Abstract

In [Mis94], Misra introduced the powerlist data structure, which is well suited to express recursive, data-parallel algorithms. Moreover, Misra and other researchers have shown how powerlists can be used to prove the correctness of several algorithms. This success has encouraged some researchers to pursue automated proofs of theorems about powerlists[Kap97, KS95a, KS95b]. In this paper, we show how ACL2 can be used to verify theorems about powerlists. We depart from previous approaches in two significant ways. First, the powerlists we use are not the regular structures defined by Misra; that is, we do not require powerlists to be balanced trees. As we will see, this complicates some of the proofs, but on the other hand it allows us to state theorems that are otherwise beyond the language of powerlists. Second, we wish to prove the correctness of powerlist algorithms as much as possible within the logic of powerlists. Previous approaches have relied

Citations

505	A Computational Logic - Boyer, Moore - 1979
381	A Computational Logic Handbook - Boyer, Moore - 1988
66	ACL2 theorems about commercial microprocessors - Brock, Kaufmann, et al. - 1996
55	Powerlist: A structure for parallel recursion - Misra - 1994
35	Design Goals for ACL2 - Kaufmann, Moore - 1994
14	Interaction with the Boyer-Moore theorem prover: A tutorial study using the arithmetic-geometric mean theorem - Kaufmann, Pecchiari - 1996
14	ACL2: A Computational Logic for Applicative Common Lisp, The User’s - Kaufmann, Moore - 1994
8	Constructors can be partial too - Kapur - 1997
8	Automated reasoning about parallel algorithms using powerlists - Kapur, Subramaniam - 1995
7	Introduction to Algorithms, chapter 32 - Corman, Leiserson, et al. - 1990
7	Mechanical verification of adder circuits using powerlists - Kapur, Subramaniam - 1995
6	Parlists: A generalization of powerlists - Kornerup - 1997
2	Odd-even sort in powerlists - Kornerup - 1997