Easiness in graph models

Chantal Berline (1) , Antonino Salibra (2)

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

We generalize Baeten and Boerbom's method of forcing, and apply it to show that there is a fixed sequence (uk)k in N, of closed untyped λ-terms satisfying the following properties: * For any countable sequence (gk)k in N, of continuous functions (of arbitrary arity) on the power set P(D) of an arbitrary countable set D, there is a graph model (D,p) such that (λx.xx)(λx.xx)uk represents gk in the model. * For any countable sequence (tk)k in N, of closed λ-terms there is a graph model that satisfies (λx.xx)(λx.xx)uk=tk for all k. These two results bring information on the landscape of graph theories (= λ-theories that can be realized as theories of graph models), and more generally on the lattice of λ-theories (ordered by inclusion).

Mots clés: untyped lambda-calculus; graph models; easy terms; Scott's continuous semantics; lattices of lambda-theories; webbed models

Domaines: Logique [math.LO]

Chantal Berline, Antonino Salibra. Easiness in graph models. Theoretical Computer Science, 2006, 354, pp.4-23. ⟨10.1016/j.tcs.2005.11.005⟩. ⟨hal-00003751v2⟩