6,295 research outputs found
The Algebraic View of Computation
We argue that computation is an abstract algebraic concept, and a computer is
a result of a morphism (a structure preserving map) from a finite universal
semigroup.Comment: 13 pages, final version will be published elsewher
The dagger lambda calculus
We present a novel lambda calculus that casts the categorical approach to the
study of quantum protocols into the rich and well established tradition of type
theory. Our construction extends the linear typed lambda calculus with a linear
negation of "trivialised" De Morgan duality. Reduction is realised through
explicit substitution, based on a symmetric notion of binding of global scope,
with rules acting on the entire typing judgement instead of on a specific
subterm. Proofs of subject reduction, confluence, strong normalisation and
consistency are provided, and the language is shown to be an internal language
for dagger compact categories.Comment: In Proceedings QPL 2014, arXiv:1412.810
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