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14
Union Types for Semistructured Data
 University of Pennsylvania Dept. of CIS
, 1999
"... Semistructured databases are treated as dynamically typed: they come equipped with no independent schema or type system to constrain the data. Query languages that are designed for semistructured data, even when used with structured data, typically ignore any type information that may be present. ..."
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Cited by 37 (3 self)
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Semistructured databases are treated as dynamically typed: they come equipped with no independent schema or type system to constrain the data. Query languages that are designed for semistructured data, even when used with structured data, typically ignore any type information that may be present. The consequences of this are what one would expect from using a dynamic type system with complex data: fewer guarantees on the correctness of applications. For example, a query that would cause a type error in a statically typed query language will return the empty set when applied to a semistructured representation of the same data. Much semistructured data originates in structured data. A semistructured representation is useful when one wants to add data that does not conform to the original type or when one wants to combine sources of different types. However, the deviations from the prescribed types are often minor, and we believe that a better strategy than throwing away all typ...
A Filter Model for Concurrent λCalculus
 SIAM J. COMPUT
, 1998
"... Type free lazy λcalculus is enriched with angelic parallelism and demonic nondeterminism. Callbyname and callbyvalue abstractions are considered and the operational semantics is stated in terms of a must convergence predicate. We introduce a type assignment system with intersection and union ty ..."
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Cited by 9 (2 self)
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Type free lazy λcalculus is enriched with angelic parallelism and demonic nondeterminism. Callbyname and callbyvalue abstractions are considered and the operational semantics is stated in terms of a must convergence predicate. We introduce a type assignment system with intersection and union types and we prove that the induced logical semantics is fully abstract.
Discrimination by Parallel Observers: the Algorithm
 LICS '97 , IEEE COMP. SOC
, 1998
"... The main result of the paper is a constructive proof of the following equivalence: two pure λterms are observationally equivalent in the lazy concurrent λcalculus iff they have the same LévyLongo trees. An algorithm which allows to build a context discriminating any two pure λterms with diffe ..."
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Cited by 8 (3 self)
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The main result of the paper is a constructive proof of the following equivalence: two pure λterms are observationally equivalent in the lazy concurrent λcalculus iff they have the same LévyLongo trees. An algorithm which allows to build a context discriminating any two pure λterms with different LévyLongo trees is described. It follows that contextual equivalence coincides with behavioural equivalence (bisimulation) as considered by Sangiorgi. Another consequence is that the discriminating power of concurrent lambda contexts is the same as that of BoudolLaneve's contexts with multiplicities.
What is a Categorical Model of the Differential and the Resource λCalculi?
"... The differential λcalculus is a paradigmatic functional programming language endowed with a syntactical differentiation operator that allows to apply a program to an argument in a linear way. One of the main features of this language is that it is resource conscious and gives the programmer suitab ..."
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Cited by 8 (2 self)
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The differential λcalculus is a paradigmatic functional programming language endowed with a syntactical differentiation operator that allows to apply a program to an argument in a linear way. One of the main features of this language is that it is resource conscious and gives the programmer suitable primitives to handle explicitly the resources used by a program during its execution. The differential operator also allows to write the full Taylor expansion of a program. Through this expansion every program can be decomposed into an infinite sum (representing nondeterministic choice) of ‘simpler’ programs that are strictly linear. The aim of this paper is to develop an abstract ‘model theory ’ for the untyped differential λcalculus. In particular, we investigate what should be a general categorical definition of denotational model for this calculus. Starting from the work of Blute, Cockett and Seely on differential categories we provide the notion of Cartesian closed differential category and we prove that linear reflexive objects living in such categories constitute sound models of the untyped differential λcalculus. We also give sufficient conditions for Cartesian closed differential categories to model the Taylor expansion. This entails that every model living in such categories equates all programs having the same full Taylor expansion. We then
Discrimination by Parallel Observers
 LICS '97 , IEEE Comp. Soc
, 1997
"... The main result of the paper is a proof of the following equivalence: two pure lambda terms are observationally equivalent in the lazy concurrent lambda calculus iff they have the same L'evyLongo trees. It follows that contextual equivalence coincides with behavioural equivalence (bisimulat ..."
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Cited by 6 (2 self)
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The main result of the paper is a proof of the following equivalence: two pure lambda terms are observationally equivalent in the lazy concurrent lambda calculus iff they have the same L'evyLongo trees. It follows that contextual equivalence coincides with behavioural equivalence (bisimulation) as considered by Sangiorgi. Another consequence is that the discriminating power of concurrent lambda contexts is the same as that of Boudol's contexts with multiplicities. 1 Introduction The aim of this paper is to improve our understanding of what is the "meaning" of a term in the lazy calculus. To explain our result let us begin with the following few observations borrowed from the paper [1] of Abramsky and Ong. In the ordinary calculus, the most natural understanding of evaluation to a "value" is reduction to a normal form. It is however wellknown that this interpretation cannot be taken as a basis of a consistent equational theory. Indeed, equating all terms without normal forms...
Callbyvalue nondeterminism in a linear logic type discipline
 in "LFCS  Logical Foundations of Computer Science  2013
, 2013
"... Abstract. We consider the callbyvalue λcalculus extended with a mayconvergent nondeterministic choice and a mustconvergent parallel composition. Inspired by recent works on the relational semantics of linear logic and nonidempotent intersection types, we endow this calculus with a type syste ..."
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Cited by 5 (1 self)
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Abstract. We consider the callbyvalue λcalculus extended with a mayconvergent nondeterministic choice and a mustconvergent parallel composition. Inspired by recent works on the relational semantics of linear logic and nonidempotent intersection types, we endow this calculus with a type system based on the socalled Girard’s second translation of intuitionistic logic into linear logic. We prove that a term is typable if and only if it is converging, and that its typing tree carries enough information to give a bound on the length of its lazy callbyvalue reduction. Moreover, when the typing tree is minimal, such a bound becomes the exact length of the reduction.
The minimal relevant logic and the callbyvalue lambda calculus
, 1999
"... The minimal relevant logic B+, seen as a type discipline, includes an extension of Curry types known as the intersection type discipline. We will show that the full logic B+ gives a type assignment system which produces a model of Plotkin’s callbyvaluecalculus. 1 ..."
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Cited by 5 (3 self)
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The minimal relevant logic B+, seen as a type discipline, includes an extension of Curry types known as the intersection type discipline. We will show that the full logic B+ gives a type assignment system which produces a model of Plotkin’s callbyvaluecalculus. 1
A relational semantics for parallelism and nondeterminism in . . .
, 2011
"... We recently introduced an extensional model of the pure λcalculus living in a canonical cartesian closed category of sets and relations [6]. In the present paper, we study the nondeterministic features of this model. Unlike most traditional approaches, our way of interpreting nondeterminism does ..."
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Cited by 3 (0 self)
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We recently introduced an extensional model of the pure λcalculus living in a canonical cartesian closed category of sets and relations [6]. In the present paper, we study the nondeterministic features of this model. Unlike most traditional approaches, our way of interpreting nondeterminism does not require any additional powerdomain construction. We show that our model provides a straightforward semantics of nondeterminism (may convergence) by means of unions of interpretations, as well as of parallelism (must convergence) by means of a binary, nonidempotent operation available on the model, which is related to the mix rule of Linear Logic. More precisely, we introduce a λcalculus extended with nondeterministic choice and parallel composition, and we define its operational semantics (based on the may and must intuitions underlying our two additional operations). We describe the interpretation of this calculus in our model and show that this interpretation is ‘sensible’ with respect to our operational semantics: a term
A Convex Powerdomain over Lattices: its Logic and λCalculus
, 1997
"... To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive fro ..."
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Cited by 1 (1 self)
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To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive from the algebras of P the logic of D 1 , that is the axiomatic description of its compact elements. We then define a calculus and a type assignment system using the logic of D 1 as the related type theory. We prove that the filter model of this calculus, which is isomorphic to D 1 , is fully abstract with respect to the observational preorder of the λcalculus.