Verifikation reaktiver Systeme - Universität Kaiserslautern

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many classical mathematical theorems and therefore require a certain body of
mathematical concepts. Thus, there is a need for semi-automated theorem proving
systems that allows the statement and verification of correctness properties
at higher levels of abstraction.
Theorem proving has shown to be a powerful method in this area. But it
is not the magic bullet: Users must spend a lot of time to guide the prove
process. Automation of this work is still a complex task with a lot of work to
be done. Even reasoning about finite state machine logic is tedious in a theorem
proving environments, since theorem provers are not good at reasoning about
large amounts of random logic.
To combine the advantages of the various formal methods, various research
groups (both at universities and in industry) work on a tight integration between
semi-automated theorem proving and other property verification tools.
This approach seems to be the most promising to push back the boundaries on
the today’s application of formal methods. Hardware verification is the largest
industrial application of automated theorem proving: AMD, IBM, and Intel are
among the companies that employ automated theorem proving technology for
verification.
The rest of this article is organised as follows: Section 2 introduces the HOL
system and its foundations. In section 3, three examples are presented: The first
one is a simple parity checker demonstrates basic techniques to verify hardware
components with a theorem proover. The second one shows the proof of a basic
arithmetic algorithm used in hardware designs, the binary greatest common
divisor algorithm. The last example illustrates the definition of new types, a
basic concept of extending and building new theories. In Section 4 finally, some
conclusions are drawn.
2 The HOL System
2.1 Overview
HOL4 is the lastest version of the HOL automated proof system for higher order
logic. It provides an environment with an expressive notation for writing system
specifications and powerful facilities for creating formal proofs of properties of
specifications. It features built-in decision procedures that automate some lowlevel
details of proofs. But one of its most important properties is its rigorous
and well-understood theoretical basis that allows users to extend the system
without compromising security (due to Robin Milner’s LCF approach). The HOL
system is built on top of Moscow ML, a light-weight implementation of the strict
functional language of Standard ML (SML). It has been used in many areas,
including the definition of HDL semantics (e.g. VHDL, Verilog), hardware design
and verification, reasoning about security, reasoning about real-time systems and
software verification.
The HOL system comes with an extensive library containing hundreds of predefined
types, functions, tactics and proved theorems. For verifying arithmetic