and Seldin’s substitution lemmas and
Third Order Matching is Decidable
 Annals of Pure and Applied Logic
, 1999
"... The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed calculus, i.e. to solve the equation a = b where a and b are simply typed terms and b is ground. The decidability of this problem is still open. We prove the decidability of ..."
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The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed calculus, i.e. to solve the equation a = b where a and b are simply typed terms and b is ground. The decidability of this problem is still open. We prove the decidability of the particular case in which the variables occurring in the problem are at most third order. Introduction The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed calculus i.e. to solve the equation a = b where a and b are simply typed terms and b is ground. Pattern matching algorithms are used to check if a proposition can be deduced from another by elimination of universal quantifiers or by introduction of existential quantifiers. In automated theorem proving, elimination of universal quantifiers and introduction of existential quantifiers are mixed and full unification is required, but in proofchecking and semiaut...
An Algorithm for TypeChecking Dependent Types
 Science of Computer Programming
, 1996
"... We present a simple typechecker for a language with dependent types and let expressions, with a simple proof of correctness. Introduction Type Theory provides an interesting approach to the problem of (interactive) proofchecking. Instead of introducing, like in LCF [10], an abstract data type of t ..."
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We present a simple typechecker for a language with dependent types and let expressions, with a simple proof of correctness. Introduction Type Theory provides an interesting approach to the problem of (interactive) proofchecking. Instead of introducing, like in LCF [10], an abstract data type of theorems, it uses the proofsasprograms analogy and reduces the problem of proof checking to the problem of typechecking in a programming language with dependent types [5]. This approach presents several advantages, well described in [11,5], among those being the possibility of independent proof verification and of a uniform treatment for naming constants and theorems. It is crucial however for this approach to proofchecking to have a simple and reliable typechecking algorithm. Since the core part of such languages, like the ones described in [5,7], seems very simple, there may be some hope for such a short and simple typechecker for dependent types. Indeed, de Bruijn sketches such an al...
The Conservation Theorem revisited
, 1993
"... This paper describes a method of proving strong normalization based on an extension of the conservation theorem. We introduce a structural notion of reduction that we call fi S , and we prove that any term that has a fi I fi Snormal form is strongly finormalizable. We show how to use this result ..."
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This paper describes a method of proving strong normalization based on an extension of the conservation theorem. We introduce a structural notion of reduction that we call fi S , and we prove that any term that has a fi I fi Snormal form is strongly finormalizable. We show how to use this result to prove the strong normalization of different typed calculi.
Intersection Types and Bounded Polymorphism
, 1996
"... this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a typetheoretic model of objectoriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higherorder polymorph ..."
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Cited by 38 (0 self)
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this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a typetheoretic model of objectoriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higherorder polymorphism and dependent types have been studied by Pfenning (Pfenning, 1993). Following a more detailed discussion of the pure systems of intersections and bounded quantification (Section 2), we describe, in Section 3, a typed calculus called F ("Fmeet ") integrating the features of both. Section 4 gives some examples illustrating this system's expressive power. Section 5 presents the main results of the paper: a prooftheoretic analysis of F 's subtyping and typechecking relations leading to algorithms for checking subtyping and for synthesizing minimal types for terms. Section 6 discusses semantic aspects of the calculus, obtaining a simple soundness proof for the typing rules by interpreting types as partial equivalence relations; however, another prooftheoretic result, the nonexistence of least upper bounds for arbitrary pairs of types, implies that typed models may be more difficult to construct. Section 7 offers concluding remarks. 2. Background