Skip Ackermann constraints for derived arrays (weak equivalence)

[tautschnig]

Skip generating Ackermann constraints for arrays that are derived from other arrays via with (store), if, array_of, array constants, array_comprehension, typecast, or let expressions.

For a derived array such as x = y with [k := v], the Ackermann constraint i1 = i2 => x[i1] = x[i2] is already implied by:
(1) the with constraint: k != j => x[j] = y[j], and
(2) the Ackermann constraint on the base array y.
This is the read-over-weakeq optimisation from the theory of weakly equivalent arrays (Christ & Hoenicke, 2014).

The same reasoning applies to if, array_of, and other derived array expressions, all of which already have constraints connecting them element-wise to their constituent arrays.

With 5 stores to the same unbounded array the Ackermann constraint count drops from 110 to 60; with 40 stores it drops from 63180 to 31980 (approximately 50% reduction in all cases).

Co-authored-by: Kiro

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[Copilot]

Pull request overview

This PR implements the "weak equivalence" optimization for array constraints in the SMT solver, specifically reducing redundant Ackermann constraints for derived arrays. The optimization recognizes that arrays created through operations like with (store), if, array_of, and similar expressions don't need separate Ackermann constraints because these are already implied by the combination of the operation's own constraints and the Ackermann constraints on the base arrays.

Changes:

• Modified add_array_Ackermann_constraints() to skip generating constraints for derived array expressions
• Added regression test demonstrating ~50% reduction in Ackermann constraints (from 110 to 60 for 5 stores)

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated no comments.

File	Description
src/solvers/flattening/arrays.cpp	Added logic to skip Ackermann constraint generation for derived arrays (with, if, array_of, etc.)
regression/cbmc/Array_UF23/test.desc	Test configuration verifying the constraint count reduction from 110 to 60
regression/cbmc/Array_UF23/main.c	Test case with 5 array stores to demonstrate the optimization

Comments suppressed due to low confidence (1)

src/solvers/flattening/arrays.cpp:355

• The let_exprt check is separated from the other ID checks. Consider adding ID_let to the compound condition above (lines 347-350) for consistency and to avoid the need for a dynamic cast.

    if(expr_try_dynamic_cast<let_exprt>(arr))
      continue;

---

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 80.02%. Comparing base (708e3fe) to head (86a9c39).
⚠️ Report is 5 commits behind head on develop.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #8841      +/-   ##
===========================================
+ Coverage    80.00%   80.02%   +0.01%     
===========================================
  Files         1700     1700              
  Lines       188252   188280      +28     
  Branches        73       73              
===========================================
+ Hits        150613   150664      +51     
+ Misses       37639    37616      -23     

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[tautschnig]

Needs #8851 for CI to pass.