## Linear realizability and full completeness for typed lambda calculi (2005)

Venue: | Annals of Pure and Applied Logic |

Citations: | 3 - 1 self |

### BibTeX

@ARTICLE{Abramsky05linearrealizability,

author = {Samson Abramsky and Marina Lenisa},

title = {Linear realizability and full completeness for typed lambda calculi},

journal = {Annals of Pure and Applied Logic},

year = {2005},

volume = {134},

pages = {2005}

}

### OpenURL

### Abstract

We present the model construction technique called Linear Realizability. It consists in building a category of Partial Equivalence Relations over a Linear Combinatory Algebra. We illustrate how it can be used to provide models, which are fully complete for various typed λ-calculi. In particular, we focus on special Linear Combinatory 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 λ-calculus with finitely many ground constants, and the maximal theory on an infinitary version of this latter calculus. Key words: Typed lambda-calculi, ML-polymorphic types, linear logic, hyperdoctrines, PER models, Geometry of Interaction, (axiomatic) full completeness