Hans Langmaack

Formal Methods for Industrial Applications

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VDM '90 VDM and Z — Formal Methods in Software Development

Object orientation and formal techniques.- An algebraic approach to refinement.- Modal logic programming.- Z specification of an object manager.- Correctness in the small.- A formal approach to hypertext using post-prototype formal specification.- Programming with VDM domains.- A buffering system implementation using VDM.- Formal specifications as reusable frameworks.- Z and the refinement calculus.- Modularizing the formal description of a database system.- Modular extensions to Z.- Adding abstract datatypes to Meta-IV.- Towards a semantics for object-Z.- HOOD and Z for the development of complex software systems.- Using Z as a specification calculus for object-oriented systems.- Specifying open distributed systems with Z.- Refinement of state-based concurrent systems.- Refining data to processes.- Two approaches towards the formalisation of VDM.- Type checking BSI/VDM-SL.- Type inference in Z.- Recursive definitions revisited.- Towards the semantics of the definitional language of MetaSoft.- On conservative extensions of syntax in the process of system development.- A formal semantics for Z and the link between Z and the relational algebra.- A naive domain universe for VDM.

Present-Day Hoare-Like Systems for Programming Languages with Procedures: Power, Limits and most Likely Expressions

This paper indicates that presently known Hoare-like systems for ALGOL-like languages with static scope semantics can deal only with programs which can effectively be transformed into formally equivalent programs without procedure nesting (Remark 4 and 5 and Section 8). There are not yet methods to attack PASCAL-like programs (sample program \(\tilde \pi\) in section 9), programs without self-application of procedures (Conjecture 1) and program classes for which the formal termination problem is solvable (Conjecture 2).

Provably Correct Compiler Development and Implementation

This paper reports on provably correct compiler implementation in the ESPRIT basic research action 3104 ProCoS (Provably Correct Systems). A sharp distinction is drawn between correctness of the specification of a compiler and correctness of the actual implementation. The first covers semantical correctness of the code to be generated, whereas the second concerns correctness of the compiler program with respect to the specification. The compiler construction framework presented aims at minimizing the amount of handcoding during implementation and at reusing specification correctness arguments for proving the implementation correct. The classical technique of bootstrapping compilers is revisited with respect to implementation correctness.

On termination problems for finitely interpreted ALGOL-like programs

SummaryMain issue is: The actual termination problem for finitely interpreted non-deterministic ALGOL-like programs without procedure selfapplication and without global variables is algorithmically solvable. This result offers a new and substantial application of a theorem of Lipton: The above mentioned programs, restricted to deterministic ones, have a sound and relatively complete Hoare logic. So we conjecture: ALGOL-like programs (even non-deterministic ones with formal sharing of variables) without procedure selfapplication and without global variables have a sound and relatively complete Hoare deduction system with axioms and inference rules which reflect the syntactical structure of programs.

The ProCoS Approach to Correct Systems

PorCoS is the name of the ESPRIT project “Provably Correct Systems”. A system is seen as a technological system with embedded controlling processors, sensors, actuators, connecting channels and timers in a physical environment, especially a real-time or hybrid system with digital and continuous components. The goal of PorCoS is to contribute to mathematical foundation for analysis and synthesis and to mathematical principles, techniques and tools for systematic and correct design and construction of systems, especially in safety-critical applications. The article discusses the notion of system correctness and explains its non-absolute nature. Two forerunners of ProCoS are described, the so-called stack of Computational Logic Inc., Austin, Texas, and the three views of concurrent processes – nets, terms and formulas – of E.-R. Olderog. ProCoS is going beyond the forerunners and has extended the description levels: Requirements and systems architectural language, specification language, high-level programming language, machine language, hardware description language and description language for asynchronuous circuits. A major achievement of ProCoS is to have related the semantic models of several different system development levels and to have shown up how to mathematically prove correct the transitions between these levels w.r.t. the semantic relations. The Duration Calculus gives a basis for semantics and verification and crosses the boundary between discrete and continuous models.The lecture has been given at the Dagstuhl-Seminar “High Integrity Programmable Electronic Systems”, 27. 02. - 03. 03. 95, organized by W. J. Cullyer, W. A. Halang and B. J. Krämer.

Application of regular canonical systems to grammars translatable from left to right

In [2] Knu th consideres a special class of context free grammars (~ which he calls translatable from left to right with bound k>--O (~ E L R (k)). Knuth shows tha t for fixed bound k it can be decided in a finite number of steps whether a context free g rammar is an L R (k) grammar. Here we shall give a different simple proof of the decidability of the class L R (k). The proof is based on a characterization of L R (k) grammars by the help of k-pushdown classes which we introduce in this paper and on a result of Btichi on regular canonical systems [1 ~. A regular canonical system • over a finite a lphabet ~ is a special canonical sys tem with a finite number of product ions of the form ~a = ~b,a, b E~*. ~ is a variable over ~* and indicates tha t replacements m a y be done only at the right end of a word: u is directly derivable from v (v / u) : M v ---xa and u = x b where a = ~ b is a product ion of 27. The transit ive closure I x of ~ in ~* defines the relat ion of general derivability. Biichi shows: If u and v are words in ~* then the genera ted set of words. ~(u,27,v) : =(x~.q*:u ~xv}

Contribution to Goodenough's and Gerhart's Theory of Software Testing and Verification: Relation between Strong Compiler Test and Compiler Implementation Verification

In view of J. B. Goodenoughs and S. L. Gerharts theory compiler πtS shows up to be a very well selected test datum to do translator implementation verification for πT supported by testing.

On an algorithm determining direct superclasses in Java and similar languages with inner classes---Its correctness, completeness and uniqueness of solutions

Some object oriented programming languages allow inner classes. All of them admit inheritance. This combination of inner classes and inheritance is very fruitful however less known. On the other hand it creates a serious problem: how to determine the direct superclass of a given class C, i.e. the class which class C directly inherits from. For there may be several classes of the same name in one program. A specification of the problem and a non-deterministic algorithm are provided. We prove that the algorithm is correct w.r.t. the specification and complete, i.e. if the algorithm signals an error then no solution exists. We show that the specification itself has at most one solution, in other words, it is a complete specification. This proves also that the corresponding parts of Java Language Specification are consistent and define uniquely a fragment of Java semantics.

Characterization of Acceptable by ALGOL-Like Programming Languages

It is proved that the procedure concept of ALGOL60-like programming languages with the standard call-by-name static scope semantics without arithmetic and without array allows any effective computation over arbitrary signatures.