## Defthms about zip and tie: Reasoning about powerlists in ACL2 (1997)

Venue: | Univ. of Texas Comp. Sci. Tech. Rep |

Citations: | 8 - 3 self |

### BibTeX

@ARTICLE{Gamboa97defthmsabout,

author = {Ruben A. Gamboa},

title = {Defthms about zip and tie: Reasoning about powerlists in ACL2},

journal = {Univ. of Texas Comp. Sci. Tech. Rep},

year = {1997},

pages = {97--02}

}

### Years of Citing Articles

### OpenURL

### 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

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(Show Context)
Citation Context ...first-elem x))) Finding these intermediate lemmas is the "art" of proving theorems with ACL2, and also with Nqthm. Much has been written on the process of finding these key lemmas. Besides [=-=BM88] and [BM79]-=-, the reader interested in using ACL2 is especially encouraged to read [KP94]. While the development above is illustrative of how ACL2 can be used to prove program correctness, it tells only part of t... |

409 |
A Computational Logic Handbook
- Boyer, Moore
(Show Context)
Citation Context ...rse x)) (p-first-elem x))) Finding these intermediate lemmas is the "art" of proving theorems with ACL2, and also with Nqthm. Much has been written on the process of finding these key lemmas=-=. Besides [BM88]-=- and [BM79], the reader interested in using ACL2 is especially encouraged to read [KP94]. While the development above is illustrative of how ACL2 can be used to prove program correctness, it tells onl... |

68 | ACL2 theorems about commercial microprocessors - Brock, Kaufmann, et al. - 1996 |

60 | Powerlists: A Structure for Parallel Recursion
- Misra
- 1994
(Show Context)
Citation Context ...epartment The University of Texas at Austin Taylor Hall 2.124 Austin, TX 78712-1188 ruben@lim.com, ruben@cs.utexas.edu http://www.lim.com/~ruben/research/acl2/powerlists/ January 22, 1997 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 pro... |

37 | Design goals for ACL2 - Kaufmann, JS - 1994 |

14 | Interaction with the Boyer-Moore and Theorem Prover: A Tutorial Study Using the Arithmetic-Geometric Mean Theorem
- Kaufmann, Pecchiari
- 1996
(Show Context)
Citation Context ...orems with ACL2, and also with Nqthm. Much has been written on the process of finding these key lemmas. Besides [BM88] and [BM79], the reader interested in using ACL2 is especially encouraged to read =-=[KP94]-=-. While the development above is illustrative of how ACL2 can be used to prove program correctness, it tells only part of the story. In particular, our correctness result would still hold if p-gray-se... |

14 |
ACL2: A Computational Logic for Applicative Common Lisp, The User’s
- Kaufmann, Moore
- 1994
(Show Context)
Citation Context ... construct theories in a modular fashion. For example, we will construct a powerlist “book” with all the commonly used definitions and theorems about powerlists, i.e., the requisite powerlist algebra =-=[KM97]-=-. Other researchers have also attempted to use automated theorem provers to reason about powerlists, notably [Kap97], [KS95a] and [KS95b]. While there are some similarities in our respective approache... |

9 | Constructors can be partial too
- Kapur
- 1997
(Show Context)
Citation Context ...monly used definitions and theorems about powerlists, i.e., the requisite powerlist algebra. Other researchers have also attempted to use automated theorem provers to reason about powerlists, notably =-=[Kap96]-=-, [KS94] and [KS95]. While there are some similarities in our respective approaches, there are significant differences as well. In [Kap96], Kapur is interested in extending a theorem prover to facilit... |

9 |
M.: Automated reasoning about parallel algorithms using powerlists
- Kapur, Subramaniam
- 1995
(Show Context)
Citation Context ...d definitions and theorems about powerlists, i.e., the requisite powerlist algebra. Other researchers have also attempted to use automated theorem provers to reason about powerlists, notably [Kap96], =-=[KS94]-=- and [KS95]. While there are some similarities in our respective approaches, there are significant differences as well. In [Kap96], Kapur is interested in extending a theorem prover to facilitate reas... |

8 |
Introduction to Algorithms: Chapter 32
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...⊙ 0 = 0, x ⊙ 1 = 1 and x ⊙ p = x will generate the required carry bits. It is easily seen that the operator ⊙ is associative, with left-identity p. This informal argument, as described for example in =-=[CLR90]-=-, can be made precise in ACL2. In doing so, we found that the formal proof follows the informal one rather closely. That is, the hardest step in the proof is the establishment that the prefix sum comp... |

7 |
Mechanical verification of adder circuits using powerlists
- Kapur, Subramaniam
- 1995
(Show Context)
Citation Context ...ns and theorems about powerlists, i.e., the requisite powerlist algebra. Other researchers have also attempted to use automated theorem provers to reason about powerlists, notably [Kap96], [KS94] and =-=[KS95]-=-. While there are some similarities in our respective approaches, there are significant differences as well. In [Kap96], Kapur is interested in extending a theorem prover to facilitate reasoning about... |

6 | Parlists: A generalization of powerlists
- Kornerup
- 1997
(Show Context)
Citation Context ...nd L3. The choice to use generalized powerlists was made taking these tradeoffs into account. Similar tradeoffs can be found in other approaches to generalized powerlists, such as Kornerup’s parlists =-=[Kor97b]-=-. We must be careful here that the resulting theory is nevertheless faithful to the original theory due to Misra. That is, we must ensure that the original axioms of zip and tie hold in the new theory... |

2 | Odd-even sort in powerlists
- Kornerup
- 1997
(Show Context)
Citation Context ...and prefix sums, as well as the relevant correctness results. In the same spirit, other researchers have used powerlists to find elegant proofs of parallel algorithms, for example odd-even sorting in =-=[Kor96]-=-. In this paper, we focus not on the discovery or expression of correctness results, but on their mechanical verification. Specifically, we wish to show how a library of provably correct functions on ... |