Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 2. BACKGROUND AND RELATED WORK 27
processing language. Models of all kinds of systems can be built in ACL2 and, once written,
can be executed as Lisp programs.
Since ACL2 is based on a first-order logic it is considerably less expressive than theorem
provers such as HOL which use higher-order logic, however the simply logic allows a very
high degree of automation with little user intervention required. The user directs the proof
search procedure by proving supporting lemmas.
ACL2 has been used to verify some industrial processors, for example a Motorola digital
signal processing chip [10].
Isabelle [61] is a descendant of the LCF system [21]. Unlike most theorem provers which
focus on providing a single underlying formalism, Isabelle is intended to be used as a general
platform for the implementation of theorem provers in a large variety of logics. The motiva-
tion behind the creation of Isabelle is that, while theorem proving is an extremely difficult
problem, most of the difficulties have to do with logic in general rather than any particular
logic. A generic theorem prover will probably never provide the full range of support that a
dedicated prover for each logic could, however by reducing the “barriers to entry” it makes it
more likely that some proof support will be available for less common or application specific
logics. Furthermore, since it is currently easier to learn a logic than to learn how to use
a theorem prover it is also easier for users to learn a single prover and then use the most
appropriate logic for their needs.
2.4.6 Embeddings
In order to using theorem proving for verification of hardware written in a description lan-
guage it is necessary to develop an implementation of the language in a logic within a theorem
prover. This process is referred to as embedding and broadly speaking these can be further
sub-divided [8] into deep embeddings and shallow embeddings.
A shallow embedding, or semantic embedding, involves the definition of the meaning of the
language directly in terms of the connectives in the logic. A deep embedding is characterised
by the definition of the syntax of a language in a formal logic, typically as some sort of
abstract data type and the definition of a semantic meaning function.