A relational model of a parallel and non-deterministic lambda-calculus

Antonio Bucciarelli (1) , Thomas Ehrhard (1) , Giulio Manzonetto (1)

1 PPS - Preuves, Programmes et Systèmes

We define a new model of a lambda-calculus endowed with must and may non-determinism, implemented by parallel composition and non-deterministic choice respectively. The model presents new features with respect to powerdomain-based approaches : for instance, parallel composition is interpreted by a non-idempotent operation, leading to the possibility of a resource-aware semantic analysis of parallel computation. The ambient category of the model is the category of sets and relations: our claim is that in this framework, non-determinism and parallelism may be dealt with directly and naturally. The main technical result of the paper is the adequacy of the model : the interpretation of a term is non-empty if and only if it is solvable.

Mots clés: lambda-calculus; relational model; non-determinism; parallel composition; denotational semantics

Domaines: Logique en informatique [cs.LO]

Antonio Bucciarelli, Thomas Ehrhard, Giulio Manzonetto. A relational model of a parallel and non-deterministic lambda-calculus. 2008. ⟨hal-00283095v1⟩