We present an algebraic theory for a fragment of predicate logic. The fragment has disjunction, existential quantification and equality. It is not an algebraic theory in the classical sense, but rather within a new framework that we call ‘parameterized algebraic theories’.

We demonstrate the relevance of this algebraic presentation to computer science by identifying a programming language in which every type carries a model of the algebraic theory. The result is a simple functional logic programming language.

We provide a syntax-free representation theorem which places terms in bijection with sieves, a concept from category theory.

We study presentation-invariance for general parameterized algebraic theories by providing a theory of clones. We show that parameterized algebraic theories characterize a class of enriched monads.


Logic Program Logic Programming Function Symbol Algebraic Theory Predicate Logic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sam Staton
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeUK

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