the solve_eqs_tactic is to be replaced by a re-implementation that uses solve_eqs in the simplifiers directory.
The re-implementation should address efficiency issues with the previous code.
At this point it punts on low level proofs. The plan is to use coarser
dependency tracking instead of low level proofs for pre-processing. Dependencies can be converted into a proof hint representation that can be checked using a stronger checker.
simplifiers layer is a common substrate for global non-incremental and incremental processing.
The first two layers are new, but others are to be ported form tactics.
- bv::slice - rewrites equations to cut-dice-slice bit-vector extractions until they align. It creates opportunities for rewriting portions of bit-vectors to common sub-expressions, including values.
- euf::completion - generalizes the KB simplifcation from asserted formulas to use the E-graph to establish a global and order-independent canonization.
The interface dependent_expr_simplifier is amenable to forming tactics. Plugins for asserted-formulas is also possible but not yet realized.
- ensure mk_extract performs simplification to distribute over extract and removing extract if the range is the entire bit-vector
- ensure bool_rewriter simplifeis disjunctions when applicable.
move self-checking functionality to inside sat/smt so it can be used on-line and not just off-line.
when self-validation fails, use vs, not clause, to check. It allows self-validation without checking and maintaining RUP validation.
new options sat.smt.proof.check_rup, sat.smt.proof.check for online validation.
z3 sat.smt.proof.check=true sat.euf=true /v:1 sat.smt.proof.check_rup=true /st file.smt2 sat.smt.proof=p.smt2
EUF proofs are checked modulo union-find.
Equalities are added to to union-find if they are assumptions or if they can be derived using congruence closure. The congruence closure assumptions are added as proof-hints.
Note that this proof format does not track equality inferences, symmetry and transitivity. Instead they are handled by assuming a union-find based checker.
The bug was that axiom generation was not enabled on last_index, so no axioms got created to constrain last-index.
With default settings the solver is now very slow on this example. It is related to that the smallest size of a satisfying assignment is above 24. Pending a good heuristic to find initial seeds and increments for iterative deepening, I am adding another parameter smt.seq.min_unfolding that when set to 30 helps for this example.
The literal "emp" can be true in the current assignment, in which case the clause
cnt or emp or ~postf is true and does not contribute to propagation.
This saves, potentially, for generating lemmas for postf.
Add a lemma a = "" or |s| >= idx when a = tail(s, idx)
The lemma ensures that length bounding on s is enforced
(the branch that expands not-contains for long sequences s is closed).
