Metric Reasoning About λ-Terms: The Affine Case

Raphaëlle Crubillé (1) , Ugo Dal Lago (2, 3)

1 ENS de Lyon - École normale supérieure de Lyon
2 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
3 FOCUS - Foundations of Component-based Ubiquitous Systems

Terms of Church's λ-calculus can be considered equivalent along many different definitions, but context equivalence is certainly the most direct and universally accepted one. If the underlying calculus becomes probabilistic, however, equivalence is too discriminating: terms which have totally unrelated behaviours are treated the same as terms which behave very similarly. We study the problem of evaluating the distance between affine λ-terms. A natural generalisation of context equivalence , is shown to be characterised by a notion of trace distance, and to be bounded from above by a coinductively defined distance based on the Kantorovich metric on distributions. A different, again fully-abstract, tuple-based notion of trace distance is shown to be able to handle nontrivial examples.

Domaines: Logique en informatique [cs.LO]

Raphaëlle Crubillé, Ugo Dal Lago. Metric Reasoning About λ-Terms: The Affine Case. LICS 2015, Jul 2015, Kyoto, Japan. ⟨10.1109/LICS.2015.64⟩. ⟨hal-01231814⟩