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Disunification: a Survey
 Computational Logic: Essays in Honor of Alan
, 1991
"... Solving an equation in an algebra of terms is known as unification. Solving more complex formulas combining equations and involving in particular negation is called disunification. With such a broad definition, many works fall into the scope of disunification. The goal of this paper is to survey the ..."
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Cited by 56 (9 self)
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Solving an equation in an algebra of terms is known as unification. Solving more complex formulas combining equations and involving in particular negation is called disunification. With such a broad definition, many works fall into the scope of disunification. The goal of this paper is to survey these works and bring them together in a same framework. R'esum'e On appelle habituellement (algorithme d') unification un algorithme de r'esolution d'une 'equation dans une alg`ebre de termes. La r'esolution de formules plus complexes, comportant en particulier des n'egations, est appel'ee ici disunification. Avec une d'efinition aussi 'etendue, de nombreux travaux peuvent etre consid'er'es comme portant sur la disunification. L'objet de cet article de synth`ese est de rassembler tous ces travaux dans un meme formalisme. Laboratoire de Recherche en Informatique, Bat. 490, Universit'e de ParisSud, 91405 ORSAY cedex, France. Email: comon@lri.lri.fr i Contents 1 Syntax 5 1.1 Basic Defini...
A theory of contracts for web services
 In POPL ’08, 35th ACM Symposium on Principles of Programming Languages
, 2008
"... Contracts are behavioral descriptions of Web services. We devise a theory of contracts that formalizes the compatibility of a client to a service, and the safe replacement of a service with another service. The use of contracts statically ensures the successful completion of every possible interacti ..."
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Cited by 52 (4 self)
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Contracts are behavioral descriptions of Web services. We devise a theory of contracts that formalizes the compatibility of a client to a service, and the safe replacement of a service with another service. The use of contracts statically ensures the successful completion of every possible interaction between compatible clients and services. The technical device that underlies the theory is the filter, which is an explicit coercion preventing some possible behaviors of services and, in doing so, make services compatible with different usage scenarios. We show that filters can be seen as proofs of a sound and complete subcontracting deduction system which simultaneously refines and extends Hennessy’s classical axiomatization of the must testing preorder. The relation is decidable and the decision algorithm is obtained via a cutelimination process that proves the coherence of subcontracting as a logical system. Despite the richness of the technical development, the resulting approach is based on simple ideas and basic intuitions. Remarkably, its application is mostly independent of the language used to program the services or the clients. We outline the practical aspects of our theory by studying two different concrete syntaxes for contracts and applying each of them to Web services languages. We also explore implementation issues of filters and discuss the perspectives of future research
Implementing Regular Tree Expressions
 In Proceedings of the 1991 Conference on Functional Programming Languages and Computer Architecture
, 1991
"... Regular tree expressions are a natural formalism for describing the sets of treestructured values that commonly arise in programs; thus, they are wellsuited to applications in program analysis. We describe an implementation of regular tree expressions and our experience with that implementation in ..."
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Cited by 49 (5 self)
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Regular tree expressions are a natural formalism for describing the sets of treestructured values that commonly arise in programs; thus, they are wellsuited to applications in program analysis. We describe an implementation of regular tree expressions and our experience with that implementation in the context of the FL type system. A combination of algorithms, optimizations, and fast heuristics for computationally difficult problems yields an implementation efficient enough for practical use. 1 Introduction Regular tree expressions are a natural formalism for describing the sets of treestructured values that commonly arise in programs. As such, several researchers have proposed using (variations on) regular tree expressions in type inference and program analysis algorithms [JM79, Mis84, MR85, HJ90, HJ91, AM91]. We are not aware of any implementations based on regular tree expressions, however, except for our own work on type analysis for the functional language FL [B + 89]. A p...
Efficient Recursive Subtyping
, 1995
"... Subtyping in the presence of recursive types for the *calculus was studied by Amadio and Cardelli in 1991 [1]. In that paper they showed that the problem of deciding whether one recursive type is a subtype of another is decidable in exponential time. In this paper we give an O(n2) algorithm. Our ..."
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Cited by 48 (14 self)
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Subtyping in the presence of recursive types for the *calculus was studied by Amadio and Cardelli in 1991 [1]. In that paper they showed that the problem of deciding whether one recursive type is a subtype of another is decidable in exponential time. In this paper we give an O(n2) algorithm. Our algorithm is based on a simplification of the definition of the subtype relation, which allows us to reduce the problem to the emptiness problem for a certain finite automaton with quadratically many states. It is known that equality of recursive types and the covariant B&quot;ohm order can be decided efficiently by means of finite automata, since they are just language equality and language inclusion, respectively. Our results extend the automatatheoretic approach to handle orderings based on contravariance.
A FirstOrder Axiomatization of the Theory of Finite Trees
, 1995
"... We provide firstorder axioms for the theories of finite trees with bounded branching and finite trees with arbitrary (finite) branching. The signature is chosen to express, in a natural way, those properties of trees most relevant to linguistic theories. These axioms provide a foundation for result ..."
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Cited by 47 (3 self)
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We provide firstorder axioms for the theories of finite trees with bounded branching and finite trees with arbitrary (finite) branching. The signature is chosen to express, in a natural way, those properties of trees most relevant to linguistic theories. These axioms provide a foundation for results in linguistics that are based on reasoning formally about such properties. We include some observations on the expressive power of these theories relative to traditional language complexity classes.
Macro Tree Transducers, Attribute Grammars, and MSO Definable Tree Translations
 Inform. and Comput
, 1998
"... A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with reg ..."
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Cited by 47 (20 self)
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A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with regular lookahead that are single use restricted. For this the single use restriction known from attribute grammars is generalized to MTTs. Since MTTs are closed under regular lookahead, this implies that every MSO definable tree translation can be realized by an MTT. The second main result is that the class of MSO definable tree translations can also be obtained by restricting MTTs with regular lookahead to be finite copying, i.e., to require that each input subtree is processed only a bounded number of times. The single use restriction is a rather strong, static restriction on the rules of an MTT, whereas the finite copying restriction is a more liberal, dynamic restriction on the ...
VLISP: A verified implementation of Scheme
 Lisp and Symbolic Computation
, 1995
"... VLISP has produced a rigorously verified compiler from Scheme to byte codes, and a verified interpreter for the resulting byte codes. The official denotational semantics for Scheme provides the main criterion of correctness. The WandClinger technique was used to prove correctness of the main compil ..."
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Cited by 45 (3 self)
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VLISP has produced a rigorously verified compiler from Scheme to byte codes, and a verified interpreter for the resulting byte codes. The official denotational semantics for Scheme provides the main criterion of correctness. The WandClinger technique was used to prove correctness of the main compiler step. Then a state machine operational semantics is proved to be faithful to the denotational semantics. The remainder of the implementation is verified by a succession of state machine refinement proofs. These include proofs that garbage collection is a sound implementation strategy,
Polymorphism and Type Inference in Database Programming
"... In order to find a static type system that adequately supports database languages, we need to express the most general type of a program that involves database operations. This can be achieved through an extension to the type system of ML that captures the polymorphic nature of field selection, toge ..."
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Cited by 39 (10 self)
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In order to find a static type system that adequately supports database languages, we need to express the most general type of a program that involves database operations. This can be achieved through an extension to the type system of ML that captures the polymorphic nature of field selection, together with a technique that generalizes relational operators to arbitrary data structures. The combination provides a statically typed language in which generalized relational databases may be cleanly represented as typed structures. As in ML types are inferred, which relieves the programmer of making the type assertions that may be required in a complex database environment. These extensions may also be used to provide static polymorphic typechecking in objectoriented languages and databases. A problem that arises with objectoriented databases is the apparent need for dynamic typechecking when dealing with queries on heterogeneous collections of objects. An extension of the type system needed for generalized relational operations can also be used for manipulating collections of dynamically typed values in a statically typed language. A prototype language based on these ideas has been implemented. While it lacks a proper treatment of persistent data, it demonstrates that a wide variety of database structures can be cleanly represented in a polymorphic programming language.
Recursive Subtyping Revealed
 Journal of Functional Programming
, 2000
"... Algorithms for checking subtyping between recursive types lie at the core of many programming language implementations. But the fundamental theory of these algorithms and how they relate to simpler declarative specifications is not widely understood, due in part to the difficulty of the available in ..."
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Cited by 38 (4 self)
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Algorithms for checking subtyping between recursive types lie at the core of many programming language implementations. But the fundamental theory of these algorithms and how they relate to simpler declarative specifications is not widely understood, due in part to the difficulty of the available introductions to the area. This tutorial paper offers an "endtoend" introduction to recursive types and subtyping algorithms, from basic theory to efficient implementation, set in the unifying mathematical framework of coinduction. 1. INTRODUCTION Recursively defined types in programming languages and lambdacalculi come in two distinct varieties. Consider, for example, the type X described by the equation X = Nat!(Nat\ThetaX): An element of X is a function that maps a number to a pair consisting of a number and a function of the same form. This type is often written more concisely as X.Nat!(Nat\ThetaX). A variety of familiar recursive types such as lists and trees can be defined analogou...