Section: New Results

Algebra of programming

We have pursued our study of the algebraic structures of programming languages, from a syntactic as well as semantics perspective. Tackling the semantics aspect, Pierre-Évariste Dagand published a journal article introducing the theory of ornaments [11] to a general audience of functional programmers. Ornaments amount to a domain-specific language, usually described in type theory, for describing structure-preserving changes in algebraic datatypes. Such descriptions can be used to improve code reuse as well as ease of refactoring in functional languages. This work is part of a wider effort by our community to foster the adoption of ornaments when programming with algebraic datatypes, be it in type theory  [48] or general-purpose functional programming languages  [65], [89]. Tackling the syntactic aspect and in collaboration with researchers at the University of Utrecht (Victor Miraldo, Wouter Swierstra), Pierre-Évariste Dagand has worked on a formalization of diff s for structured data [20]. This preliminary and foundational work aims at providing a typed specification to the problem of computing the difference of two pieces of structured data. Unlike previous approaches  [43], following a type-theoretical approach allowed us to formalize the difference of two structure as a typed object. The task of computing the difference of two structured objects is then able to exploit this typing information to control the search space (which is otherwise gigantic). Having a typed difference also ensures that applying such a diff to a well-structured data results in either a failure (the difference is in conflict with the given file) or another well-structured data.