Results 11  20
of
113
A typed foundation for directional logic programming
 In Proc. Workshop on Extensions to Logic Programming
, 1992
"... Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and d ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
(Show Context)
Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and deadlockfreedom) and controlling concurrency. By using Girard’s linear logic, we are able to devise a type system that combines types and modes into a unified framework, and enables one to express directionality declaratively. The rich power of the type system allows outputs to be embedded in inputs and vice versa. Type checking guarantees that values have unique producers, but multiple consumers are still possible. From a theoretical point of view, this work provides a “logic programming interpretation ” of (the proofs of) linear logic, adding to the concurrency and functional programming interpretations that are already known. It also brings logic programming into the broader world of typed languages and typesaspropositions paradigm, enriching it with static scoping and higherorder features.
Efficient Parsing for CCGs with Generalized TypeRaised Categories
, 1997
"... A type of ‘nontraditional constituents’ motivates an extended class of Combinatory Categorial Grammars, CCGs with Generalized TypeRaised Categories (CCGGTRC) involving variables. Although the class of standard CCGs is known to be polynomially parsable, use of variables suggests more complexity fo ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
A type of ‘nontraditional constituents’ motivates an extended class of Combinatory Categorial Grammars, CCGs with Generalized TypeRaised Categories (CCGGTRC) involving variables. Although the class of standard CCGs is known to be polynomially parsable, use of variables suggests more complexity for processing GTRCs. This paper argues that polynomial parsing is still possible for CCGGTRC from practical and theoretical points of view. First, we show that an experimental parser runs polynomially in practice on a realistic fragment of Japanese by eliminating spurious ambiguity and excluding genuine ambiguities. Then, we present a worstcase polynomial recognition algorithm for CCGGTRC by extending the polynomial algorithm for the standard CCGs.
Constructively Formalizing Automata Theory
 Proof, Language and Interaction: Essays in Honour of Robert Milner
, 1997
"... We present a constructive formalization of the MyhillNerode theorem on the minimization of finite automata that follows the account in Hopcroft and Ullman's book Formal Languages and Their Relation to Automata. We chose to formalize this theorem because it illustrates many points critical to f ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
We present a constructive formalization of the MyhillNerode theorem on the minimization of finite automata that follows the account in Hopcroft and Ullman's book Formal Languages and Their Relation to Automata. We chose to formalize this theorem because it illustrates many points critical to formalization of computational mathematics, especially the extraction of an important algorithm from a proof as a method of knowing that the algorithm is correct. It also gave us an opportunity to experiment with a constructive implementation of quotient sets. We carried out the formalization in Nuprl, an interactive theorem prover based on constructive type theory. Nuprl borrows an implementation of the ML language from the LCF system of Milner, Gordon, and Wadsworth, and makes heavy use of the notion of tactic pioneered by Milner in LCF. We are interested in the pedagogical value of electronic formal mathematical texts and have put our formalization on the World Wide Web. Readers are invited to ...
Formal proof of provable security by gameplaying in a proof assistant
 In ProvSec 2007
, 2007
"... Abstract. Gameplaying is an approach to write security proofs that are easy to verify. In this approach, security definitions and intractable problems are written as programs called games and reductionist security proofs are sequences of game transformations. This bias towards programming languages ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Gameplaying is an approach to write security proofs that are easy to verify. In this approach, security definitions and intractable problems are written as programs called games and reductionist security proofs are sequences of game transformations. This bias towards programming languages suggests the implementation of a tool based on compiler techniques (syntactic program transformations) to build security proofs, but it also raises the question of the soundness of such a tool. In this paper, we advocate the formalization of gameplaying in a proof assistant as a tool to build security proofs. In a proof assistant, starting from just the formal definition of a probabilistic programming language, all the properties required in gamebased security proofs can be proved internally as lemmas whose soundness is ensured by proof theory. Concretely, we show how to formalize the gameplaying framework of Bellare and Rogaway in the Coq proof assistant, how to prove formally reusable lemmas such as the fundamental lemma of gameplaying, and how to use them to formally prove the PRP/PRF Switching Lemma. 1
TypeBased Structural Analysis for Modular Systems of Equations
 Proceedings of the 2nd International Workshop on EquationBased ObjectOriented Languages and Tools
"... This paper investigates a novel approach to a type system for modular systems of equations; i.e., equation systems constructed by composition of individual equation system fragments. The purpose of the type system is to ensure, to the extent possible, that the composed system is solvable. The centra ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
(Show Context)
This paper investigates a novel approach to a type system for modular systems of equations; i.e., equation systems constructed by composition of individual equation system fragments. The purpose of the type system is to ensure, to the extent possible, that the composed system is solvable. The central idea is to attribute a structural type to equation system fragments that reflects which variables occur in which equations. In many instances, this allows over and underdetermined system fragments to be identified separately, without first having to assemble all fragments into a complete system of equations. The setting of the paper is equationbased, noncausal modelling, specifically Functional Hybrid Modelling (FHM). However, the central ideas are not tied to FHM, but should be applicable to equationbased modelling languages in general, like Modelica, as well as to applications featuring modular systems of equations outside the field of modelling and simulation.
Probabilistic Modelling, Inference and Learning using Logical Theories
"... This paper provides a study of probabilistic modelling, inference and learning in a logicbased setting. We show how probability densities, being functions, can be represented and reasoned with naturally and directly in higherorder logic, an expressive formalism not unlike the (informal) everyday l ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
This paper provides a study of probabilistic modelling, inference and learning in a logicbased setting. We show how probability densities, being functions, can be represented and reasoned with naturally and directly in higherorder logic, an expressive formalism not unlike the (informal) everyday language of mathematics. We give efficient inference algorithms and illustrate the general approach with a diverse collection of applications. Some learning issues are also considered.
Using Modes to Ensure Subject Reduction for Typed Logic Programs with Subtyping
, 2000
"... We consider a general prescriptive type system with parametric polymorphism and subtyping for logic programs. The property of subject reduction expresses the consistency of the type system w.r.t. the execution model: if a program is welltyped, then all derivations starting in a welltyped goal are ..."
Abstract

Cited by 8 (7 self)
 Add to MetaCart
We consider a general prescriptive type system with parametric polymorphism and subtyping for logic programs. The property of subject reduction expresses the consistency of the type system w.r.t. the execution model: if a program is welltyped, then all derivations starting in a welltyped goal are again welltyped. It is wellestablished that without subtyping, this property is readily obtained for logic programs w.r.t. their standard (untyped) execution model. Here we give syntactic conditions that ensure subject reduction also in the presence of general subtyping relations between type constructors. The idea is to consider logic programs with a xed dataow, given by modes.
Näıve computational type theory
 Proof and SystemReliability, Proceedings of International Summer School Marktoberdorf, July 24 to August 5, 2001, volume 62 of NATO Science Series III
, 2002
"... ..."
(Show Context)
Markov’s principle for propositional type theory
 Computer Science Logic, Proceedings of the 10 th Annual Conference of the EACSL
, 2001
"... Abstract. In this paper we show how to extend a constructive type theory with a principle that captures the spirit of Markov’s principle from constructive recursive mathematics. Markov’s principle is especially useful for proving termination of specific computations. Allowing a limited form of class ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we show how to extend a constructive type theory with a principle that captures the spirit of Markov’s principle from constructive recursive mathematics. Markov’s principle is especially useful for proving termination of specific computations. Allowing a limited form of classical reasoning we get more powerful resulting system which remains constructive and valid in the standard constructive semantics of a type theory. We also show that this principle can be formulated and used in a propositional fragment of a type theory.
Integrated Verification in Type Theory (Lecture Notes)
, 1996
"... Contents 1 Introduction 2 2 Type Theory as a Programming Language 3 2.1 Hello World in Type Theory . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Hiding and argument synthesis . . . . . . . . . . . . . . . . . . . . . 4 2.3 Using dependent types in programming . . . . . . . . . . . . . . . . 4 ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Contents 1 Introduction 2 2 Type Theory as a Programming Language 3 2.1 Hello World in Type Theory . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Hiding and argument synthesis . . . . . . . . . . . . . . . . . . . . . 4 2.3 Using dependent types in programming . . . . . . . . . . . . . . . . 4 2.4 Higherorder sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Logic for free 8 3.1 Propositional logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Predicate logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4 Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.5 Inductively defined relations . . . . . . . . . . . . . . . . . . . . . . . 13 4 ALF's Type Theory 14 4.1 Judgements of Type Theory . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Conventions