Program Optimisations via Hylomorphisms for Extraction of Executable Code

Generic programming with recursion schemes provides a powerful abstraction for structuring recursion and provides a rigorous reasoning principle for program optimisations which have been successfully applied to compilers for functional languages. Formalising recursion schemes in a type theory offers additional termination guarantees, but it often requires compromising on performance, requiring the assumption of additional axioms, and/or introducing unsafe casts into extracted code. This paper presents the first Rocq formalisation of hylomorphisms allowing for the mechanisation of all recognised recursive algorithms. The key contribution of this paper is that this formalisation is fully axiom-free, and it allows the extraction of safe, idiomatic functional code. We exemplify the framework by formalising a series of algorithms based on different recursive paradigms such as divide-and conquer, dynamic programming, and mutual recursion and demonstrate that the extracted functional code for the programs formalised in our framework is efficient, humanly readable, and runnable. Furthermore, we show the use of the machine-checked proofs of the laws of hylomorphisms to do program optimisations.