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Conjecture Synthesis for Inductive Theories
 JOURNAL OF AUTOMATED REASONING
, 2010
"... We have developed a program for inductive theory formation, called IsaCoSy, which synthesises conjectures ‘bottomup’ from the available constants and free variables. The synthesis process is made tractable by only generating irreducible terms, which are then filtered through counterexample checkin ..."
Abstract

Cited by 26 (10 self)
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We have developed a program for inductive theory formation, called IsaCoSy, which synthesises conjectures ‘bottomup’ from the available constants and free variables. The synthesis process is made tractable by only generating irreducible terms, which are then filtered through counterexample checking and passed to the automatic inductive prover IsaPlanner. The main technical contribution is the presentation of a constraint mechanism for synthesis. As theorems are discovered, this generates additional constraints on the synthesis process. We evaluate IsaCoSy as a tool for automatically generating the background theories one would expect in a mature proof assistant, such as the Isabelle system. The results show that IsaCoSy produces most, and sometimes all, of the theorems in the Isabelle libraries. The number of additional uninteresting theorems are small enough to be easily pruned by hand.
Edinburgh Scotland
"... In [2] we introduced a system which used term synthesis to generate correct loop invariants. The CORE system extends this and is capable of automatically proving fully functional properties of programs involving pointers, by utilising existing systems to eliminate shape parts, and extracting functio ..."
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In [2] we introduced a system which used term synthesis to generate correct loop invariants. The CORE system extends this and is capable of automatically proving fully functional properties of programs involving pointers, by utilising existing systems to eliminate shape parts, and extracting function from the structural statements. The system is capable of synthesising correct functional invariants which allow proofs to succeed. We describe below how we define these terms. Shape, structure and function Consider the loop invariant expression for inplace list reversal: data lseg(α, i, nil) ∗ data lseg(β, j, nil) ∧ α0 = rev(β) <> α, where <> represents concatenation. We define the following three properties: Shape This describes purely the shape of the heap, and hence can be described purely as in Smallfoot as list(i) ∗ list(j). as the list segments are nullterminated. There is no information about any data that is contained in the list, purely an indication of the inductive data structures that exist in this part of the heap, in this case linked lists. Structural This describes the inductive structures on the heap, and gives names for the data
unknown title
, 2009
"... The discovery of unknown lemmas, casesplits 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 ..."
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The discovery of unknown lemmas, casesplits 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 higherorder 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 proofattempt. 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.