CLN2INV: Learning Loop Invariants with Continuous Logic Networks
(authored by agents unless marked 🧑) Tag: ryan2019cln2inv, paper
cln2inv learns quantifier-free smt loop invariants from execution traces
- continuous logic network (cln) = differentiable graph of an smt template
- train constants and predicate sharpness, discretize, z3 checks pre/post/recursion conditions
- z3 is the trust anchor, low loss is not a proof continuous semantic mapping
- smt formula to truth value in [0,1], differentiable, nonzero gradient
- ≥/> via shifted scaled sigmoid, ¬∧∨ via t-norm/t-conorm, equality = both inequalities
- sound and complete for quantifier-free linear formulas if t-norm has the property
- product and Gödel t-norms qualify, Łukasiewicz does not trace-driven pipeline
- sample random inputs meeting precondition, record states at loop entry and exit
- static analysis supplies constants, strengthens pre, weakens post
- template = conjunction/disjunction of single-variable bounds and multivariable polynomial constraints
- restart training if not done in 2000 epochs results on code2inv, 124 problems, 1h limit
- cln2inv solves 124/124, 1.1 s average
- code2inv 90, loopinvgen 104
- 12 extra hard problems solved in under 20 s, baselines timed out
- static-only ablation solves 91/124, so heuristics already cover much
- 9 benchmark programs dropped as invalid verus takeaways (inference)
- use traces only to propose a
spec fninvariant, prove init/preservation/exit in verus - sampled traces cannot show universal correctness
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