[HTML][HTML] Inductive theorem proving based on tree grammars
S Eberhard, S Hetzl - Annals of Pure and Applied Logic, 2015 - Elsevier
Induction plays a key role in reasoning in many areas of mathematics and computer science.
A central problem in the automation of proof by induction is the non-analytic nature of …
A central problem in the automation of proof by induction is the non-analytic nature of …
Cyclic proofs for first-order logic with inductive definitions
J Brotherston - … Conference on Automated Reasoning with Analytic …, 2005 - Springer
We consider a cyclic approach to inductive reasoning in the setting of first-order logic with
inductive definitions. We present a proof system for this language in which proofs are …
inductive definitions. We present a proof system for this language in which proofs are …
A unified view of induction reasoning for first-order logic
S Stratulat - Turing-100, The Alan Turing Centenary Conference, 2012 - inria.hal.science
Induction is a powerful proof technique adapted to reason on sets with an unbounded
number of elements. In a first-order setting, two different methods are distinguished: the …
number of elements. In a first-order setting, two different methods are distinguished: the …
Automata-driven automated induction
A Bouhoula, JP Jouannaud - Information and Computation, 2001 - Elsevier
This work investigates inductive theorem proving techniques for first-order functions whose
meaning and domains can be specified by Horn clauses built up from the equality and …
meaning and domains can be specified by Horn clauses built up from the equality and …
Lazy generation of induction hypotheses
M Protzen - International Conference on Automated Deduction, 1994 - Springer
A novel approach for automating explicit induction is suggested. Analysis of successful
induction proofs reveals that these proofs can be guided without reference to a specific …
induction proofs reveals that these proofs can be guided without reference to a specific …
Guiding induction proofs
D Hutter - 10th International Conference on Automated Deduction …, 1990 - Springer
A crucial point in proving theorems by induction is to manipulate the induction conclusion to
enable the use of the induction hypothesis. We propose a technique to control such a …
enable the use of the induction hypothesis. We propose a technique to control such a …
Induction using term orders
F Bronsard, US Reddy, RW Hasker - Journal of Automated Reasoning, 1996 - Springer
We present a procedure for proving inductive theorems which is based on explicit induction,
yet supports mutual induction. Mutual induction allows the postulation of lemmas whose …
yet supports mutual induction. Mutual induction allows the postulation of lemmas whose …
Induction using term orderings
F Bronsard, US Reddy, RW Hasker - … Nancy, France, June 26–July 1, 1994 …, 1994 - Springer
We present a procedure for proving inductive theorems which is based on explicit induction,
yet supports mutual induction. Mutual induction allows the postulation of lemmas whose …
yet supports mutual induction. Mutual induction allows the postulation of lemmas whose …
Rippling: A heuristic for guiding inductive proofs
We describe rippling: a tactic for the heuristic control of the key part of proofs by
mathematical induction. This tactic significantly reduces the search for a proof of a wide …
mathematical induction. This tactic significantly reduces the search for a proof of a wide …
Automatic proofs by induction in theories without constructors
JP Jouannaud, E Kounalis - Information and computation, 1989 - Elsevier
Inductionless induction consists of using pure equational reasoning for proving the validity of
an equation in the initial algebra of a set of equational axioms, which would normally require …
an equation in the initial algebra of a set of equational axioms, which would normally require …