Results 1  10
of
11
Prelogical Relations
, 1999
"... this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results ..."
Abstract

Cited by 26 (5 self)
 Add to MetaCart
this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results
Lambda Definability with Sums via Grothendieck Logical Relations
, 1999
"... . We introduce a notion of Grothendieck logical relation and use it to characterise the definability of morphisms in stable bicartesian closed categories by terms of the simplytyped lambda calculus with finite products and finite sums. Our techniques are based on concepts from topos theory, how ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
. We introduce a notion of Grothendieck logical relation and use it to characterise the definability of morphisms in stable bicartesian closed categories by terms of the simplytyped lambda calculus with finite products and finite sums. Our techniques are based on concepts from topos theory, however our exposition is elementary. Introduction The use of logical relations as a tool for characterising the definable elements in a model of the simplytyped calculus originated in the work of Plotkin [10], who obtained such a characterisation of the definable elements in the full type hierarchy using a notion of Kripke logical relation. Subsequently, the more general notion of a Kripke logical relation of varying arity was developed by Jung and Tiuryn, and shown to characterise the definable elements in any Henkin model [4]. Although not emphasised in [4], relations of varying arity are powerful enough to characterise relative definability with respect to any given set of elements con...
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
(Show Context)
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
Categorical Glueing and Logical Predicates for Models of Linear Logic
, 1999
"... We give a series of glueing constructions for categorical models of fragments of linear logic. Specifically, we consider the glueing of (i) symmetric monoidal closed categories (models of Multiplicative Intuitionistic Linear Logic), (ii) symmetric monoidal adjunctions (for interpreting the modality ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
(Show Context)
We give a series of glueing constructions for categorical models of fragments of linear logic. Specifically, we consider the glueing of (i) symmetric monoidal closed categories (models of Multiplicative Intuitionistic Linear Logic), (ii) symmetric monoidal adjunctions (for interpreting the modality !) and (iii) autonomous categories (models of Multiplicative Linear Logic); the glueing construction for autonomous categories is a mild generalization of the double glueing construction due to Hyland and Tan. Each of the glueing techniques can be used for creating interesting models of linear logic. In particular, we use them, together with the free symmetric monoidal cocompletion, for deriving Kripkelike parameterized logical predicates (logical relations) for the fragments of linear logic. As an application, we show full completeness results for translations between linear type theories. Contents 1 Introduction 3 2 Preliminaries 4 2.1 Symmetric Monoidal Structures . . . . . . . ....
Girard Translation and Logical Predicates
, 2000
"... We present a short proof of a folklore result: the Girard translation from the simply typed lambda calculus to the linear lambda calculus is fully complete. The proof makes use of a notion of logical predicates for intuitionistic linear logic. While the main result is of independent interest, this p ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
We present a short proof of a folklore result: the Girard translation from the simply typed lambda calculus to the linear lambda calculus is fully complete. The proof makes use of a notion of logical predicates for intuitionistic linear logic. While the main result is of independent interest, this paper can be read as a tutorial on this proof technique for reasoning about relations between type theories.
On the geometry of intuitionistic S4 proofs
 Homology, Homotopy and Applications
, 2003
"... ..."
(Show Context)
Complete Lax Logical Relations for Cryptographic LambdaCalculi
 In Proceedings of CSL’2004, volume 3210 of LNCS
, 2004
"... Security properties are profitably expressed using notions of contextual equivalence, and logical relations are a powerful proof technique to establish contextual equivalence in typed lambda calculi, see e.g. Sumii and Pierce's logical relation for a cryptographic lambdacalculus. We clarify Su ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Security properties are profitably expressed using notions of contextual equivalence, and logical relations are a powerful proof technique to establish contextual equivalence in typed lambda calculi, see e.g. Sumii and Pierce's logical relation for a cryptographic lambdacalculus. We clarify Sumii and Pierce's approach, showing that the right tool is prelogical relations, or lax logical relations in general: relations should be lax at encryption types, notably. To explore the difficult aspect of fresh name creation, we use Moggi's monadic lambdacalculus with constants for cryptographic primitives, and Stark's name creation monad. We define logical relations which are lax at encryption and function types but strict (nonlax) at various other types, and show that they are sound and complete for contextual equivalence at all types.
Logical Relations for Monadic Types †
, 2004
"... 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. Th ..."
Abstract
 Add to MetaCart
(Show Context)
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, mono factorization systems, and monad morphisms. Our approach has a number of interesting applications, including cases for lambdacalculi with nondeterminism (where being in logical relation means being bisimilar), dynamic name
and
"... We study a weakening of the notion of logical relations, called prelogical relations, that has many of the features that make logical relations so useful as well as further algebraic properties including composability. The basic idea is simply to require the reverse implication in the definition of ..."
Abstract
 Add to MetaCart
We study a weakening of the notion of logical relations, called prelogical relations, that has many of the features that make logical relations so useful as well as further algebraic properties including composability. The basic idea is simply to require the reverse implication in the definition of logical relations to hold only for pairs of functions that are expressible by the same lambda term. Prelogical relations are the minimal weakening of logical relations that gives composability for extensional structures and simultaneously the most liberal definition that gives the Basic Lemma. Prelogical predicates (i.e., unary prelogical relations) coincide with sets that are invariant under Kripke logical relations with varying arity as introduced by Jung and Tiuryn, and prelogical relations are the closure under projection and intersection of logical relations. These conceptually independent characterizations of prelogical relations suggest that the concept is rather intrinsic and robust. The use of prelogical relations gives an improved version of Mitchell’s representation independence theorem which characterizes observational equivalence for all signatures rather than just for firstorder signatures. Prelogical relations can be used in place of logical relations to give an account of data refinement where the fact that prelogical relations compose explains why stepwise refinement is sound.
Under consideration for publication in Math. Struct. in Comp. Science Logical Relations for Monadic Types †
, 2005
"... 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. Th ..."
Abstract
 Add to MetaCart
(Show Context)
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, mono factorization systems, and monad morphisms. Our approach has a number of interesting applications, including cases for lambdacalculi with nondeterminism (where being in logical relation means being bisimilar), dynamic name