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Benjamin Werner - One of the best experts on this subject based on the ideXlab platform.

  • On the strength of proof-irrelevant type theories
    Lecture Notes in Computer Science, 2006
    Co-Authors: Benjamin Werner
    Abstract:

    We present a type theory with some proof-irrelevance built into the Conversion Rule. We argue that this feature is particularly useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types of the theory of PVS. Finally we show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of equality, that is, almost classical logic.

  • IJCAR - On the strength of proof-irrelevant type theories
    Automated Reasoning, 2006
    Co-Authors: Benjamin Werner
    Abstract:

    We present a type theory with some proof-irrelevance built into the Conversion Rule. We argue that this feature is particularly useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types of the theory of PVS. Finally we show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of equality, that is, almost classical logic.

Xiangxiaodong - One of the best experts on this subject based on the ideXlab platform.

David W. Cheung - One of the best experts on this subject based on the ideXlab platform.

  • Discovering and Reconciling Value Conflicts for Data Integration
    SSRN Electronic Journal, 2002
    Co-Authors: Weiguo Fan, Cheng Hian Goh, Stuart E. Madnick, David W. Cheung
    Abstract:

    The integration of data from autonomous and heterogeneous sources calls for the prior identification and resolution of semantic conflicts that may be present. Unfortunately, this requires the system integrator to sift through the data from disparate systems in a painstaking manner. In this paper, we suggest that this process can be (at least) partially automated by presenting a methodology and techniques for the discovery of potential semantic conflicts as well as the underlying data transformation needed to resolve the conflicts. Our methodology begins by classifying data value conflicts into two categories: context independent and context dependent. While context independent conflicts are usually caused by unexpected errors, the context dependent conflicts are primarily a result of the heterogeneity of underlying data sources. To facilitate data integration, data value Conversion Rules are proposed to describe the quantitative relationships among data values involving context dependent conflicts. A general approach is proposed to discover data value Conversion Rules from the data. The approach consists of five major steps: relevant attribute analysis, candidate model selection, Conversion function generation, Conversion function selection and Conversion Rule formation. It is being implemented in a prototype system, DIRECT, for business data using statistics based techniques. Preliminary study indicated that the proposed approach is promising.

  • Discovering and reconciling value conflicts for numerical data integration
    Information Systems, 2001
    Co-Authors: Weiguo Fan, Stuart E. Madnick, David W. Cheung
    Abstract:

    The built-up in Information Technology capital fueled by the Internet and cost-effectiveness of new telecommunications technologies has led to a proliferation of information systems that are in dire need to exchange information but incapable of doing so due to the lack of semantic interoperability. It is now evident that physical connectivity (the ability to exchange bits and bytes) is no longer adequate: the integration of data from autonomous and heterogeneous systems calls for the prior identification and resolution of semantic conflicts that may be present. Unfortunately, this requires the system integrator to sift through the data from disparate systems in a painstaking manner. We suggest that this process can be partially automated by presenting a methodology and technique for the discovery of potential semantic conflicts as well as the underlying data transformation needed to resolve the conflicts. Our methodology begins by classifying data value conflicts into two categories: context independent and context dependent. While context independent conflicts are usually caused by unexpected errors, the context dependent conflicts are primarily a result of the heterogeneity of underlying data sources. To facilitate data integration, data value Conversion Rules are proposed to describe the quantitative relationships among data values involving context dependent conflicts. A general approach is proposed to discover data value Conversion Rules from the data. The approach consists of the five major steps: relevant attribute analysis, candidate model selection, Conversion function generation, Conversion function selection and Conversion Rule formation. It is being implemented in a prototype system, DIRECT, for business data using statistics based techniques. Preliminary study using both synthetic and real world data indicated that the proposed approach is promising. r 2001 Elsevier Science Ltd. All rights reserved.

Lichong - One of the best experts on this subject based on the ideXlab platform.

Pierre-yves Strub - One of the best experts on this subject based on the ideXlab platform.

  • Coq without Type Casts: A Complete Proof of Coq Modulo Theory
    2017
    Co-Authors: Jean-pierre Jouannaud, Pierre-yves Strub
    Abstract:

    Incorporating extensional equality into a dependent intensional type system such as the Calculus of Constructions provides with stronger type-checking capabilities and makes the proof development closer to intuition. Since strong forms of extensionality lead to undecidable type-checking, a good trade-off is to extend intensional equality with a decidable first-order theory T, as done in CoqMT, which uses matching modulo T for the weak and strong elimination Rules, we call these Rules T-elimination. So far, type-checking in CoqMT is known to be decidable in presence of a cumulative hierarchy of universes and weak T-elimination. Further, it has been shown by Wang with a formal proof in Coq that consistency is preserved in presence of weak and strong elimination Rules, which actually implies consistency in presence of weak and strong T-elimination Rules since T is already present in the Conversion Rule of the calculus. We justify here CoqMT's type-checking algorithm by showing strong normalization as well as the Church-Rosser property of β-reductions augmented with CoqMT's weak and strong T-elimination Rules. This therefore concludes successfully the meta-theoretical study of CoqMT.

  • LPAR - Coq without Type Casts: A Complete Proof of Coq Modulo Theory
    2017
    Co-Authors: Jean-pierre Jouannaud, Pierre-yves Strub
    Abstract:

    Incorporating extensional equality into a dependent intensional type system such as the Calculus of Constructions provides with stronger type-checking capabilities and makes the proof development closer to intuition. Since strong forms of extensionality lead to undecidable type-checking, a good trade-off is to extend intensional equality with a decidable first-order theory T, as done in CoqMT, which uses matching modulo T for the weak and strong elimination Rules, we call these Rules T-elimination. So far, type-checking in CoqMT is known to be decidable in presence of a cumulative hierarchy of universes and weak T-elimination. Further, it has been shown by Wang with a formal proof in Coq that consistency is preserved in presence of weak and strong elimination Rules, which actually implies consistency in presence of weak and strong T-elimination Rules since T is already present in the Conversion Rule of the calculus.We justify here CoqMT’s type-checking algorithm by showing strong normalization as well as the Church-Rosser property of β-reductions augmented with CoqMT’s weak and strong T -elimination Rules. This therefore concludes successfully the meta-theoretical study of CoqMT.

  • Building Decision Procedures in the Calculus of Inductive Constructions
    2007
    Co-Authors: Frédéric Blanqui, Jean-pierre Jouannaud, Pierre-yves Strub
    Abstract:

    It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P' obtained from P thanks to possibly complex calculations. In this paper, we investigate a new version of the calculus of inductive constructions which incorporates arbitrary decision procedures into deduction via the Conversion Rule of the calculus. The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.