src/Symantic/Reify.hs

   1 {-# LANGUAGE TemplateHaskell #-}
   2 {-# OPTIONS_GHC -Wno-incomplete-patterns #-} -- For reifyTH
   3 -- | Reify an Haskell value using type-directed normalisation-by-evaluation (NBE).
   4 module Symantic.Reify where
   5
   6 import Control.Monad (Monad(..))
   7 import qualified Data.Function as Fun
   8 import qualified Language.Haskell.TH as TH
   9
  10 import Symantic.Classes (Abstractable(..))
  11
  12 -- | 'ReifyReflect' witnesses the duality between @meta@ and @(repr a)@.
  13 --  It indicates which type variables in @a@ are not to be instantiated
  14 --  with the arrow type, and instantiates them to @(repr _)@ in @meta@.
  15 --  This is directly taken from: http://okmij.org/ftp/tagless-final/course/TDPE.hs
  16 --
  17 -- * @meta@ instantiates polymorphic types of the original Haskell expression
  18 --   with @(repr _)@ types, according to how 'ReifyReflect' is constructed
  19 --   using 'base' and @('-->')@. This is obviously not possible
  20 --   if the orignal expression uses monomorphic types (like 'Int'),
  21 --   but remains possible with constrained polymorphic types (like @(Num i => i)@),
  22 --   because @(i)@ can still be inferred to @(repr _)@,
  23 --   whereas the finally chosen @(repr)@
  24 --   (eg. 'E', or 'Identity', or 'TH.CodeQ', or ...)
  25 --   can have a 'Num' instance.
  26 -- * @(repr a)@ is the symantic type as it would have been,
  27 --   had the expression been written with explicit 'lam's
  28 --   instead of bare haskell functions.
  29 -- DOC: http://okmij.org/ftp/tagless-final/cookbook.html#TDPE
  30 -- DOC: http://okmij.org/ftp/tagless-final/NBE.html
  31 -- DOC: https://www.dicosmo.org/Articles/2004-BalatDiCosmoFiore-Popl.pdf
  32 data ReifyReflect repr meta a = ReifyReflect
  33   { -- | 'reflect' converts from a *represented* Haskell term of type @a@
  34     -- to an object *representing* that value of type @a@.
  35     reify   :: meta -> repr a
  36     -- | 'reflect' converts back an object *representing* a value of type @a@,
  37     -- to the *represented* Haskell term of type @a@.
  38   , reflect :: repr a -> meta
  39   }
  40
  41 -- | The base of induction : placeholder for a type which is not the arrow type.
  42 base :: ReifyReflect repr (repr a) a
  43 base = ReifyReflect{reify = Fun.id, reflect = Fun.id}
  44
  45 -- | The inductive case : the arrow type.
  46 infixr 8 -->
  47 (-->) :: Abstractable repr =>
  48          ReifyReflect repr m1 o1 -> ReifyReflect repr m2 o2 ->
  49          ReifyReflect repr (m1 -> m2) (o1 -> o2)
  50 r1 --> r2 = ReifyReflect
  51   { reify   = \meta -> lam (reify r2 Fun.. meta Fun.. reflect r1)
  52   , reflect = \repr -> reflect r2 Fun.. (.@) repr Fun.. reify r1
  53   }
  54
  55 -- * Using TemplateHaskell to fully auto-generate 'ReifyReflect'
  56
  57 -- | @$(reifyTH 'Foo.bar)@ calls 'reify' on 'Foo.bar'
  58 -- with an 'ReifyReflect' generated from the infered type of 'Foo.bar'.
  59 reifyTH :: TH.Name -> TH.Q TH.Exp
  60 reifyTH name = do
  61   info <- TH.reify name
  62   case info of
  63     TH.VarI n (TH.ForallT _vs _ctx ty) _dec ->
  64       [| reify $(genReifyReflect ty) $(return (TH.VarE n)) |]
  65     where
  66     genReifyReflect (TH.AppT (TH.AppT TH.ArrowT a) b) = [| $(genReifyReflect a) --> $(genReifyReflect b) |]
  67     genReifyReflect TH.VarT{} = [| base |]