Abstract
AbstractIn this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite models, one based on finite sets and the other on finite vector spaces. The first model is shown to be fully complete with respect to the operational semantics of the language. The second model is not complete, but we develop an algebraic extension of the finite lambda calculus that recovers completeness. The relationship between the two semantics is described, and several examples based on Church numerals are presented.KeywordsVector SpaceOperational SemanticLinear LogicAlgebraic ExtensionLambda CalculusThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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