## Fast Tactic-based Theorem Proving (2000)

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- [www.cs.cornell.edu]
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- [www.cs.cornell.edu]
- [files.metaprl.org]
- [www.cs.cornell.edu]
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### Other Repositories/Bibliography

Venue: | TPHOLs 2000, LNCS 1869 |

Citations: | 10 - 4 self |

### BibTeX

@INPROCEEDINGS{Hickey00fasttactic-based,

author = {Jason Hickey and Aleksey Nogin},

title = {Fast Tactic-based Theorem Proving},

booktitle = {TPHOLs 2000, LNCS 1869},

year = {2000},

pages = {252--266},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Theorem provers for higher-order logics often use tactics to implement automated proof search. Tactics use a general-purpose meta-language to implement both general-purpose reasoning and computationally intensive domain-specific proof procedures. The generality of tactic provers has a performance penalty; the speed of proof search lags far behind special-purpose provers. We present a new modular proving architecture that significantly increases the speed of the core logic engine.

### Citations

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(Show Context)
Citation Context ...edness (verication) conditions. Using type annotations, Howe was able to speed up rewriting in NuPRL-4 by a factor of 10. Basin and Kaufmann [3] give a comparison between the NuPRL3 system and nqthm [=-=-=-5] (the predecessor of the ACL2 [17] system). The nqthm prover uses a quantier-free variant of Peano arithmetic. Basin and Kaufmann's measurements showed that nqthm was roughly 15 times faster for die... |

437 | The Foundation of a Generic Theorem Prover - Paulson - 1989 |

141 |
Contraction-free sequent calculi for intuitionistic logic
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(Show Context)
Citation Context ... pigeonT tactic performs an efficient search customized to this domain, and the propDecideT tactic is a generic decision procedure for intuitionistic propositional logic (based on Dyckoff's algorithm =-=[9]-=-). Both search algorithms explore an exponential number of cases in i. Problem size Memory Configuration Tactic 2 3 4 (Max MB) Term std pigeonT !0.1 2.46 93.8 170 Term ds pigeonT !0.1 0.59 15.1 32 Ter... |

124 | The type theoretic interpretation of constructive set theory
- Aczel
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(Show Context)
Citation Context ...lications of unication (likesrst-order logic). MetaPRL, our testbed, is implemented in Objective Caml [19]. It includes logics likesrst-order logic, the NuPRL type theory, and Aczel's CZF set theory [=-=1]-=-. We include performance measurements that compare MetaPRL's performance with NuPRL-4 on the NuPRL type theory. In our measurements, we also show how particular module implementations change the perfo... |

110 | An industrial strength theorem prover for a logic based on common lisp
- KAUFMAN, MOORE
- 1997
(Show Context)
Citation Context ...s compiled to Common Lisp, and the NuPRL-4 rener is implemented in Common Lisp. Insrst-order logics, we estimate that an order of magnitude speed factor remains between MetaPRL and provers like ACL2 [=-=-=-17]. Some of this dierence can be addressed with a specic rener modules: asrst-order term module would contain custom representations for terms in disjunctive normal form and sequents (sequents provid... |

108 | Introduction to HOL - Gordon, Melham - 1994 |

90 | The semantics of reflected proof
- Allen, Constable, et al.
- 1990
(Show Context)
Citation Context ...ic and component of a term; 2) a list of parameters representing constant values; and 3) a set of possibly-bound subterms. We use the following syntax to describe terms, based on the Nuprl definition =-=[2]-=-: opname --- --zsoperator name [p 1 ; \Delta \Delta \Delta ; pn ] --- --zsparameters fv 1 :t 1 ; \Delta \Delta \Delta ; vm :t m g --- --zssubterms Here are a few examples: Displayed form Term 1 natura... |

73 | HOL Light: A Tutorial Introduction
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(Show Context)
Citation Context ...cant overhead in composing and saving the primitive proof trees. In some domains, we may be able to perform proof compression, or delay the composition of proofs. 8 Related work Harrison's HOL-Light [=-=13]-=- shares some common features with the MetaPRL implementation. Harrison's system is implemented in Caml-Light, and both systems require fewer computational resources than their predecessors. Howe [16] ... |

51 |
Obective ML: A simple object-oriented extension of ML
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(Show Context)
Citation Context ... with frequent applications of substitution (like type theory), and for domains with frequent applications of unication (likesrst-order logic). MetaPRL, our testbed, is implemented in Objective Caml [=-=19]-=-. It includes logics likesrst-order logic, the NuPRL type theory, and Aczel's CZF set theory [1]. We include performance measurements that compare MetaPRL's performance with NuPRL-4 on the NuPRL type ... |

36 | G.: The COQ Proof Assistant User’s Guide - Dowek, Felty, et al. - 1993 |

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26 | The Boyer-Moore prover and Nuprl: An experimental comparison
- Basin, Kaufmann
- 1991
(Show Context)
Citation Context ...ry is untyped, leading to frequent production of well-formedness (verication) conditions. Using type annotations, Howe was able to speed up rewriting in NuPRL-4 by a factor of 10. Basin and Kaufmann [=-=3-=-] give a comparison between the NuPRL3 system and nqthm [5] (the predecessor of the ACL2 [17] system). The nqthm prover uses a quantier-free variant of Peano arithmetic. Basin and Kaufmann's measureme... |

25 |
Writing programs that construct proofs
- Constable, Knoblock, et al.
- 1984
(Show Context)
Citation Context ...ogics function builds the union of two logics, and the add rule and add rewrite function add rules/rewrites from their syntactical description as terms. The proof type represents a partial proof tree =-=[6-=-], which may be modied by applying a tactic to the proof goal with the refine function. The compose function is used to stitch together partial proofs into larger proofs. Accounting must be performed ... |

16 |
Contraction-free sequent calculi for intuitionistic logic
- Dyckho
- 1992
(Show Context)
Citation Context ...\holes." The pigeonT tactic performs a search customized to this domain, and the propDecideT tactic is a generic decision procedure for intuitionistic propositional logic (based on Dycko's algori=-=thm [10-=-]). Both search algorithms use only propositional reasoning and both explore an exponential number of cases in i. Problem size Memory Conguration Tactic 2 3 4 (Max MB) 5 Term std pigeonT 0.1 2.57 94.5... |

13 |
A Logic for Correct Program Development
- Bates
- 1979
(Show Context)
Citation Context ...ample, the NuPRL type theory denes abstraction and application, with the following equivalence: (x:b) as! b[a=x]: (3) 4. Theorems provide proofs for derived inference rules and axioms. The rener [4] performs two basic operations. First, it builds automation procedures from the parts of a logic. 1. Syntax denitions are compiled to functions for constructing logical formulas. 2. Rewrite primitive... |

13 | NuPRL-Light: An implementation framework for higer-order logics - Hickey - 1997 |

12 |
Le langage Caml. Dunod
- Weis, Leroy
- 1999
(Show Context)
Citation Context ... with frequent applications of substitution (like type theory), and for domains with frequent applications of unication (likesrst-order logic). MetaPRL, our testbed, is implemented in Objective Caml [=-=19]-=-. It includes logics likesrst-order logic, the NuPRL type theory, and Aczel's CZF set theory [1]. We include performance measurements that compare MetaPRL's performance with NuPRL-4 on the NuPRL type ... |

10 |
Judicaël Courant, JeanChristophe Filliâtre, Eduardo Giménez, Hugo Herbelin, Gérard Huet
- Barras, Boutin, et al.
- 1997
(Show Context)
Citation Context ...specic basis. Our architecture is used in the MetaPRL logical framework, with speedups of more than two orders of magnitude over traditional tactic-based proof search. 1 Introduction Several provers [=-=8,9,3,11,12,15,18]-=- use higher-order logics for reasoning because the expressivity of the logics permits concise problem descriptions, and because meta-principles that characterize entire classes of problems can be prov... |

8 | Fault-tolerant distributed theorem proving
- Hickey
- 1999
(Show Context)
Citation Context ... general architecture of a tactic prover can be divided into three parts, shown in Figure 1. A logic contains the following kinds of objects: 1 It should be noted that MetaPRL is a distributed prover =-=[14-=-], leading to additional speedups if multiple processors are used. Distribution is implemented by inserting a scheduling and communication layer between the rener and the tactic interface. For this pa... |

7 |
The Semantics of Re ected Proof
- Allen, Constable, et al.
- 1990
(Show Context)
Citation Context ...gic and component of a term; 2) a list of parameters representing constant values; and 3) a set of possibly-bound subterms. We use the following syntax to describe terms, based on the Nuprl de nition =-=[2]-=-: opname | {z } operator name Here are a few examples: [p1; ; pn] fv1:t1; ; vm:tmg | {z } parameters | {z } subterms Displayed form Term 1 natural number["1"]fg x:b lambda[]fx. bg f(a) apply[]ff; ag v... |

5 |
The Semantics of Re Proof
- Allen, Constable, et al.
- 1990
(Show Context)
Citation Context ... of a term; 2) a list of parameters representing constant values; and 3) a set of subterms with possible variable bindings. We use the following syntax to describe terms, based on the NuPRL denition [=-=2]: o-=-pname | {z } operator name [p 1 ; ; pn ] | {z } parameters fv 1 :t 1 ; ; vm :t m g | {z } subterms 4 Here are a few examples: Displayed form Term 1 natural number["1"]fg x:b lambda[]fx... |

3 |
A type annotation scheme for Nuprl
- Howe
- 1998
(Show Context)
Citation Context ... [13] shares some common features with the MetaPRL implementation. Harrison's system is implemented in Caml-Light, and both systems require fewer computational resources than their predecessors. Howe =-=[1-=-6] has taken another approach to enhancing speed in NuPRL-4. The programming language dened by the NuPRL type theory is untyped, leading to frequent production of well-formedness (verication) conditio... |