# Multiplate

## Contents

## Making a Multiplate instance

The easiest way to understand how to use Multiplate is to look at a simple example. We assume you have the transformers library installed.

> import Data.Generics.Multiplate > import Data.Functor.Constant > import Data.Functor.Identity

Suppose you defined the follow set of mutually recursive data types for a simple language.

> data Expr = Con Int > | Add Expr Expr > | Mul Expr Expr > | EVar Var > | Let Decl Expr > deriving (Eq, Show) > > data Decl = Var := Expr > | Seq Decl Decl > deriving (Eq, Show) > > type Var = String

The first thing we are going to define is a 'plate' for this language.

> data Plate f = Plate > { expr :: Expr -> f Expr > , decl :: Decl -> f Decl > }

A plate is a record type that is parametrized by an applicative functor `f`

. There is one field for each type in the mutually recursive structure we want to write generic functions for. Each field has type `A -> f A`

where `A`

is one of the data types.

To use the Multiplate library we have to make `Plate`

and instance of the `Multiplate`

class. The instance requires that we write two functions: `multiplate`

and `mkPlate`

. Let's define each of these functions in turn.

> instance Multiplate Plate where

We have to write one piece of boilerplate code for `multiplate`

. However, once this is implemented, no further boilerplate code need be written.
`multiplate`

takes a `Plate`

as a parameter. The idea is that for each expression in our language we will call this a function from this `Plate`

parameter on the children of our expression and then combine the results.

> multiplate child = Plate buildExpr buildDecl > where > buildExpr (Add e1 e2) = Add <$> expr child e1 <*> expr child e2 > buildExpr (Mul e1 e2) = Mul <$> expr child e1 <*> expr child e2 > buildExpr (Let d e) = Let <$> decl child d <*> expr child e > buildExpr e = pure e > buildDecl (v := e) = (:=) <$> pure v <*> expr child e > buildDecl (Seq d1 d2) = Seq <$> decl child d1 <*> decl child d2

Notice that when an expression has no children, as in the case of `v`

in `v := e`

, we simply use `pure v`

.
`pure`

is used to handle the default case in `buildExpr`

, also have no subexpressions.

Next we have to define `mkPlate`

. `mkPlate`

is a function that builds a `Plate`

given a generic builder function that produces values of type `a -> f a`

. However these generic builder functions require a bit of help. The need to know what the projection function for the field that they are building is, so we pass that as a parameter to them.

> mkPlate build = Plate (build expr) (build decl)

That's it. Now we are ready to use out generic library to process our mutually recursive data structure without using any more boilerplate.

## Generic Programing with Multiplate

### Monoids

Suppose we we want to get a list of all variables used in an expression. To do this we would use `preorderFold`

with the list monoid. The first step is to build a `Plate`

that handles the cases we care about. What we can do is use the default `purePlate`

which does nothing, and modify it to handle the cases we care about.

getVariablesPlate :: Plate (Constant [Var]) getVariablesPlate = purePlate { exprPlate = exprVars } where exprVars (EVar v) = Constant [v] exprVars x = pure x

This can be written alternatively using some list comprehension tricks

getVariablesPlate = purePlate {expr = \x -> Constant [s|EVar s <- [x]]}

Now we can can build a plate that will get variables from all subexpressions and concatenate them together into one big list

variablesPlate = preorderFold getVariablesPlate

In a real program we would either put `getVariablesPlate`

into `variablesPlates`

's `where`

clause or else simply inline
the definition.

`variablesPlate`

is a record of functions that will give a list of variables for each type in our mutually recursive record. Say we have an `Expr`

we want to apply this to.

e1 :: Expr e1 = Let ("x" := Con 42) (Add (EVar "x") (EVar "x"))

We can project out the function for `Expr`

's from our plate apply it to `e1`

and then unwrap the `Constant`

wrapper. There is a little helper function, called `foldFor`

, that will upgrade of projection function to remove the `Constant`

wrapper for us.

>>> foldFor expr variablesPlate e1 ["x","x"]

### Traversing

Suppose we want to recursively evaluate constant expressions in the language.
We can use `mapFamily`

for this.
We define a `Plate Identity`

for the functionality we care about.

doConstFold :: Plate Identity doConstFold = purePlate { expr = exprConst } where expr (Add (Con x) (Con y)) = return (Con (x + y)) expr (Mul (Con x) (Con y)) = return (Con (x * y)) expr x = pure x

Now we can can build a plate that will repeatedly apply this transformation from bottom up.

constFoldPlate = mapFamily doConstFold

Let's build an declaration to test.

d1 :: Decl d1 = "x" := (Add (Mul (Con 42) (Con 68)) (Con 7))

We can project out the function for `Decl`

's from our plate apply it to `d1`

and then unwrap the `Identity`

wrapper. Again, there is a little helper function, called `traverseFor`

, that will upgrade of projection function to remove the `Identity`

wrapper for us.

>>> traverseFor decl constFoldPlate d1 "x" := Con 2863

## Alternative Plates

Multiplate does not have to be used in the above way. Any structure can be made an instance of `Multiplate`

as long as the following two Multiplate laws are satisfied:

`multiplate purePlate = purePlate`

`multiplate (composePlate p1 p2) = composePlate (multiplate p1) (multiplate p2)`

For example, Sjoerd Visscher gives an example of a plate where each constructor of each data type has its own field in a record structure.