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Physics, Topology, Logic and Computation: A Rosetta Stone
, 2009
"... Category theory is a very general formalism, but there is a certain special way that physicists use categories which turns out to have close analogues in topology, logic and computation. A category has objects and morphisms, which represent things and ways to go between things. In physics, the objec ..."
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Category theory is a very general formalism, but there is a certain special way that physicists use categories which turns out to have close analogues in topology, logic and computation. A category has objects and morphisms, which represent things and ways to go between things. In physics, the objects are often physical systems, and the morphisms are processes turning a state of one physical system into a state of another system — perhaps
Four Equivalent Equivalences of Reductions
, 2002
"... Two coinitial reductions in a term rewriting system are said to be equivalent if they perform the same steps, albeit maybe in a di#erent order. We present four characterisations of such a notion of equivalence, based on permutation, standardisation, labelling and projection, respectively. We prove ..."
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Two coinitial reductions in a term rewriting system are said to be equivalent if they perform the same steps, albeit maybe in a di#erent order. We present four characterisations of such a notion of equivalence, based on permutation, standardisation, labelling and projection, respectively. We prove that the characterisations all yield the same notion of equivalence, for the class of firstorder leftlinear term rewriting systems. A crucial role in our development is played by the notion of a proof term. 1