PureCake: A Verified Compiler for a Lazy Functional Language

We present PureCake, a mechanically-verified compiler for PureLang, a lazy, purely functional programming language with monadic effects. PureLang syntax is Haskell-like and indentation-sensitive, and its constraint-based Hindley-Milner type system guarantees safe execution. We derive sound equational reasoning principles over its operational semantics, dramatically simplifying some proofs. We prove end-to-end correctness for the compilation of PureLang down to machine code-the first such result for any lazy language-by targeting CakeML and composing with its verified compiler. Multiple optimisation passes are necessary to handle realistic lazy idioms effectively. We develop PureCake entirely within the HOL4 interactive theorem prover.