Extending a brainiac prover to lambda-free higher-order logic

Decades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms of efficiency. Instead of developing a new higher-order prover from the ground up, we propose to start wi...

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Bibliographic Details
Published in:International journal on software tools for technology transfer Vol. 24; no. 1; pp. 67 - 87
Main Authors: Vukmirović, Petar, Blanchette, Jasmin, Cruanes, Simon, Schulz, Stephan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Computer Science
Data structures
Logic
Logic in Computer Science
Software Engineering
Software Engineering/Programming and Operating Systems
Theory of Computation
Automatic theorem provers
First-order logic
Higher-order logic
ISSN:1433-2779, 1433-2787
Online Access:Get full text
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Summary:Decades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms of efficiency. Instead of developing a new higher-order prover from the ground up, we propose to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features. We explain how to extend the prover’s data structures, algorithms, and heuristics to λ -free higher-order logic, a formalism that supports partial application and applied variables. Our extension outperforms the traditional encoding and appears promising as a stepping stone toward full higher-order logic.
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ISSN:1433-2779
1433-2787
DOI:10.1007/s10009-021-00639-7