Modular Reifiable Matching, A List-of-Functors Approach to Two-Level Types
Haskell Agda
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Modular Reifiable Matching, A List-of-Functors Approach to Two-Level Types

Modular Reifiable Matching (MRM) is a new approach to two level types using a fixpoint of list-of-functors representation. MRM allows the modular definition of datatypes and functions by pattern matching, using a style similar to the widely popular Datatypes à la Carte (DTC) approach. However, unlike DTC, which uses the more conventional two-level types approach using fixpoints of functors, MRM uses a fixpoint of list-of-functors.

This approach has advantages that help with various aspects of extensibility, modularity and reuse. Firstly, modular pattern matching definitions are collected using a list of matches that is fully reifiable. This allows for extensible pattern matching definitions to be easily reused/inherited, and particular matches to be overridden. Such flexibility is used, among other things, to implement extensible generic traversals.

Secondly, the subtyping relation between lists of functors is quite simple, does not require backtracking, and is easy to model in languages like Haskell.

This repository implements MRM as a Haskell library, and illustrates its use and applicability through some examples.

More details of MRM can be found in Bruno C. d. S. Oliveira, Shin-Cheng Mu, and Shu-Hung You. Modular reifiable matching: a list-of-functors approach to two-level types. In the 8th ACM SIGPLAN Symposium on Haskell (Haskell 2015), pages 82-93. Sep. 2015.