A Theorem Proving Approach to Programming Language Semantics

The semantics of programming languages is one of the core topics in computer science. This topic is formalism-heavy and requires the student to attempt numerous proofs for a deep understanding. We argue that modern theorem provers are excellent aids to teaching and understanding programming language semantics. As pen-and-paper proofs get automated via the theorem prover, it allows an experiment-driven strategy at exploring this topic. This article provides an encoding of the semantics of the WHILE language in the most popular styles—operational, denotational, and axiomatic—within the F* proof assistant. We show that once the program and its semantics are encoded, modern proof assistants can prove exciting language features with minimal human assistance. We believe that teaching programming languages via proof assistants will not only provide a more concrete understanding of this topic but also prepare future programming language researchers to use theorem provers as fundamental tools in their research and not as an afterthought.