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Metatheoretical Results for a Modal λCalculus
, 2000
"... This paper presents the proofs of the strong normalization, subject reduction, and ChurchRosser theorems for a presentation of the intuitionistic modal calculus S4. It is adapted from Healfdene Goguen's thesis, where these properties are shown for the simply typed  calculus and for Luo's type ..."
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This paper presents the proofs of the strong normalization, subject reduction, and ChurchRosser theorems for a presentation of the intuitionistic modal calculus S4. It is adapted from Healfdene Goguen's thesis, where these properties are shown for the simply typed  calculus and for Luo's type theory UTT. Following this method, we introduce the notion of typed operational semantics for our system. We dene a notion of typed substitution for our system, which has context stacks instead of the usual contexts. This latter peculiarity leads to the main diculties and consequently to the main original features in our proofs. The techniques elaborated in this work have already been found useful in recent works [DL98, DL99] and should be further exploited to prove the properties of other systems based on modality. 1 Introduction We present here proofs of metatheoretic results for the modal calculus IS4 (see, for example, [Che90] for a classication of modal logics), in the ...
Metatheoretical Results for a Modal λCalculus
, 2000
"... This paper presents the proofs of the strong normalization, subject reduction, and ChurchRosser theorems for a presentation of the intuitionistic modal λcalculus S4. It is adapted from Healfdene Goguen's thesis, where these properties are shown for the simply typed λcalculus and for Luo's type ..."
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Cited by 3 (0 self)
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This paper presents the proofs of the strong normalization, subject reduction, and ChurchRosser theorems for a presentation of the intuitionistic modal λcalculus S4. It is adapted from Healfdene Goguen's thesis, where these properties are shown for the simply typed λcalculus and for Luo's type theory UTT. Following this method, we introduce the notion of typed operational semantics for our system. We define a notion of typed substitution for our system, which has context stacks instead of the usual contexts. This latter peculiarity leads to the main diculties and consequently to the main original features in our proofs. The techniques elaborated in this work have already been found useful in recent works [DL98, DL99] and should be further exploited to prove the properties of other systems based on modality.
Refinement Types for Logical Frameworks
, 2010
"... The logical framework LF and its metalogic Twelf can be used to encode and reason about a wide variety of logics, languages, and other deductive systems in a formal, machinecheckable way. Recent studies have shown that MLlike languages can profitably be extended with a notion of subtyping called r ..."
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The logical framework LF and its metalogic Twelf can be used to encode and reason about a wide variety of logics, languages, and other deductive systems in a formal, machinecheckable way. Recent studies have shown that MLlike languages can profitably be extended with a notion of subtyping called refinement types. A refinement type discipline uses an extra layer of term classification above the usual type system to more accurately capture certain properties of terms. I propose that adding refinement types to LF is both useful and practical. To support the claim, I exhibit an extension of LF with refinement types called LFR, work out important details of its metatheory, delineate a practical algorithm for refinement type reconstruction, and present several case studies that highlight the utility of refinement types for formalized mathematics. In the end I find that refinement types and LF are a match made in heaven: refinements enable many rich new modes of expression, and the simplicity of
Characterizing Strongly Normalizing Terms of a lambdaCalculus with Generalized Applications via Intersection Types
"... An intersection type assignment system for the extension LJ of the untyped lcalculus, introduced by Joachimski and Matthes, is given and proven to characterize the strongly normalizing terms of LJ. Since LJ's generalized applications naturally allow permutative/commuting conversions, this is th ..."
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An intersection type assignment system for the extension LJ of the untyped lcalculus, introduced by Joachimski and Matthes, is given and proven to characterize the strongly normalizing terms of LJ. Since LJ's generalized applications naturally allow permutative/commuting conversions, this is the first analysis of a term rewrite system with permutative conversions by help of intersection types. Two proofs are given for the fact that the typable terms are strongly normalizing: One by the computability predicates method a la Tait and one showing directly that strongly normalizing typable terms are closed under (generalized) application and substitution. It is also shown that a straightforward extension of the type assignment for lcalculus fails to capture the strongly normalizing terms. Keywords Intersection Types, Strong Normalization, Permutative Conversions, Saturated Sets. 1 Introduction In [5] an extension LJ of lcalculus with generalized applications inspired by vo...
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, 2010
"... Technology Institute (ICTI) at Carnegie Mellon University, and by generous support from ..."
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Technology Institute (ICTI) at Carnegie Mellon University, and by generous support from
Equality to Equals and Unequals: A Revisit of the Equivalence and Nonequivalence Criteria in ClassLevel Testing of ObjectOriented Software
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2013
"... Algebraic specifications have been used in the testing of objectoriented programs and received much attention since the 1990s. It is generally believed that classlevel testing based on algebraic specifications involves two independent aspects: the testing of equivalent and nonequivalent ground ter ..."
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Algebraic specifications have been used in the testing of objectoriented programs and received much attention since the 1990s. It is generally believed that classlevel testing based on algebraic specifications involves two independent aspects: the testing of equivalent and nonequivalent ground terms. Researchers have cited intuitive examples to illustrate the philosophy that even if an implementation satisfies all the requirements specified by the equivalence of ground terms, it may still fail to satisfy some of the requirements specified by the nonequivalence of ground terms. Thus, both the testing of equivalent ground terms and the testing of nonequivalent ground terms have been considered as significant and cannot replace each other. In this paper, we present an innovative finding that, given any canonical specification of a class with proper imports, a complete implementation satisfies all the observationally equivalent ground terms if and only if it satisfies all the observationally nonequivalent ground terms. As a result, these two aspects of software testing cover each other and can therefore replace each other. These findings provide a deeper understanding of software testing based on algebraic specifications, rendering the theory more elegant and complete. We also highlight a couple of important practical implications of our theoretical results.