Language/Symantic/Transforming/Trans.hs

   1 module Language.Symantic.Transforming.Trans where
   2
   3 -- |
   4 -- * 'trans_lift' is generally not /surjective/
   5 -- * 'trans_apply' is not /injective/
   6 -- * 'trans_apply' . 'trans_lift' == 'id'
   7 -- * 'trans_lift' . 'trans_apply' /= 'id'
   8 --
   9 -- NOTE: @DefaultSignatures@ can be used
  10 -- when declaring a symantic type class
  11 -- to provide default definition of the methods:
  12 -- implementing their identity transformation
  13 -- in order to avoid boilerplate code
  14 -- when writting 'Trans' instances which
  15 -- do not need to alterate those methods.
  16 class Trans t term where
  17         -- | Lift a term to the transformer's.
  18         trans_lift  :: term a -> t term a
  19         -- | Unlift a term from the transformer's.
  20         trans_apply :: t term a -> term a
  21
  22         -- | Convenient method to define the identity transformation for a unary symantic method.
  23         trans_map1 :: (term a -> term b) -> (t term a -> t term b)
  24         trans_map1 f = trans_lift . f . trans_apply
  25
  26         -- | Convenient method to define the identity transformation for a binary symantic method.
  27         trans_map2
  28          :: (term a -> term b -> term c)
  29          -> (t term a -> t term b -> t term c)
  30         trans_map2 f e1 e2 = trans_lift (trans_apply e1 `f` trans_apply e2)
  31
  32         -- | Convenient method to define the identity transformation for a ternary symantic method.
  33         trans_map3
  34          :: (term a -> term b -> term c -> term d)
  35          -> (t term a -> t term b -> t term c -> t term d)
  36         trans_map3 f e1 e2 e3 = trans_lift $ f (trans_apply e1) (trans_apply e2) (trans_apply e3)
  37
  38 -- | Closed type family extracting the term
  39 -- upon which a transformer is applied.
  40 --
  41 -- This is useful to write default associated types in symantics.
  42 type family Term_of_Trans (term :: * -> *) :: (* -> *) where
  43         Term_of_Trans (t term) = term