SEMBridge: Tagless-Final Program Semantics with Weakest-Precondition and Bounded-Checking Interpretations

SEMBridge is a tagless-final framework that enables developers to write program semantics once and automatically generate multiple interpretations, including executable code, weakest-precondition verification conditions, and bounded-checking validators. The Python prototype demonstrates synchronization of formal verification artifacts with executable semantics across loop-free imperative programs, addressing the practical gap between formal methods and software engineering.

SEMBridge addresses a fundamental challenge in formal methods: the disconnect between executable software and verification artifacts. Traditionally, developers either commit to a single abstract syntax tree representation or maintain separate codebases for execution and formal analysis, creating synchronization problems. This framework consolidates those concerns through a tagless-final interpreter pattern, allowing object programs to be interpreted into multiple semantic domains simultaneously.

The research builds on decades of work in denotational semantics and abstract interpretation, where different program meanings can be extracted without duplicating core logic. The tagless-final style, popularized in functional programming communities, proves particularly effective for this use case because it eliminates boilerplate abstract syntax handling and enables compositional semantic extension. By treating programs as functions rather than data structures, developers gain flexibility in interpretation without sacrificing clarity.

For the formal methods and software verification community, this architecture reduces maintenance burden when keeping executable implementations synchronized with verification conditions. The prototype's handling of weakest-precondition semantics—a cornerstone of Hoare logic—demonstrates practical applicability to security-critical domains. The bounded checking up to 729 states shows capacity for realistic program analysis beyond toy examples.

Looking forward, the framework's extensibility toward proof-assistant and SMT backends suggests a pathway for deeper integration between testing, bounded verification, and full formal proof. As software complexity increases and verification becomes increasingly critical for security, tools that unify executable semantics with formal artifacts could reshape how development teams approach correctness guarantees.

• →SEMBridge unifies executable semantics and formal verification through a single tagless-final framework, eliminating manual synchronization.
• →The approach generates weakest-precondition conditions and bounded-checking validators from identical program definitions.
• →Python prototype validates the architecture on loop-free imperative programs with assignments, conditionals, and assertions.
• →Bounded checking successfully validates over domains up to 729 states, demonstrating practical scalability beyond theoretical constructs.
• →Framework designed for extensibility toward proof assistants and SMT backends, bridging executable and formally verified code.