27,007 research outputs found
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
Theorem proving support in programming language semantics
We describe several views of the semantics of a simple programming language
as formal documents in the calculus of inductive constructions that can be
verified by the Coq proof system. Covered aspects are natural semantics,
denotational semantics, axiomatic semantics, and abstract interpretation.
Descriptions as recursive functions are also provided whenever suitable, thus
yielding a a verification condition generator and a static analyser that can be
run inside the theorem prover for use in reflective proofs. Extraction of an
interpreter from the denotational semantics is also described. All different
aspects are formally proved sound with respect to the natural semantics
specification.Comment: Propos\'e pour publication dans l'ouvrage \`a la m\'emoire de Gilles
Kah
Did Lobachevsky Have A Model Of His "imaginary Geometry"?
The invention of non-Euclidean geometries is often seen through the optics of
Hilbertian formal axiomatic method developed later in the 19th century. However
such an anachronistic approach fails to provide a sound reading of
Lobachevsky's geometrical works. Although the modern notion of model of a given
theory has a counterpart in Lobachevsky's writings its role in Lobachevsky's
geometrical theory turns to be very unusual. Lobachevsky doesn't consider
various models of Hyperbolic geometry, as the modern reader would expect, but
uses a non-standard model of Euclidean plane (as a particular surface in the
Hyperbolic 3-space). In this paper I consider this Lobachevsky's construction,
and show how it can be better analyzed within an alternative non-Hilbertian
foundational framework, which relates the history of geometry of the 19th
century to some recent developments in the field.Comment: 31 pages, 8 figure
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