3 research outputs found
Best-First Rippling
Rippling is a form of rewriting that guides search by only performing steps that reduce the syntactic differences between formulae. Termination is normally ensured by a measure that is decreases with each rewrite step. Because of this restriction, rippling will fail to prove theorems about, for example, mutual recursion as steps that temporarily increase the differences are necessary. Best-first rippling is an extension to rippling where the restrictions have been recast as heuristic scores for use in best-first search. If nothing better is available, previously illegal steps can be considered, making best-first rippling more flexible than ordinary rippling. We have implemented best-first rippling in the IsaPlanner system together with a mechanism for caching proof-states that helps remove symmetries in the search space, and machinery to ensure termination based on term embeddings. Our experiments show that the implementation of best-first rippling is faster on average than IsaPlanner’s version of traditional depth-first rippling, and solves a range of problems where ordinary rippling fails
Automated discovery of inductive lemmas
The discovery of unknown lemmas, case-splits and other so called eureka steps are
challenging problems for automated theorem proving and have generally been assumed
to require user intervention. This thesis is mainly concerned with the automated
discovery of inductive lemmas. We have explored two approaches based on
failure recovery and theory formation, with the aim of improving automation of firstand
higher-order inductive proofs in the IsaPlanner system.
We have implemented a lemma speculation critic which attempts to find a missing
lemma using information from a failed proof-attempt. However, we found few proofs
for which this critic was applicable and successful. We have also developed a program
for inductive theory formation, which we call IsaCoSy.
IsaCoSy was evaluated on different inductive theories about natural numbers, lists
and binary trees, and found to successfully produce many relevant theorems and lemmas.
Using a background theory produced by IsaCoSy, it was possible for IsaPlanner
to automatically prove more new theorems than with lemma speculation.
In addition to the lemma discovery techniques, we also implemented an automated
technique for case-analysis. This allows IsaPlanner to deal with proofs involving conditionals,
expressed as if- or case-statements.
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Best-First Rippling
Abstract. Rippling is a form of rewriting that guides search by only performing steps that reduce the differences between formulae. Termination is normally ensured by a defined measure that is required to decrease with each step. Because of these restrictions, rippling will fail to prove theorems about, for example, mutual recursion where steps that temporarily increase the differences are necessary. Best-first rippling is an extension to rippling where the restrictions have been recast as heuristic scores for use in best-first search. If nothing better is available, previously illegal steps can be considered, making best-first rippling more flexible than ordinary rippling. We have implemented best-first rippling in the IsaPlanner system together with a mechanism for caching proof-states that helps remove symmetries in the search space, and machinery to ensure termination based on term embeddings. Our experiments show that the implementation of best-first rippling is faster on average than Isa-Planner’s version of traditional depth-first rippling, and solves a range of problems where ordinary rippling fails.