Relational Graph Models, Taylor Expansion and Extensionality

Giulio Manzonetto (1) , Domenico Ruoppolo (1)

1 LCR - Logic, Computation and Reasoning [Villetaneuse]

We define the class of relational graph models and study the induced order-and equational-theories. Using the Taylor expansion, we show that all λ-terms with the same Böhm tree are equated in any relational graph model. If the model is moreover extensional and satisfies a technical condition, then its order-theory coincides with Morris's observational pre-order. Finally, we introduce an extensional version of the Taylor expansion, then prove that two λ-terms have the same extensional Taylor expansion exactly when they are equivalent in Morris's sense.

Mots clés: Taylor expansion; extensional Böhm trees; differential nets; linear logic; lambda calculus

Domaines: Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]; Langage de programmation [cs.PL]; Catégories et ensembles [math.CT]

Giulio Manzonetto, Domenico Ruoppolo. Relational Graph Models, Taylor Expansion and Extensionality. Electronic Notes in Theoretical Computer Science, 2014, Proceedings of the 30th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXX), 308, pp.45-272. ⟨10.1016/j.entcs.2014.10.014⟩. ⟨hal-01140878⟩