Refining Properties of Filter Models: Sensibility, Approximability and Reducibility

Author: Flavien Breuvart

Paper Information

Title:Refining Properties of Filter Models: Sensibility, Approximability and Reducibility
Authors:Flavien Breuvart
Proceedings:HOR Pre-proceedings
Editor: Stefano Guerrini
Keywords:untyped lambda calculus, denotational semantics, sensibility, approximation theorem, filter models, realisability

ABSTRACT. In this paper, we study the tedious link between the properties of sensibility and approximability of models of untyped λ-calculus. Approximability is known to be a slightly, but strictly stronger property that sensibility. However, we will see that so far, each and every (filter) model that have been proven sensible are in fact approximable. We explain this result as a weakness of the sole known approach of sensibility: the Tait reducibility candidates and its realizability variants.

In fact, we will reduce the approximability of a filter model D for the λ-calculus to the sensibility of D but for an extension of the λ-calculus that we call λ-calculus with D-tests. Then we show that traditional proofs of sensibility of D for the λ-calculus are smoothly extendable for this λ-calculus with D-tests.

Talk:Jul 07 15:00 (Session 30B)