Implementing theorem provers in a purely functional style

1999 ◽  
Vol 9 (2) ◽  
pp. 147-166 ◽  
Author(s):  
KEITH HANNA
Keyword(s):  
Partial Algebra ◽  
Proof Assistant ◽  
Theorem Provers ◽  
Executable Specification ◽  
Efficient Representation

This paper discusses the principles of implementing an LCF-style proof assistant using a purely functional metalanguage. Two approaches are described; in both, signatures are treated as ordinary values, rather than as mutable components within an abstract datatype. The first approach treats the object logic as a partial algebra and represents it as a partial datatype, that is, a datatype in which the domains of the constructors are restricted by predicate functions. This results in a compact, executable specification of the logic. The second approach uses an abstract type to allow an efficient representation of the logic, whilst keeping the same interface. A case study describes how these principles were put into practice in implementing a fairly complex dependently-sorted logic.

Interface Reduction in Craig-Bampton Component Mode Synthesis by Orthogonal Polynomial Series

2017 ◽  
Author(s):  
Luigi Carassale ◽  
Mirko Maurici
Keyword(s):  
Degrees Of Freedom ◽  
Axial Compressor ◽  
Component Mode Synthesis ◽  
Reduction Techniques ◽  
Interface Reduction ◽  
Reduction Methods ◽  
Interface Displacement ◽  
Polynomial Series ◽  
Efficient Representation

The component mode synthesis based on the Craig-Bampton method has two strong limitations that appear when the number of the interface degrees of freedom is large. First, the reduced-order model obtained is overweighed by many unnecessary degrees of freedom. Second, the reduction step may become extremely time consuming. Several interface reduction techniques addressed successfully the former problem, while the latter remains open. In this paper we tackle this latter problem through a simple interface-reduction technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing interface reduction methods on a case study regarding a rotor blade of an axial compressor.

scholarly journals Cooperating Theorem Provers: A Case Study Combining HOL-Light and CVC Lite

2006 ◽  
Vol 144 (2) ◽  
pp. 43-51 ◽  
Author(s):  
Sean McLaughlin ◽  
Clark Barrett ◽  
Yeting Ge
Keyword(s):  
Theorem Provers ◽  
Hol Light

Interface Reduction in Craig–Bampton Component Mode Synthesis by Orthogonal Polynomial Series

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Luigi Carassale ◽  
Mirko Maurici
Keyword(s):  
Degrees Of Freedom ◽  
Axial Compressor ◽  
Component Mode Synthesis ◽  
Order Model ◽  
Reduced Order ◽  
Interface Reduction ◽  
Interface Displacement ◽  
Polynomial Series ◽  
Efficient Representation

The component mode synthesis (CMS) based on the Craig–Bampton (CB) method has two strong limitations that appear when the number of the interface degrees-of-freedom (DOFs) is large. First, the reduced-order model (ROM) obtained is overweighed by many unnecessary DOF. Second, the reduction step may become extremely time consuming. Several interface reduction (IR) techniques addressed successfully the former problem, while the latter remains open. In this paper, we tackle this latter problem through a simple IR technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing IR methods on a case study regarding a rotor blade of an axial compressor.

scholarly journals Rewrite rule inference using equality saturation

2021 ◽  
Vol 5 (OOPSLA) ◽  
pp. 1-28
Author(s):  
Chandrakana Nandi ◽  
Max Willsey ◽  
Amy Zhu ◽  
Yisu Remy Wang ◽  
Brett Saiki ◽  
...  
Keyword(s):  
Open Source ◽  
Promising Technique ◽  
Rule Based ◽  
Domain Experts ◽  
Open Source Tool ◽  
Theorem Provers ◽  
Large Sets ◽  
Rewrite Rules ◽  
Rule Inference

Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets must be rechecked or extended whenever semantics are tweaked. Large rulesets can also be challenging to apply: redundant rules slow down rule-based search and frustrate debugging. This paper explores how equality saturation, a promising technique that uses e-graphs to apply rewrite rules, can also be used to infer rewrite rules. E-graphs can compactly represent the exponentially large sets of enumerated terms and potential rewrite rules. We show that equality saturation efficiently shrinks both sets, leading to faster synthesis of smaller, more general rulesets. We prototyped these strategies in a tool dubbed Ruler. Compared to a similar tool built on CVC4, Ruler synthesizes 5.8× smaller rulesets 25× faster without compromising on proving power. In an end-to-end case study, we show Ruler-synthesized rules which perform as well as those crafted by domain experts, and addressed a longstanding issue in a popular open source tool.

scholarly journals Verification of Concurrent Programs Using the Coq Proof Assistant: A Case Study

2005 ◽  
Vol 1 ◽  
pp. 117-127 ◽  
Author(s):  
Reynald Affeldt ◽  
Naoki Kobayashi ◽  
Akinori Yonezawa
Keyword(s):  
Concurrent Programs ◽  
Proof Assistant ◽  
The Coq Proof Assistant ◽  
Coq Proof Assistant

scholarly journals Robust, Semi-Intelligible Isabelle Proofs from ATP Proofs

10.29007/zbdb ◽  
2018 ◽  
Author(s):  
Steffen Juilf Smolka ◽  
Jasmin Christian Blanchette
Keyword(s):  
Companion Paper ◽  
Proof Assistant ◽  
Theorem Provers ◽  
Automatic Theorem Provers ◽  
Proof Methods ◽  
The Right ◽  
Automatic Theorem

Sledgehammer integrates external automatic theorem provers (ATPs) in the Isabelle/HOL proof assistant. To guard against bugs, ATP proofs must be reconstructed in Isabelle. Reconstructing complex proofs involves translating them to detailed Isabelle proof texts, using suitable proof methods to justify the inferences. This has been attempted before with little success, but we have addressed the main issues: Sledgehammer now transforms the proofs by contradiction into direct proofs (as described in a companion paper); it reconstructs skolemization inferences; it provides the right amount of type annotations to ensure formulas are parsed correctly without overwhelming them with types; and it iteratively tests and compresses the output, resulting in simpler and faster proofs.

scholarly journals Bayesian Optimisation for Premise Selection in Automated Theorem Proving (Student Abstract)

2020 ◽  
Vol 34 (10) ◽  
pp. 13919-13920
Author(s):  
Agnieszka Słowik ◽  
Chaitanya Mangla ◽  
Mateja Jamnik ◽  
Sean B. Holden ◽  
Lawrence C. Paulson
Keyword(s):  
Parameter Space ◽  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Search Space ◽  
Large Set ◽  
Probabilistic Framework ◽  
Formal Proofs ◽  
Dimensional Parameter ◽  
Theorem Provers

Modern theorem provers utilise a wide array of heuristics to control the search space explosion, thereby requiring optimisation of a large set of parameters. An exhaustive search in this multi-dimensional parameter space is intractable in most cases, yet the performance of the provers is highly dependent on the parameter assignment. In this work, we introduce a principled probabilistic framework for heuristic optimisation in theorem provers. We present results using a heuristic for premise selection and the Archive of Formal Proofs (AFP) as a case study.

ASP with non-herbrand partial functions: a language and system for practical use

2013 ◽  
Vol 13 (4-5) ◽  
pp. 547-561 ◽  
Author(s):  
MARCELLO BALDUCCINI
Keyword(s):  
Knowledge Representation ◽  
Constraint Programming ◽  
Industrial Application ◽  
Answer Set Programming ◽  
Quantitative Information ◽  
Partial Functions ◽  
Supporting System ◽  
Qualitative And Quantitative ◽  
Efficient Representation

AbstractDealing with domains involving substantial quantitative information in Answer Set Programming (ASP) often results in cumbersome and inefficient encodings. Hybrid “CASP” languages combining ASP and Constraint Programming aim to overcome this limitation, but also impose inconvenient constraints – first and foremost that quantitative information must be encoded by means of total functions. This goes against central knowledge representation principles that contribute to the power of ASP, and makes the formalization of certain domains difficult. ASP{f} is being developed with the ultimate goal of providing scientists and practitioners with an alternative to CASP languages that allows for the efficient representation of qualitative and quantitative information in ASP without restricting one's ability to deal with incompleteness or uncertainty. In this paper we present the latest outcome of such research: versions of the language and of the supporting system that allow for practical, industrial-size use and scalability. The applicability of ASP{f} is demonstrated by a case study on an actual industrial application.

The Genesis and Internal Dynamics of El Salvador's People's Revolutionary Army, 1970–1976

2014 ◽  
Vol 38 (01) ◽  
pp. 102-129
Author(s):  
ALBERTO MARTÍN ÁLVAREZ ◽  
EUDALD CORTINA ORERO
Keyword(s):  
Latin America ◽  
El Salvador ◽  
Early Years ◽  
Left Wing ◽  
Internal Dynamics ◽  
Internal Coherence ◽  
The 1960S

AbstractUsing interviews with former militants and previously unpublished documents, this article traces the genesis and internal dynamics of the Ejército Revolucionario del Pueblo (People's Revolutionary Army, ERP) in El Salvador during the early years of its existence (1970–6). This period was marked by the inability of the ERP to maintain internal coherence or any consensus on revolutionary strategy, which led to a series of splits and internal fights over control of the organisation. The evidence marshalled in this case study sheds new light on the origins of the armed Salvadorean Left and thus contributes to a wider understanding of the processes of formation and internal dynamics of armed left-wing groups that emerged from the 1960s onwards in Latin America.

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