## WALDMEISTER: Development of a High Performance Completion-Based Theorem Prover (1996)

Citations: | 14 - 0 self |

### BibTeX

@TECHREPORT{Buch96waldmeister:development,

author = {Arnim Buch and Thomas Hillenbrand},

title = {WALDMEISTER: Development of a High Performance Completion-Based Theorem Prover},

institution = {},

year = {1996}

}

### Years of Citing Articles

### OpenURL

### Abstract

: In this report we give an overview of the development of our new Waldmeister prover for equational theories. We elaborate a systematic stepwise design process, starting with the inference system for unfailing Knuth--Bendix completion and ending up with an implementation which avoids the main diseases today's provers suffer from: overindulgence in time and space. Our design process is based on a logical three--level system model consisting of basic operations for inference step execution, aggregated inference machine, and overall control strategy. Careful analysis of the inference system for unfailing completion has revealed the crucial points responsible for time and space consumption. For the low level of our model, we introduce specialized data structures and algorithms speeding up the running system and cutting it down in size --- both by one order of magnitude compared with standard techniques. Flexible control of the mid--level aggregation inside the resulting prover is made po...

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Citation Context ...e term again instead of starting backtracking immediately. This is because termination holds only under a certain normalization strategy (innermost combined with a special backtracking mechanism; cf. =-=[WZ95]-=-). Result: The parameter setting of the backtracking behavior is worthwhile although we could not recognize a tendency. Once again it turns out that even slight changes of the inference machine can in... |

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Citation Context ... !E ;l=r u with s ? l Delete an equation E [ fs = sg; R; G E; R; G 2 Waldmeister is also able to deal with existentially quantified goals, which requires additional inference rules for narrowing. See =-=[Den93]-=- for more details. 4 Subsume an equation E [ fs : = t; u[oe(s)] : = u[oe(t)]g; R; G E [ fs : = tg; R; G Simplify the right--hand side of a rule E; R [ fs ! tg; G E; R [ fs ! ug; G if t !R[E u Simplify... |

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Citation Context ...0 161.0 3 mv2.pr LCL111-2 225.8 16.5 1487 ?6000 136.5 274 p9a.pr GRP178-1 7.3 7.1 2253 90.2 25.9 807 ra2.pr ROB023-1 6.3 2.8 2356 ?6000 118.0 21 ra3.pr ROB005-14 96.1 5.6 1174 ?6000 100.4 16 sims2.cp =-=[Sim91]-=- 50.8 3.8 807 365.5 61.6 443 z22.cp [Den93] 0.9 2.5 2726 3.7 3.9 1743 Table 19: Comparison of Inference Machines To that purpose, both provers were run with the same primitive search strategy. In this... |

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Citation Context ...rs. Apart from that, the development of data structures and algorithms for specialized high--speed operations like retrieval of generalizations and instances of terms has made good progress ([McC92], =-=[Gra96]-=-). In contrast, not enough attention is yet paid to the question how the single inference steps should be aggregated into an inference machine. If research focusses on one of the three levels, usually... |

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Citation Context ...NS C(T,p) = p C(p,C(q,p)) = T C(C(p,C(q,r)),C(C(p,q),C(p,r))) = T C(C(p,C(q,r)),C(q,C(p,r))) = T C(C(p,q),C(N(q),N(p))) = T C(N(N(p)),p) = T C(p,N(N(p))) = T CONCLUSION C(N(Ap),C(Ap,Aq)) = T Lusk5.pr =-=[LO85]-=- NAME Lusk5 MODE PROOF SORTS ANY SIGNATURE f: ANY ANY ANY -? ANY g: ANY -? ANY a, b: -?ANY ORDERING LPO 82 g ? f ? b ? a VARIABLES v,w,x,y,z: ANY EQUATIONS f(f(v,w,x),y,f(v,w,z)) = f(v,w,f(x,y,z)) f(y... |

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Citation Context ...pproach is promising (Sect. 9). Although we have not yet spent much effort on specialized heuristics we gain impressive results on standard problems. Furthermore, Waldmeister solves two problems from =-=[LW92]-=- never proved unaided with standard unfailing completion be1 In German this means woodruff and is composed of forrest and master. 2 fore (Sect. 10). The completely machine generated proof of one of th... |

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Citation Context ...NG LPO i ? n ? T ? a ? b VARIABLES x,y,z: ANY EQUATIONS i(T,x) = x i(i(x,y),y) = i(i(y,x),x) i(i(n(x),n(y)),i(y,x)) = T i(i(x,y),i(i(y,z),i(x,z))) = T CONCLUSION i(i(i(a,b),i(b,a)),i(b,a)) = T p9a.pr =-=[Fuc94]-=- NAME p9a MODE PROOF SORTS ANY SIGNATURE i: ANY -? ANY f, n, u: ANY ANY -? ANY 1, a, b, c: -? ANY ORDERING LPO i ? f ? n ? u ? 1 ? a ? b ? c VARIABLES x,y,z: ANY EQUATIONS u(x,x) = x n(x,x) = x f(1,x)... |

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Citation Context ...t approach, the reduction of reorganization effort caused by orphan murder led us to a related dynamic data structure, the so--called pairing--heap (cf. Fig. 10) which was introduced in [FSST86] (see =-=[SV87]-=- for an evalutation). Double--chaining its entries allows arbitrary deletion and reweighting of elements in constant time. For the purpose of immediate orphan murder, the unprocessed equations are add... |