Certainty in Formalising SMT-LIB for Strings in Isabelle

The prevalence of string solvers in formal program analysis has led to an increasing demand for more effective and dependable solving techniques. However, solving the satisfiability problem of string constraints, which is a generally undecidable problem, requires a deep understanding of the structure of the constraints. To address this challenge, the community has relied on SMT solvers to tackle the quantifier-free first-order logic fragment of string constraints, usually stated in SMT-LIB format. In 2020, the SMT-LIB Initiative issued the first official standard for string constraints. However, SMT-LIB states the semantics in a semi-formal manner, lacking a level of formality that is desirable for validating SMT solvers. In response, we formalise the SMT-LIB theory of strings using Isabelle, an interactive theorem prover known for its ability to formalise and verify mathematical and logical theorems. We demonstrate the usefulness of having a formally defined theory by deriving, to the best of our knowledge, the first automated verified model verification method for SMT-LIB string constraints and highlight potential future applications.