Plaid: Pattern Language for Abstract Datatypes

The expressiveness of traditional syntactic pattern matching is severely limited by its lack of abstraction. Because syntax patterns are mired in the builtin types understood by the pattern matching system, they lack the ability to express patterns over abstract data types (ADT’s). More advanced pattern matching techniques, such as semantic matching, can overcome this, but at the per-ADT cost of the complex code required to add new pattern combinators to the system. Plaid defines a new pattern language that captures a strict subset of Scheme capable of both regular computation, as well as reverse computation. This allows it to overcome both the limitations of syntactic patterns and the cost of semantic patterns by providing a means by which programmers can write a single specification of the mapping between the abstract and concrete representations of an ADT that simultaneously serves as constructor, predicate, accessor, and pattern combinator for that ADT. This specification is written virtually identically to how a regular constructor would be written. Furthermore, the Plaid pattern language is capable of capturing non-determinism and decisions within pattern matching, thus admitting a very broad interpretation of what can be considered an ADT constructor. This leads to variety of interesting capabilities, such as the ability to view concrete data in multiple abstract ways, the ability to canonicalize multiple concrete representations in one abstract way, and the ability to imagine more convenient representations of existing data.