An Extensible Encoding of Object-oriented Data Models in hol

Abstract

We present an extensible encoding of object-oriented data models into higher-order logic (hol). Our encoding is supported by a datatype package that leverages the use of the shallow embedding technique to object-oriented specification and programming languages. The package incrementally compiles an objectoriented data model, i. e., a class model, to a theory containing object-universes, constructors, accessor functions, coercions (casts) between static types (and providing a foundation for the notion of dynamic types), characteristic sets, and coinductive class invariants. The package is conservative, i. e., all properties are derived entirely from constant definitions, including the constraints over object structures. As an application, we use the package for an object-oriented core-language called imp++, for which we formally prove the correctness of a Hoare logic with respect to a denotational semantics.

Semantics, calculi, and analysis for object-oriented specifications

“…In contrast to these approaches, HOL-OCL generates a conservative model for objects and states (see [9,10]). Furthermore, HOL-OCL is geared towards top-down development via refinement, therefore complementary to these approaches.…”

“…The presented "axioms" are then derived from them. Due to space limitations, we will not go into detail and refer the interested reader to [6,10] for details.…”

“…Moreover, the HOL-OCL class model compiler also generates functions that allow to construct a state; i. e., there is an infrastructure to create objects, update attributes in them, and determine even their object-identifier or reference within a state. These more powerful constructions are described elsewhere [6,10].…”

A Specification-Based Test Case Generation Method for UML/OCL

“…Of course, not any recursive predicate is consistent; however these recursive predicates can be derived from the invariants by using a greatest fixed-point construction and proving that the body of the invariant is monotone-the reader interested in the details is referred to HOL-OCL [9] where this is done automatically (albeit for OCL 2.0, i. e., without null):…”

“…Instead of verifying concrete code via a Hoare-Calculus for a specific programming language against OCL method contracts-a technique developed in detail for OCL in [9,11]-test generation can be a more light-weighted (but logically less safe) formal method to reveal errors both in specification and implementations. A particular advantage of black-box testing is that implementations may consist of arbitrary mixtures of (dirty) programming languages.…”