Predicate Transformers and Linear Logic, yet another denotational model

Pierre Hyvernat (1, 2)

1 IML - Institut de mathématiques de Luminy
2 LAMA - Laboratoire de Mathématiques

In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this structure to make predicate transformers into a de notational model of full linear logic: all the logical constructions have a natural interpretation in terms of predicate transformers (i.e. in terms of specifications). We then interpret proofs of a formula by a safety property for the corresponding specification.

Mots clés: Predicate Transformers; Linear Logic; Denotational Semantics

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Pierre Hyvernat. Predicate Transformers and Linear Logic, yet another denotational model. Computer Science and Logic 2004, Sep 2004, Karpacz, Poland. pp.115--129. ⟨hal-00387490⟩