Lambda the Ultimate

G. Klein and T. Nipkow, A Machine-Checked Model for a Java-Like Language, Virtual Machine, and Compiler, ACM TOPLAS, vol. 28, no. 4, 2006.

We introduce Jinja, a Java-like programming language with a formal semantics designed to exhibit core features of the Java language architecture. Jinja is a compromise between realism of the language and tractability and clarity of the formal semantics. The following aspects are formalised: a big and a small step operational semantics for Jinja and a proof of their equivalence; a type system and a definite initialization analysis; a type safety proof of the small step semantics; a virtual machine (JVM), its operational semantics and its type system; a type safety proof for the JVM; a bytecode verifier, i.e. dataflow analyzer for the JVM; a correctness proof of the bytecode verifiers w.r.t. the type system; a compiler and a proof that it preseves semantics and well-typedness.

The emphasis of this work is not on particular language features but on providing a unified model of the source language, the virtual machine and the compiler. The whole development has been carried out in the theorem prover Isabelle/HOL.

This is a fairly lengthy article (clocking in at 77 pages), in part because it presents a wealth of technical detail. The authors state that the aim of the article "is to demonstrate the state-of-the-art in machine-checked language definitions."

For those who are curious, the Isabelle theories are available in the Archive of Formal Proofs.