yoko: Generic Programming with Disbanded Data Types

Based off of the paper "A Pattern for Almost Homomorphic Functions" at http://www.ittc.ku.edu/~nfrisby/frisby-wgp-2012.pdf, presented at the Workshop on Generic Programming 2012. Also, my dissertation http://www.ittc.ku.edu/~nfrisby/frisby-dissertation.pdf

yoko views a nominal datatype as a band of constructors, each a nominal type in its own right. Such datatypes can be disbanded via the disband function into an anonymous sum of nominal constructors, and vice versa via the band function. This library uses extensive type-level programming to enrich its instant-generics foundation with capabilities derived from the constructor-centric perspective.

For example, consider the following nominal datatype.

data Beatles = John ... | Paul ... | George ... | Ringo ...

This type can of course be understood as a sum of the individual fields types.

data John   = John   ...
data Paul   = Paul   ...
data George = George ...
data Ringo  = Ringo  ...

yoko's conceptual foundations start there. In particular, this allows a constructor, say John, to be used independently of its original range type and sibling constructors.

As a generic programming library, yoko extends instant-generics with support for constructor-centric generic programming. The Examples/LambdaLift/LambdaLift.hs file distributed with the yoko source demonstrates defining a lambda-lifting conversion between the two types ULC, which has lambdas, and Prog, which has top-level function declarations instead.

data ULC = Lam Type ULC | Var Int | Let [Decl] ULC | App ULC ULC

data Decl = Decl Type ULC



data Prog = Prog [FunDec] TLF
type FunDec = ([Type], [Type], Type, TLF)

data TLF = Top Int [Occ] | Occ Occ | App TLF TLF
data Occ = Par Int | Env Int

These types are defined in separate modules, since they have constructors with the same name. Indeed, the fact that they having matching constructors named App is crucial for yoko's automatic conversion from ULC's App to TLF's App. As written, the generic lambda-lifter would continue to work for any new ULC constructors (e.g. syntax for tuples or mutable references) as long as constructors with the same names and analogous fields were added to TLF and the semantics of those constructors doesn't involve binding. This default generic behavior of the lambda-lifter is specified in about ten lines of user code.

The non-generic code is much more complicated. This is intentional: I wanted to show that sometimes shoehorning an algorithm into the requisite type (ie a -> m a') can be difficult and require subtleties like backwards state.

Existing generic libraries don't use constructor names to the degree that yoko does, and so cannot accomodate generic conversions as well.

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