Results 21  30
of
36
An interpretation of isabelle/hol in hol light
 In Furbach and Shankar [20
"... Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabe ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabelle logic that cannot be represented directly are elaborated to functors in OCaml. We demonstrate the effectiveness of the interpretation via an implementation, translating a significant part of the Isabelle standard library into HOL Light. 1
Hypergraphs and degrees of parallelism: A completeness result, in: I. Walukiewicz (Ed
 Proceedings of the 7th International Conference of Foundations of Software Science and Computation Structures – FOSSACS 2004
, 2004
"... Abstract. In order to study relative PCFdefinability of boolean functions, we associate a hypergraph Hf to any boolean function f (following [3, 5]). We introduce the notion of timed hypergraph morphism and show that it is: – Sound: if there exists a timed morphism from Hf to Hg then f is PCFdefin ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. In order to study relative PCFdefinability of boolean functions, we associate a hypergraph Hf to any boolean function f (following [3, 5]). We introduce the notion of timed hypergraph morphism and show that it is: – Sound: if there exists a timed morphism from Hf to Hg then f is PCFdefinable relatively to g. – Complete for subsequential functions: if f is PCFdefinable relatively to g, and g is subsequential, then there exists a timed morphism from Hf to Hg. We show that the problem of deciding the existence of a timed morphism between two given hypergraphs is NPcomplete. 1
Formalizing NonTermination of Recursive Programs
 J. of Logic and Algebraic Programming
, 2001
"... In applicative theories the recursion theorem provides a term rec which solves recursive equations. However, it is not provable that a solution obtained by rec is minimal. In the present paper we introduce an applicative theory in which it is possible to dene a least xed point operator. Still, o ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In applicative theories the recursion theorem provides a term rec which solves recursive equations. However, it is not provable that a solution obtained by rec is minimal. In the present paper we introduce an applicative theory in which it is possible to dene a least xed point operator. Still, our theory has a standard recursion theoretic interpretation. 1
Matching typed and untyped realizability (Extended abstract)
"... Realizability interpretations of logics are given by saying what it means for computational objects of some kind to realize logical formulae. The computational objects in question might be drawn from an untyped universe of computation, such as a partial combinatory algebra, or they might be typed ob ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Realizability interpretations of logics are given by saying what it means for computational objects of some kind to realize logical formulae. The computational objects in question might be drawn from an untyped universe of computation, such as a partial combinatory algebra, or they might be typed objects such as terms of a PCFstyle programming language. In some instances, one can show that a particular untyped realizability interpretation matches a particular typed one, in the sense that they give the same set of realizable formulae. In this case, we have a very good fit indeed between the typed language and the untyped realizability model—we refer to this condition as (constructive) logical full abstraction. We give some examples of this situation for a variety of extensions of PCF. Of particular interest are some models that are logically fully abstract for typed languages including nonfunctional features. Our results establish connections between what is computable in various programming languages, and what is true inside various realizability toposes. We consider some examples of logical formulae to illustrate these ideas, in particular their application to exact realnumber computability. The present article summarizes the material I presented at the Domains IV workshop, plus a few subsequent developments; it is really an extended abstract for a projected journal paper. No proofs are included in the present version. 0
Theory for Software Verification
, 2009
"... Semantic models are the basis for specification and verification of software. Operational, denotational, and axiomatic or algebraic methods offer complementary insights and reasoning techniques which are surveyed here. Unifying theories are needed to link models. Also considered are selected program ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Semantic models are the basis for specification and verification of software. Operational, denotational, and axiomatic or algebraic methods offer complementary insights and reasoning techniques which are surveyed here. Unifying theories are needed to link models. Also considered are selected programming features for which new models are needed.
Program Verification in Synthetic Domain Theory
, 1995
"... Synthetic Domain Theory provides a setting to consider domains as sets with certain closure properties for computing suprema of ascending chains. As a consequence the notion of domain can be internalized which allows one to construct and reason about solutions of recursive domain equations. Moreover ..."
Abstract
 Add to MetaCart
Synthetic Domain Theory provides a setting to consider domains as sets with certain closure properties for computing suprema of ascending chains. As a consequence the notion of domain can be internalized which allows one to construct and reason about solutions of recursive domain equations. Moreover, one can derive that all functions are continuous. In this thesis such a synthetic theory of domains (#domains) is developed based on a few axioms formulated in an adequate intuitionistic higherorder logic. This leads to an elegant theory of domains. It integrates the positive features of several approaches in the literature. In contrast to those, however, it is model independent and can therefore be formalized. A complete formalization of the whole theory of #domains has been coded into a proofchecker (Lego) for impredicative type theory. There one can exploit dependent types in order to express program modules and modular specifications. As an application of this theory an entirely fo...
Motivation and Background
"... P, also called the enumeration operators, are characterized by the equation F (x) = [ \Phi F (y) fi fi y x \Psi 1 for all x 2 P, where y x means that y is a finite subset of x. It follows that a continuous function is completely determined by the relation n 2 F (y) for n 2 N and y N: (1 ..."
Abstract
 Add to MetaCart
P, also called the enumeration operators, are characterized by the equation F (x) = [ \Phi F (y) fi fi y x \Psi 1 for all x 2 P, where y x means that y is a finite subset of x. It follows that a continuous function is completely determined by the relation n 2 F (y) for n 2 N and y N: (1) We say a continuous function F : P ! P is computable when the corresponding relation (1) is recursively enumerable. Relation (1) can also be identified with sets in P using suitable encodings. Whenever a topological space X is represented as a subspace of<F8.35
On Natural Nondcpo Domains
"... in his 87th year whose influence on me and help cannot be overstated. model for PCF of hereditarily sequential functionals is not ωcomplete and therefore not continuous in the traditional terminology (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to ..."
Abstract
 Add to MetaCart
in his 87th year whose influence on me and help cannot be overstated. model for PCF of hereditarily sequential functionals is not ωcomplete and therefore not continuous in the traditional terminology (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to a wider class of models such as the recently constructed by the author fully abstract (universal) model for PCF + = PCF + parallel if. Here we will present an outline of a general approach to this kind of “natural ” domains which, although being nondcpos, allow considering “naturally ” continuous functions (with respect to existing directed “pointwise”, or “natural ” least upper bounds) and also have appropriate version of “naturally ” algebraic and “naturally ” bounded complete “natural ” domains. This is the nondcpo analogue of the wellknown concept of Scott domains, or equivalently, the complete fspaces of Ershov. In fact, the latter version of natural domains, if considered under “natural ” Scott topology, exactly corresponds to the class of fspaces, not necessarily complete. 1
Equational Incompleteness and Incomparability Results for Lambda Calculus Functional Semantics
"... In this paper we establish the existence of a lambda theory which can be modeled in continuous semantics but neither in stable nor hypercoherent semantics. That give us ..."
Abstract
 Add to MetaCart
In this paper we establish the existence of a lambda theory which can be modeled in continuous semantics but neither in stable nor hypercoherent semantics. That give us