Softcover reprint of the original 1st ed. 1997, VII, 403 p.
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The Marktoberdorf Summer School 1995 'Logic of Computation' was the 16th in a series of Advanced Study Institutes under the sponsorship of the NATO Scientific Affairs Division held in Marktoberdorf. Its scientific goal was to survey recent progress on the impact of logical methods in software development. The courses dealt with many different aspects of this interplay, where major progress has been made. Of particular importance were the following. • The proofs-as-programs paradigm, which makes it possible to extract verified programs directly from proofs. Here a higher order logic or type theoretic setup of the underlying language has developed into a standard. • Extensions of logic programming, e.g. by allowing more general formulas and/or higher order languages. • Proof theoretic methods, which provide tools to deal with questions of feasibility of computations and also to develop a general mathematical understanding of complexity questions. • Rewrite systems and unification, again in a higher order context. Closely related is the now well-established Grabner basis theory, which recently has found interesting applications. • Category theoretic and more generally algebraic methods and techniques to analyze the semantics of programming languages. All these issues were covered by a team of leading researchers. Their courses were grouped under the following headings.
Content Level »Research
Keywords »Typentheorie - computer - logic - logic programming - program specification - program verification - programming - proof theory - type theory - verification
Lectures on Semantics: The Initial Algebra and Final Coalgebra Perspectives.- to Gröbner Bases.- Bounded Arithmetic and Propositional Proof Complexity.- The Structure of Nuprl’s Type Theory.- Axiomatisations, Proofs, and Formal Specifications of Algorithms: Commented Case Studies in the Coq Proof Assistant.- Some Proof Theory of First Order Logic Programming.- Timed Rewriting Logic for the Specification of Time-Sensitive Systems.- Logic Programming and Meta-Logic.- Proofs, Lambda Terms and Control Operators.- Basic Proof Theory with Applications to Computation.