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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)
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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 ".
Object Languages in a TypeTheoretic MetaFramework
 Workshop of Proof Transformation and Presentation and Proof Complexities (PTP'01
, 2001
"... . This paper concerns techniques for providing a convenient syntax for object languages implemented via a typetheoretic Logical Framework, and reports on work in progress. We first motivate the need for a typetheoretic logical framework. Firstly, we take the logical framework seriously as a me ..."
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Cited by 3 (3 self)
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. This paper concerns techniques for providing a convenient syntax for object languages implemented via a typetheoretic Logical Framework, and reports on work in progress. We first motivate the need for a typetheoretic logical framework. Firstly, we take the logical framework seriously as a metalanguage for implementing object languages (including object type theories). Another reason is the goal of building domainspecific reasoning tools which are implemented using type theory technology but do not require great expertise in type theory to use productively. We then present several examples of bidirectional translations between an encoding in the framework language and a more convenient syntax. The paper ends by discussing several techniques for implementing the translations and properties that we may require for the translation. Coercive subtyping is shown to help in the translation. 1
Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:
"... The formal system λδ is a typed λcalculus that pursues the unification of terms, types, environments and contexts as the main goal. λδ takes some features from the Automathrelated λcalculi and some from the pure type systems, but differs from both in that it does not include the Π construction wh ..."
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The formal system λδ is a typed λcalculus that pursues the unification of terms, types, environments and contexts as the main goal. λδ takes some features from the Automathrelated λcalculi and some from the pure type systems, but differs from both in that it does not include the Π construction while it provides for an abbreviation mechanism at the level of terms. λδ enjoys some important desirable properties such as the confluence of reduction, the correctness of types, the uniqueness of types up to conversion, the subject reduction of the type assignment, the strong normalization of the typed terms and, as a corollary, the decidability of type inference problem.
LambdaFree Logical Frameworks ✩
, 804
"... We present the definition of the logical framework TF, the Type Framework. TF is a lambdafree logical framework; it does not include lambdaabstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and show how it can be conservatively embedded in the logical f ..."
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We present the definition of the logical framework TF, the Type Framework. TF is a lambdafree logical framework; it does not include lambdaabstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and show how it can be conservatively embedded in the logical framework LF: its judgements can be seen as the judgements of LF that are in betanormal, etalong normal form. We show how several properties, such as the injectivity of constants and the strong normalisation of an object theory, can be proven more easily in TF, and then ‘lifted ’ to LF. Key words: logical framework, type theory, lambdafree
The Formal System λδ
, 2008
"... The formal system λδ is a typed λcalculus that pursues the unification of terms, types, environments and contexts as the main goal. λδ takes some features from the Automathrelated λcalculi and some from the pure type systems, but differs from both in that it does not include the Π construction wh ..."
Abstract
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The formal system λδ is a typed λcalculus that pursues the unification of terms, types, environments and contexts as the main goal. λδ takes some features from the Automathrelated λcalculi and some from the pure type systems, but differs from both in that it does not include the Π construction while it provides for an abbreviation mechanism at the level of terms. λδ enjoys some important desirable properties such as the confluence of reduction, the correctness of types, the uniqueness of types up to conversion, the subject reduction of the type assignment, the strong normalization of the typed terms and, as a corollary, the decidability of type inference problem.
The Formal System λδ
, 2008
"... The formal system λδ is a typed λcalculus that pursues the unification of terms, types, environments and contexts as the main goal. λδ takes some features from the Automathrelated λcalculi and some from the pure type systems, but differs from both in that it does not include the Π construction wh ..."
Abstract
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The formal system λδ is a typed λcalculus that pursues the unification of terms, types, environments and contexts as the main goal. λδ takes some features from the Automathrelated λcalculi and some from the pure type systems, but differs from both in that it does not include the Π construction while it provides for an abbreviation mechanism at the level of terms. λδ enjoys some important desirable properties such as the confluence of reduction, the correctness of types, the uniqueness of types up to conversion, the subject reduction of the type assignment, the strong normalization of the typed terms and, as a corollary, the decidability of type inference problem.
λTypes on the λCalculus with Abbreviations
, 2007
"... In this paper the author presents λδ, a λtyped λcalculus with a single λ binder and abbreviations. This calculus pursues the reuse of the term constructions both at the level of types and at the level of contexts as the main goal. Up to conversion λδ shares with Church λ → the subset of typable te ..."
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In this paper the author presents λδ, a λtyped λcalculus with a single λ binder and abbreviations. This calculus pursues the reuse of the term constructions both at the level of types and at the level of contexts as the main goal. Up to conversion λδ shares with Church λ → the subset of typable terms but in the “propositions as types ” perspective it can encode the implicative fragment of predicative logic without quantifiers because dependent types are allowed. λδ enjoys the properties of Church λ → (mainly subject conversion, strong normalization and decidability of type inference) and, in addition, it satisfies the correctness of types and the uniqueness of types up to conversion. We stress that λδ differs from the Automathrelated λcalculi in that they do not provide for an abbreviation construction at the level of terms. Moreover, unlike many λcalculi, λδ features a type hierarchy with an infinite number of levels both above and below any reference point.