Quantifier and Heap Reasoning Improvements - #3961
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Improves treatment of quantified formulas involving arrays with affine integer indexes. Trigger matching compares the structure of two terms, so a fact about b[srcStart + t] cannot be used on a term about a[x]: the witness x - srcStart occurs nowhere in the proof. Re-indexing therefore had to be written as a lemma and discharged by SMT. A theory can now solve a trigger subterm against the term it should match, through a new method on QuantifierTheorySupport. Integer arithmetic solves k*t + rest = s for t by exact division, for a pattern affine in one unbound variable. A wrong solution costs one instantiation, since instantiating a universal with any term is sound. (created with AI tooling support)
Applying a method contract anonymises the heap. A quantified formula from before the call has its triggers over the old heap, so trigger matching finds no instance and the property cannot be used afterwards. For an array read select(h,a,arr(i)) the heap theory now adds the trigger select(H,a,arr(i)) with a metavariable H for the heap, which matches the read over any heap. Such a trigger is matched by unification and by basic matching. An instantiation that basic matching gets by solving a subterm costs 10000 more, so it is tried after the ones from ordinary matches. AdjacencyStore.storeValidList, added here, needs this across its call to storeList. runAllProofs: 101 of 672 proofs change, 793103 against 803745 nodes. (created with AI tooling supported)
…alues then o != u Some heap simplification rules rely in their assumes on the fact that two objects are different, i.e., \assumes (==> o = u). this change makes it more likely for that formula to be actually present
Approval should only be called on taclets whose assumes clause has been matched.
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Second of three of the last AI supported work
Improves the quantifier heuristics and heap reasoning by providing triggers if array access is an affine integer expression. It also makes inequality of objects explicit in the sequents enabling more heap simplification rules to be applied automatically. The added taclet has been proven sound and the proof has been added.
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Ensuring quality
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Created with AI tooling support
The contributions within this pull request are licensed under GPLv2 (only) for inclusion in KeY.