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ACL2A Computational Logic for Applicative Common Lisp
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As a conclusion, a direct approach using ACL2 (similar to that of Eilenberg-Zilber theorem) was not considered possible.
Several formal developments in ACL2 and Coq/SSReflect about this process have been documented at [20, 21, 24].
Namely, ACL2 when we want to be near the Common Lisp Kenzo code, Isabelle/HOL when constructiveness is not ensured and Coq/SSReflect when the objective is to execute higher order programs in a certified environment.
For instance, Isabelle/HOL (as Coq) is based on higher-order logic, while ACL2 is based on a (restricted) first order logic.
The challenge was to translate in an automated way the Isabelle specifications (not proofs nor definitions: only statements) to ACL2. The idea behind this shallow translation is that the set of statements provides a kind of draft of a proof (a roadmap).
The mandatory reporting regime proposed by ACL2 has the following features:
We will not know whether, in fact, and, if so, how these provisions will be incorporated into ACL2, but there are three key areas to watch:
ACL2 represents the first step in this area, with the proposed legislation allowing the ACCC to apply to the Court to seek an order to redress loss or damage suffered by a non-party in relation to contraventions of a certain industry codes.
The ability to tackle these real-world problems is primarily the result of the improved capabilities of interactive systems such as NQTHM, ACL2, PVS, NUPRL, HOL, COQ (Coquand and Huet [INRIA] 1988), and ISABELLE (Paulson [Cambridge] 1994).
However, many other systems now have user communities of their own, some sizable: NQTHM, ACL2, and RRL, for example, and the higher-order logic systems HOL, NUPRL, ISABELLE, PVS, COQ, and TPS.
Some systems that are partially successful in combining techniques are PVS, NQTHM, ACL2, HOL, EVES (Craigen et al.
Verification, the most immediate commercial application, need not be done by using higher-order logic, as NQTHM and ACL2 demonstrate.