Add a template haskell procedure to unify the construction of values and values in UnionM

[lsrcz]

Suppose we have a type:

data AST
  = Add (UnionM AST) (UnionM AST)
  | Mul (UnionM AST) (UnionM AST)
  | Lit SymInteger
   deriving (Show, Generic)
   deriving (Mergeable) via (Default AST)

Consider how to construct a value of this type. To construct the value (a + b) * (c + d), we may have to write:

Mul
  (mrgReturn $ Add (mrgReturn $ Lit "a") (mrgReturn $ Lit "b"))
  (mrgReturn $ Add (mrgReturn $ Lit "c") (mrgReturn $ Lit "d"))

This is ridiculously verbose.

A better way to construct this is to provide a type class that constructs an AST or a UnionM AST in a unified way:

class ASTBuilder ast where
  add :: UnionM AST -> UnionM AST -> ast
  mul :: UnionM AST -> UnionM AST -> ast
  lit :: SymInteger -> ast

and implement the following two instances:

instance ASTBuilder AST where
  add = Add
  mul = Mul
  lit = Lit

instance ASTBuilder (UnionM AST) where
  add l r = mrgReturn $ Add l r
  mul l r = mrgReturn $ Mul l r
  lit v = mrgReturn $ Lit v

Then we can construct (a + b) * (c + d) by

Mul (add (lit "a") (lit "b")) (add (lit "c") (lit "d"))

as expected.

This can be done with Template Haskell. It may be a good idea to have a way to configure the function names to avoid name clash.

[lsrcz]

This issue is superseded by our design on unified interfaces.