multiplate-simplified- Shorter, more generic functions for Multiplate.



0. Given these data types for a simple language:

data Prog a = Prog a [Decl]

data Decl = VarDecl Var Expr
          | FunDecl Var [Var] [Decl]
          | Return Expr

data Expr = Ref String
          | Number Int
          | Add Expr Expr
          | Mul Expr Expr

data Var = Var String


1. Define a Plate f data type

The name of the fields should refer to the actual data type: they will be prefixed with a "p" here. These field accessors are called projectors for the given plate and the actual data type (see the Projector p a type alias). You have to use projectors to provide definition for the multiplate method, and also for functions like foldFor. With this module, you only need projectors for the IsProjector instance definition. (However you do have to use projectors anyway if List, Maybe, (,), etc. are not part of the plate, in which case you have to explicitly traverse them to expose their structure to Multiplate. See: point 3.)

data Plate f = Plate
  { pProg :: forall a. Prog a -> f (Prog a)
  , pDecl :: Decl -> f Decl
  , pExpr :: Expr -> f Expr
  , pVar  :: Var  -> f Var


2. Define IsProjector instances for Plate and all the actual data types

instance IsProjector Plate (Prog a) where
  getProjector _ _ = pProg

instance IsProjector Plate Decl where
  getProjector _ _ = pDecl

instance IsProjector Plate Expr where
  getProjector _ _ = pExpr

instance IsProjector Plate Var where
  getProjector _ _ = pVar


3. Define a single Multiplate instance for Plate

Definitions required without this module are given in the comments. (The "b" prefixes in functions stand for "build".)

instance Multiplate Plate where
  mkPlate build = Plate (build pProg) (build pDecl) (build pExpr) (build pVar)
  multiplate p  = Plate bProg bDecl bExpr bVar where
    -- you have to define these here to capture the 'p' parameter
    constr <$>: a = constr <$> (getProjector p a) p a
    appl   <*>: a = appl   <*> (getProjector p a) p a
    infixl 4 <$>:
    infixl 4 <*>:
    -- definitions:
    -- lists, maybe values, etc. have a Traversable instance, which has to be used for these [*]
    bProg (Prog a decls)           = Prog <$> pure a <*> traverse (pDecl p) decls    
    bDecl (VarDecl var expr)       = VarDecl <$>: var <*>: expr
    -- bDecl (VarDecl str expr)    = VarDecl <$> pVar p var <*> pExpr p expr
    bDecl (FunDecl var vars decls) = FunDecl <$>: var <*> traverse (pVar p) vars <*> traverse (pDecl p) decls
    bDecl (Return expr)            = Return <$>: expr
    -- bDecl (Return expr)         = Return <$> pExpr p expr
    bExpr (Ref str)                = Ref <$> pure str
    bExpr (Number int)             = Number <$> pure int
    bExpr (Add expr expr')         = Add <$>: expr <*>: expr'
    -- bExpr (Add expr expr')      = Add <$> pExpr p expr <*> pExpr p expr'
    bExpr (Mul expr expr')         = Mul <$>: expr <*>: expr'
    -- bExpr (Mul expr expr')      = Mul <$> pExpr p expr <*> pExpr p expr'
    bVar (Var str)                 = Var <$> pure str

[*] However, tuples for example are not Traversable (since they don't have the appropriate kind) so instead of traverse one can use a function like this:

traverseTuple fa fb (a, b) = (,) <$> fa a <*> fb b

bConstr (Constr a b) = Constr <$> traverseTuple (pTypeOfA p) (pTypeOfB p) (a, b)

OR simply add tuples for the plate definition, just like Expr or Decl. This also can be done for List, Maybe, etc., and then the traverse functions can be replaced with <$>:, <*>:, and generic functions defined in this module can be used for these too.


4. Using multiplate

In a given program:

var a = 1;
function func(arg1, arg2){
  return a + arg1

and its representation:

prog :: Prog ()
prog = Prog () [VarDecl (Var "a") (Number 1)
               ,FunDecl (Var "func") [(Var "arg1"), (Var "arg2")]
                    [Return (Add (Ref "a") (Ref "arg1"))]]

to get the list of variables one has to define a plate by updating another plate containing defaults for all types (purePlate) by modifying the field that correpsondes to Var data type. Then create another plate where the order of traversal is set (preorderFold), and finally call gfoldFor with the plate we defined, and then with the actual data type. Without this module instead of gfoldFor one can only use foldFor, which requires an extra argument (a projector), which corresponds to the root datatype: in this case it's pProg because our program has a Prog data type. But gfoldFor, gtraverseFor, etc. can be used with any data type, because in the IsProjector instances we already defined what it's projector is.

variablesPlate :: Plate (Constant [String])
variablesPlate = preorderFold purePlate { pVar = ((Var str) -> Constant [str]) }

vars :: (IsProjector Plate a) => a -> [String]
vars  x = gfoldFor       variablesPlate x

vars' :: Prog a -> [String]
vars' x =  foldFor pProg variablesPlate x
> vars prog


All of this code is included in the source at the end of this file for easier copying.

Multiplate documentation:


class Multiplate p => IsProjector p a whereSource


getProjector :: p appl -> a -> Projector p aSource

gtraverseMFor :: (IsProjector p a, Monad m) => p m -> a -> m aSource

gfoldFor :: IsProjector p a => p (Constant o) -> a -> oSource

gunwrapFor :: IsProjector p a => (o -> b) -> p (Constant o) -> a -> bSource

gsumFor :: IsProjector p a => p (Constant (Sum n)) -> a -> nSource

gproductFor :: IsProjector p a => p (Constant (Product n)) -> a -> nSource

gallFor :: IsProjector p a => p (Constant All) -> a -> BoolSource

ganyFor :: IsProjector p a => p (Constant Any) -> a -> BoolSource

gfirstFor :: IsProjector p a => p (Constant (First b)) -> a -> Maybe bSource

glastFor :: IsProjector p a => p (Constant (Last b)) -> a -> Maybe bSource