Minimal lambda-theories by ultraproducts

Alberto Carraro (1, 2) , Antonino Salibra (2) , Antonio Bucciarelli (1)

1 PPS - Preuves, Programmes et Systèmes
2 Dipartimento di Informatica

A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the $\lambda\beta$ or the least sensible lambda-theory $\cH$ (generated by equating all the unsolvable terms). A related question is whether, given a class of lambda models, there is a minimal lambda-theory represented by it. In this paper, we give a general tool to answer positively to this question and we apply it to a wide class of webbed models: the i-models. The method then applies also to graph models, Krivine models, coherent models and filter models. In particular, we build an i-model whose theory is the set of equations satisfied in all i-models.

Domaines: Logique en informatique [cs.LO]

Alberto Carraro, Antonino Salibra, Antonio Bucciarelli. Minimal lambda-theories by ultraproducts. 2012. ⟨hal-00710340⟩