We introduce an automatic method for producing stateful ML programs together with proofs of correctness from monadic functions in HOL. Our mechanism supports references, exceptions, and I/O operations, and can generate functions manipulating local state, which can then be encapsulated for use in a pure context. We apply this approach to several non-trivial examples, including the instruction encoder and register allocator of the otherwise pure CakeML compiler, which now benefits from better runtime performance. This development has been carried out in the HOL4 theorem prover.

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.