Kripke Models and the (In)equational Logic of the Second-Order Lambda-Calculus

Thumbnail Image
Penn collection
IRCS Technical Reports Series
Degree type
Grant number
Copyright date
Related resources

We define a new class of Kripke structures for the second-order λ-calculus, and investigate the soundness and completeness of some proof systems for proving inequalities (rewrite rules) as well as equations. The Kripke structures under consideration are equipped with preorders that correspond to an abstract form of reduction, and they are not necessarily extensional. A novelty of our approach is that we define these structures directly as functors A:W → Preor equipped with certain natural transformations corresponding to application and abstraction (where W is a preorder, the set of worlds, and Preor is the category of preorders). We make use of an explicit construction of the exponential of functors in the Cartesian-closed category PreorW, and we also define a kind of exponential ∏ Φ (As) sЄТ to take care of type abstraction. However, we strive for simplicity, and we only use very elementary categorical concepts. Consequently, we believe that the models described in this paper are more palatable than abstract categorical models which require much more sophisticated machinery,(and are not models of rewrite rules anyway). We obtain soundness and completeness theorems that generalize some results of Mitchell and Moggi to the second-order λ-calculus, and to sets of inequalities (rewrite rules).

Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
Volume number
Issue number
Publisher DOI
Journal Issue
University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-95-25.
Recommended citation