80 research outputs found
A standardisation proof for algebraic pattern calculi
This work gives some insights and results on standardisation for call-by-name
pattern calculi. More precisely, we define standard reductions for a pattern
calculus with constructor-based data terms and patterns. This notion is based
on reduction steps that are needed to match an argument with respect to a given
pattern. We prove the Standardisation Theorem by using the technique developed
by Takahashi and Crary for lambda-calculus. The proof is based on the fact that
any development can be specified as a sequence of head steps followed by
internal reductions, i.e. reductions in which no head steps are involved.Comment: In Proceedings HOR 2010, arXiv:1102.346
Physics, Topology, Logic and Computation: A Rosetta Stone
In physics, Feynman diagrams are used to reason about quantum processes. In
the 1980s, it became clear that underlying these diagrams is a powerful analogy
between quantum physics and topology: namely, a linear operator behaves very
much like a "cobordism". Similar diagrams can be used to reason about logic,
where they represent proofs, and computation, where they represent programs.
With the rise of interest in quantum cryptography and quantum computation, it
became clear that there is extensive network of analogies between physics,
topology, logic and computation. In this expository paper, we make some of
these analogies precise using the concept of "closed symmetric monoidal
category". We assume no prior knowledge of category theory, proof theory or
computer science.Comment: 73 pages, 8 encapsulated postscript figure
Non-parametric statistical analysis of spatially distributed functional data
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