Cylindric Kleene Lattices for Program Construction

Abstract

Cylindric algebras have been developed as an algebraisation of equational first order logic. We adapt them to cylindric Kleene lattices and their variants and present relational and relational fault models for these. This allows us to encode frames and local variable blocks, and to derive Morgan’s refinement calculus as well as an algebraic Hoare logic for while programs with assignment laws. Our approach thus opens the door for algebraic calculations with program and logical variables instead of domain-specific reasoning over concrete models of the program store. A refinement proof for a small program is presented as an example.