On the Representation of Imperative Programs in a Logical Framework

Abstract

Research on formal verification of imperative programs using some form of representing them in a type theory has been done for years. Generally, the different approaches include a verification conditions generator, which from an annotated program including variants and invariants for while-loops and using a Hoare logic-like specification, produces some propositions to be proved in a logical framework, expressing the program correctness and termination. In this paper we present a direct use of Coq [3] to model imperative programs. This method, and the fact that it is not possible to have not-ending programs in Coq, should allow a more deep understanding of imperative programs semantics [15], and people without big knowledge on type theory could use this theorem prover to verify imperative programs properties. This approach is based on using a fixed-point equality theorem [2] that represents the appropriate reduction rule to be used in our model. In our approach no Hoare logic rules are used for verification of program specifications. This verification is achieved, in a pure constructive setting, directly with the type theory model.