1,731 research outputs found
Sequent Calculus and Equational Programming
Proof assistants and programming languages based on type theories usually
come in two flavours: one is based on the standard natural deduction
presentation of type theory and involves eliminators, while the other provides
a syntax in equational style. We show here that the equational approach
corresponds to the use of a focused presentation of a type theory expressed as
a sequent calculus. A typed functional language is presented, based on a
sequent calculus, that we relate to the syntax and internal language of Agda.
In particular, we discuss the use of patterns and case splittings, as well as
rules implementing inductive reasoning and dependent products and sums.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759
A Spectrum of Applications of Automated Reasoning
The likelihood of an automated reasoning program being of substantial
assistance for a wide spectrum of applications rests with the nature of the
options and parameters it offers on which to base needed strategies and
methodologies. This article focuses on such a spectrum, featuring W. McCune's
program OTTER, discussing widely varied successes in answering open questions,
and touching on some of the strategies and methodologies that played a key
role. The applications include finding a first proof, discovering single
axioms, locating improved axiom systems, and simplifying existing proofs. The
last application is directly pertinent to the recently found (by R. Thiele)
Hilbert's twenty-fourth problem--which is extremely amenable to attack with the
appropriate automated reasoning program--a problem concerned with proof
simplification. The methodologies include those for seeking shorter proofs and
for finding proofs that avoid unwanted lemmas or classes of term, a specific
option for seeking proofs with smaller equational or formula complexity, and a
different option to address the variable richness of a proof. The type of proof
one obtains with the use of OTTER is Hilbert-style axiomatic, including details
that permit one sometimes to gain new insights. We include questions still open
and challenges that merit consideration.Comment: 13 page
Searching for a Solution to Program Verification=Equation Solving in CCS
International audienceUnder non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in game theory and provides âagent-specificâ results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model
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