Safety of abstract interpretations for free, via logical relations and Galois connections

Authors:
Kevin Backhouse;Roland Backhouse
Affiliations:
ARM Ltd., Cambridge CB1 9NJ, UK;School of Computer Science and Information Technology, University of Nottingham, Nottingham NG8, 1BB, UK
Venue:
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
Year:
2004

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Abstract

Algebraic properties of logical relations on partially ordered sets are studied. It is shown how to construct a logical relation that extends a collection of base Galois connections to a Galois connection of arbitrary higher-order type. "Theorems-for-free" is used to show that the construction ensures safe abstract interpretation of parametrically polymorphic functions. The properties are used to show how abstract interpretations of program libraries can be constructed.