Derive.hs

{-# LANGUAGE ConstraintKinds #-} -- For type class synonyms
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE DefaultSignatures #-} -- For adding LiftDerived* constraints
module Symantic.Derive where

import Data.Function ((.))
import Data.Kind (Type)

-- * Type family 'Derived'
-- | The representation that @(repr)@ derives to.
type family Derived (repr :: Type -> Type) :: Type -> Type

-- * Class 'Derivable'
-- | Derive an interpreter to a another interpreter
-- determined by the 'Derived' open type family.
-- This is mostly useful when running the interpreter stack,
-- but also when going back from an initial encoding to a final one.
--
-- Note that 'derive' and 'liftDerived' are not necessarily reciprocical functions.
class Derivable repr where
  derive :: repr a -> Derived repr a

-- * Class 'LiftDerived'
-- | Lift the 'Derived' interpreter of an interpreter, to that interpreter.
-- This is mostly useful to give default values to class methods
-- in order to skip their definition for interpreters
-- where 'liftDerived' can already apply the right semantic.
--
-- Note that 'derive' and 'liftDerived' are not necessarily reciprocical functions.
class LiftDerived repr where
  liftDerived :: Derived repr a -> repr a

-- * Class 'LiftDerived1'
-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with a single argument.
class LiftDerived1 repr where
  liftDerived1 ::
    (Derived repr a -> Derived repr b) ->
    repr a -> repr b
  liftDerived1 f = liftDerived . f . derive
  default liftDerived1 ::
    LiftDerived repr => Derivable repr =>
    (Derived repr a -> Derived repr b) ->
    repr a -> repr b

-- * Class 'LiftDerived2'
-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with two arguments.
-- Note that the default instance relies upon 'LiftDerived', not 'LiftDerived1'.
class LiftDerived2 repr where
  liftDerived2 ::
    (Derived repr a -> Derived repr b -> Derived repr c) ->
    repr a -> repr b -> repr c
  liftDerived2 f a b = liftDerived (f (derive a) (derive b))
  default liftDerived2 ::
    LiftDerived repr => Derivable repr =>
    (Derived repr a -> Derived repr b -> Derived repr c) ->
    repr a -> repr b -> repr c

-- * Class 'LiftDerived3'
-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with three arguments.
-- Note that the default instance relies upon 'LiftDerived', not 'LiftDerived2'.
class LiftDerived3 repr where
  liftDerived3 ::
    (Derived repr a -> Derived repr b -> Derived repr c -> Derived repr d) ->
    repr a -> repr b -> repr c -> repr d
  liftDerived3 f a b c = liftDerived (f (derive a) (derive b) (derive c))
  default liftDerived3 ::
    LiftDerived repr => Derivable repr =>
    (Derived repr a -> Derived repr b -> Derived repr c -> Derived repr d) ->
    repr a -> repr b -> repr c -> repr d

-- * Class 'LiftDerived4'
-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with three arguments.
-- Note that the default instance relies upon 'LiftDerived', not 'LiftDerived3'.
class LiftDerived4 repr where
  liftDerived4 ::
    (Derived repr a -> Derived repr b -> Derived repr c -> Derived repr d -> Derived repr e) ->
    repr a -> repr b -> repr c -> repr d -> repr e
  liftDerived4 f a b c d = liftDerived (f (derive a) (derive b) (derive c) (derive d))
  default liftDerived4 ::
    LiftDerived repr => Derivable repr =>
    (Derived repr a -> Derived repr b -> Derived repr c -> Derived repr d -> Derived repr e) ->
    repr a -> repr b -> repr c -> repr d -> repr e

-- * Type synonyms @FromDerived*@
-- | Convenient type synonym for using 'liftDerived' on symantic class @(sym)@.
type FromDerived  sym repr = ( LiftDerived  repr, sym (Derived repr) )
type FromDerived1 sym repr = ( LiftDerived1 repr, sym (Derived repr) )
type FromDerived2 sym repr = ( LiftDerived2 repr, sym (Derived repr) )
type FromDerived3 sym repr = ( LiftDerived3 repr, sym (Derived repr) )
type FromDerived4 sym repr = ( LiftDerived4 repr, sym (Derived repr) )