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Linear Realizability and Full Completeness for Typed Lambda-calculi

Summary: Linear Realizability and Full Completeness for
Typed Lambda-calculi
Samson Abramsky
Oxford University Computing Laboratory, Wolfson Building,
Parks Road, OX1 3QD, England,
tel. +44 (0)1865 283558, fax: +44 (0)1865 273839
Marina Lenisa ;1
Dipartimento di Matematica e Informatica, Universita di Udine,
Via delle Scienze 206, 33100 Udine, ITALY,
tel. +39 0432 558417, fax: +39 0432 558499
We present the model construction technique called Linear Realizability. It consists
in building a category of Partial Equivalence Relations over a Linear Combina-
tory Algebra. We illustrate how it can be used to provide models, which are fully
complete for various typed -calculi. In particular, we focus on special Linear Com-
binatory Algebras of partial involutions, and we present PER models over them
which are fully complete, inter alia, w.r.t. the following languages and theories: the
fragment of System F consisting of ML-types, the maximal theory on the simply
typed -calculus with nitely many ground constants, and the maximal theory on
an in nitary version of this latter calculus.


Source: Abramsky, Samson - Computing Laboratory, University of Oxford


Collections: Computer Technologies and Information Sciences