Results 1  10
of
34
On Equivalence and Canonical Forms in the LF Type Theory
 ACM Transactions on Computational Logic
, 2001
"... Decidability of definitional equality and conversion of terms into canonical form play a central role in the metatheory of a typetheoretic logical framework. Most studies of definitional equality are based on a confluent, stronglynormalizing notion of reduction. Coquand has considered a different ..."
Abstract

Cited by 83 (16 self)
 Add to MetaCart
Decidability of definitional equality and conversion of terms into canonical form play a central role in the metatheory of a typetheoretic logical framework. Most studies of definitional equality are based on a confluent, stronglynormalizing notion of reduction. Coquand has considered a different approach, directly proving the correctness of a practical equivalence algorithm based on the shape of terms. Neither approach appears to scale well to richer languages with unit types or subtyping, and neither directly addresses the problem of conversion to canonical form.
A concurrent logical framework I: Judgments and properties
, 2003
"... The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous con ..."
Abstract

Cited by 73 (25 self)
 Add to MetaCart
The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous connectives# of intuitionistic linear logic, encapsulated in a monad. LLF is itself a conservative extension of LF with the asynchronous connectives #, & and #.
A Concurrent Logical Framework II: Examples and Applications
, 2002
"... CLF is a new logical framework with an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous connectives # of intuitionistic linear logic, encapsulated in a monad. LLF is itself a conservative extension of LF with the ..."
Abstract

Cited by 45 (29 self)
 Add to MetaCart
CLF is a new logical framework with an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous connectives # of intuitionistic linear logic, encapsulated in a monad. LLF is itself a conservative extension of LF with the asynchronous connectives #.
A languagebased approach to functionally correct imperative programming
 IN PROCEEDINGS OF THE 10TH INTERNATIONAL CONFERENCE ON FUNCTIONAL PROGRAMMING (ICFP05
, 2005
"... In this paper a languagebased approach to functionally correct imperative programming is proposed. The approach is based on a programming language called RSP1, which combines dependent types, general recursion, and imperative features in a typesafe way, while preserving decidability of type checki ..."
Abstract

Cited by 33 (8 self)
 Add to MetaCart
In this paper a languagebased approach to functionally correct imperative programming is proposed. The approach is based on a programming language called RSP1, which combines dependent types, general recursion, and imperative features in a typesafe way, while preserving decidability of type checking. The methodology used is that of internal verification, where programs manipulate programmersupplied proofs explicitly as data. The fundamental technical idea of RSP1 is to identify problematic operations as impure, and keep them out of dependent types. The resulting language is powerful enough to verify statically nontrivial properties of imperative and functional programs. The paper presents the ideas through the examples of statically verified merge sort, statically verified imperative binary search trees, and statically verified directed acyclic graphs. This paper is an extended version of [30].
A Concurrent Logical Framework: The Propositional Fragment
, 2003
"... We present the propositional fragment CLF0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations ..."
Abstract

Cited by 31 (3 self)
 Add to MetaCart
We present the propositional fragment CLF0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations. This separation leads to a tractable notion of definitional equality that identifies computations di#ering only in the order of execution of independent steps. From a logical point of view our type theory can be seen as a novel combination of lax logic and dual intuitionistic linear logic. An encoding of a small Petri net exemplifies the representation methodology, which can be summarized as "concurrent computations as monadic expressions ".
Tabled HigherOrder Logic Programming
 In 20th International Conference on Automated Deduction
, 2003
"... Elf is a general metalanguage for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each ..."
Abstract

Cited by 26 (11 self)
 Add to MetaCart
Elf is a general metalanguage for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each particular logical system. The traditional logic programming paradigm is extended by replacing firstorder terms with dependently typed terms and allowing implication and universal quantification in the bodies of clauses. These higherorder features allow us to model concisely and elegantly conditions on variables and the discharge of assumptions which are prevalent in many logical systems. However, many specifications are not executable under the traditional logic programming semantics and performance may be hampered by redundant computation. To address these problems, I propose a tabled higherorder logic programming interpretation for Elf. Some redundant computation is eliminated by memoizing subcomputation and reusing its result later. If we do not distinguish different proofs for a property, then search based on tabled logic programming is complete and terminates for programs with bounded recursion. In this proposal, I present a prooftheoretical characterization for tabled higherorder logic programming. It is the basis of the implemented prototype for tabled logic programming interpreter for Elf. Preliminary experiments indicate that many more logical specifications are executable under the tabled semantics. In addition, tabled computation leads to more efficient execution of programs. The goal of the thesis is to demonstrate that tabled logic programming allows us to efficiently automate reasoning with and about logical systems in the logical f...
Propositions as [Types]
, 2001
"... Image factorizations in regular categories are stable under pullbacks, so they model a natural modal operator in dependent type theory. This unary type constructor [A] has turned up previously in a syntactic form as a way of erasing computational content, and formalizing a notion of proof irrelevanc ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
Image factorizations in regular categories are stable under pullbacks, so they model a natural modal operator in dependent type theory. This unary type constructor [A] has turned up previously in a syntactic form as a way of erasing computational content, and formalizing a notion of proof irrelevance. Indeed, semantically, the notion of a support is sometimes used as surrogate proposition asserting inhabitation of an indexed family. We give rules for bracket types in dependent type theory and provide complete semantics using regular categories. We show that dependent type theory with the unit type, strong extensional equality types, strong dependent sums, and bracket types is the internal type theory of regular categories, in the same way that the usual dependent type theory with dependent sums and products is the internal type theory of locally cartesian closed categories. We also show how to interpret rstorder logic in type theory with brackets, and we make use of the translation to compare type theory with logic. Specically, we show that the propositionsastypes interpretation is complete with respect to a certain fragment of intuitionistic rstorder logic. As a consequence, a modied doublenegation translation into type theory (without bracket types) is complete for all of classical rstorder logic.
Dependent Session Types via Intuitionistic Linear Type Theory
"... We develop an interpretation of linear type theory as dependent session types for a term passing extension of the πcalculus. The type system allows us to express rich constraints on sessions, such as interface contracts and proofcarrying certification, which go beyond existing session type systems ..."
Abstract

Cited by 12 (10 self)
 Add to MetaCart
We develop an interpretation of linear type theory as dependent session types for a term passing extension of the πcalculus. The type system allows us to express rich constraints on sessions, such as interface contracts and proofcarrying certification, which go beyond existing session type systems, and are here justified on purely logical grounds. We can further refine our interpretation using proof irrelevance to eliminate communication overhead for proofs between trusted parties. Our technical results include type preservation and global progress, which in our setting naturally imply compliance to all properties declared in interface contracts expressed by dependent types.
On the strength of proofirrelevant type theories
 of Lecture Notes in Computer Science
, 2006
"... Vol. 4 (3:13) 2008, pp. 1–20 ..."
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 7 (5 self)
 Add to MetaCart
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.