Results 1 
7 of
7
Logical Relations for Monadic Types
, 2002
"... Logical relations and their generalizations are a fundamental tool in proving properties of lambdacalculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi's computational lambdacalculus ..."
Abstract

Cited by 19 (7 self)
 Add to MetaCart
Logical relations and their generalizations are a fundamental tool in proving properties of lambdacalculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi's computational lambdacalculus. The treatment is categorical, and is based on notions of subsconing and distributivity laws for monads. Our approach has a number of interesting applications, including cases for lambdacalculi with nondeterminism (where being in logical relation means being bisimilar), dynamic name creation, and probabilistic systems.
Logical Predicates for Intuitionistic Linear Type Theories
 In Typed Lambda Calculi and Applications (TLCA'99), Lecture Notes in Computer Science 1581
, 1999
"... We develop a notion of Kripkelike parameterized logical predicates for two fragments of intuitionistic linear logic (MILL and DILL) in terms of their categorytheoretic models. Such logical predicates are derived from the categorical glueing construction combined with the free symmetric monoidal co ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
We develop a notion of Kripkelike parameterized logical predicates for two fragments of intuitionistic linear logic (MILL and DILL) in terms of their categorytheoretic models. Such logical predicates are derived from the categorical glueing construction combined with the free symmetric monoidal cocompletion. As applications, we obtain full completeness results of translations between linear type theories.
Typedirected specialization of polymorphism
 in Proc. International Conference on Theoretical Aspects of Computer Software, Springer LNCS 1281
, 1999
"... Flexibility of programming and efficiency of program execution are two important features of a programming language. Unfortunately, however, these two features conflict each other in design and implementation of a modern statically typed programming language. Flexibility is model of computation, whi ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Flexibility of programming and efficiency of program execution are two important features of a programming language. Unfortunately, however, these two features conflict each other in design and implementation of a modern statically typed programming language. Flexibility is model of computation, while efficiency requires optimal use of lowlevel primitives specialized to individual data structures. The motivation of this work is to reconcile these two features by developing a mechanism for specializing polymorphic primitives based on static type information. We analyze the existing methods for compiling a record calculus and an unboxed calculus, extract their common structure, and develop a framework for typedirected specialization of polymorphism. 1
Logical Relations, Data Abstraction, and Structured Fibrations
"... We develop a notion of equivalence between interpretations of the simply typed calculus together with an equationally dened abstract datatype, and we show that two interpretations are equivalent if and only if they are linked by a logical relation. We show that our construction generalises from th ..."
Abstract
 Add to MetaCart
We develop a notion of equivalence between interpretations of the simply typed calculus together with an equationally dened abstract datatype, and we show that two interpretations are equivalent if and only if they are linked by a logical relation. We show that our construction generalises from the simply typed calculus to include the linear calculus and calculi with additional type and term constructors, such as those given by sum types or by a strong monad for modelling phenomena such as partiality or nondeterminism. This is all done in terms of category theoretic structure, using  brations to model logical relations following Hermida, and adapting Jung and Tiuryn's logical relations of varying arity to provide the completeness results, which form the heart of the work.
On a Semantic Definition of Data Independence
, 2002
"... A variety of results which enable model checking of important classes of infinitestate systems are based on exploiting the property of data independence. The literature contains a number of definitions of variants of data independence which are by syntactic restrictions in particular formalisms. Mo ..."
Abstract
 Add to MetaCart
A variety of results which enable model checking of important classes of infinitestate systems are based on exploiting the property of data independence. The literature contains a number of definitions of variants of data independence which are by syntactic restrictions in particular formalisms. More recently, data independence was defined for labelled transition systems using logical relations, enabling results about data independent systems to be proved without reference to a particular syntax. In this paper, we show that the semantic definition is suciently strong for this purpose. More precisely, it was known that any syntactically data independent symbolic LTS denotes a semantically data independent family of LTSs, but here we show that the converse also holds.
Logical Relations for Dynamic . . .
 IN PROC. CSL/KGL'03, VOLUME 2803 OF LNCS
, 2003
"... Pitts and Stark's nucalculus is a typed lambdacalculus which forms a basis for the study of interaction between higherorder functions and dynamically created names. A similar approach has received renewed attention recently through Sumii and Pierce's cryptographic lambdacalculus, which deals ..."
Abstract
 Add to MetaCart
Pitts and Stark's nucalculus is a typed lambdacalculus which forms a basis for the study of interaction between higherorder functions and dynamically created names. A similar approach has received renewed attention recently through Sumii and Pierce's cryptographic lambdacalculus, which deals with security protocols. Logical relations are a powerful tool to prove properties of such a calculus, notably observational equivalence. While Pitts and Stark construct a logical relation for the nucalculus, it rests heavily on operational aspects of the calculus and is hard to be extended. We propose an alternative Kripke logical relation for the nucalculus, which is derived naturally from the categorical model of the nucalculus and the general notion of Kripke logical relation. This is also related to the Kripke logical relation for the name creation monad by GoubaultLarrecq et al. (CSL'2002), which the authors claimed had similarities with Pitts and Stark's logical relation. We show that their Kripke logical relation for names is strictly weaker than Pitts and Stark's. We also show that our Kripke logical relation, which extends the de nition of GoubaultLarrecq et al., is equivalent to Pitts and Stark's up to rstorder types; our de nition rests on purely semantic constituents, and dispenses with the detours through operational semantics that Pitts and Stark use.