A formal language ccsl is introduced for describing specifications of classes in object-oriented languages. We show how class specifications in ccsl can be translated into higher order logic. This allows us to reason about these specifications. In particular, it allows us (1) to describe (various) implementations of a particular class specification, (2) to develop the logical theory of a specific class specification, and (3) to establish refinements between two class specifications. We use the (dependently typed) higher order logic of the proof-assistant pvs, so that we have extensive tool support for reasoning about class specifications. Moreover, we describe our own front-end tool to pvs, which generates from ccsl class specifications appropriate pvs theories and proofs of some elementary results.

We report on a large formal verification effort in mechanically proving correct a compiling specification for a realistic bootstrap compiler from ComLisp (a subset of ANSI Common Lisp sufficiently expressive to serve as a compiler implementation language) to binary Transputer code using the PVS system. The compilation is carried out in five steps through a series of intermediate languages. In the first phase, ComLisp is translated into a stack intermediate language (SIL), where parameter passing is implemented by a stack technique. Expressions are transformed from a prefix notation into a postfix notation according to the stack principle. SIL is then compiled into C int where the ComLisp data structures (s-expressions) and operators are implemented in linear integer memory using a run-time stack and a heap. These two steps are machine independent. In the compiler’s backend, first control structures (loops, conditionals) of the intermediate language C int are implemented by linear assembler code with relative jumps, the infinite memory model of C int is realized on the finite Transputer memory, and the basic C int statements for accessing the stack and heap are implemented by a sequence of assembler instructions. The fourth phase consists of the implementation of