Examinando por Autor "Dybjer, P."

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    Combining interactive and automatic reasoning in first order theories of functional programs
    (SPRINGER, 2012-01-01) Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    We propose a new approach to the computer-assisted verification of functional programs. We work in first order theories of functional programs which are obtained by extending Aczel's first order theory of combinatory formal arithmetic with positive inductive and coinductive predicates. Rather than building a special purpose system we implement our theories in Agda, a proof assistant for dependent type theory which can be used as a generic theorem prover. Agda provides support for interactive reasoning by encoding first order theories using the formulae-as-types principle. Further support is provided by off-the-shelf automatic theorem provers for first order logic which can be called by a program which translates Agda representations of first order formulae into the TPTP language understood by the provers. We show some examples where we combine interactive and automatic reasoning, covering both proof by induction and coinduction. © 2012 Springer-Verlag Berlin Heidelberg.
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    Embedding a logical Theory of Constructions in agda
    (2009-01-01) Bove, A.; Dybjer, P.; Sicard-Ra?irez, A.; Bove, A.; Dybjer, P.; Sicard-Ra?irez, A.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    We propose a new way to reason about general recursive functional in the dependently typed programming language Agda,is based on Martin-Löf's intuitionistic type theory. We show to embed an external programming logic, Aczel's Logical Theory Constructions (LTC) inside Agda. To this end we postulate existence of a domain of untyped functional programs and the rules for these programs. Furthermore, we represent the notions in LTC (intuitionistic predicate logic with equality,totality predicates) as inductive notions in Agda. To illustrate approach we specify an LTC-style logic for PCF, and show to prove the termination and correctness of a general recursive for computing the greatest common divisor of two numbers. © 2009.