Language/Symantic/Expr/List.hs

   1 {-# LANGUAGE DefaultSignatures #-}
   2 {-# LANGUAGE FlexibleContexts #-}
   3 {-# LANGUAGE FlexibleInstances #-}
   4 {-# LANGUAGE MultiParamTypeClasses #-}
   5 {-# LANGUAGE ScopedTypeVariables #-}
   6 {-# LANGUAGE TypeFamilies #-}
   7 {-# LANGUAGE TypeOperators #-}
   8 {-# OPTIONS_GHC -fno-warn-orphans #-}
   9 -- | Expression for 'List'.
  10 module Language.Symantic.Expr.List where
  11
  12 import Data.Proxy (Proxy(..))
  13 import Data.Type.Equality ((:~:)(Refl))
  14
  15 import Language.Symantic.Type
  16 import Language.Symantic.Repr.Dup
  17 import Language.Symantic.Trans.Common
  18 import Language.Symantic.Expr.Common
  19 import Language.Symantic.Expr.Lambda
  20 import Language.Symantic.Expr.Functor
  21
  22 -- * Class 'Sym_List_Lam'
  23 -- | Symantic.
  24 class Sym_List repr where
  25         list_empty :: repr [a]
  26         list_cons  :: repr a -> repr [a] -> repr [a]
  27         list       :: [repr a] -> repr [a]
  28
  29         default list_empty :: Trans t repr => t repr [a]
  30         default list_cons  :: Trans t repr => t repr a -> t repr [a] -> t repr [a]
  31         default list       :: Trans t repr => [t repr a] -> t repr [a]
  32         list_empty = trans_lift list_empty
  33         list_cons  = trans_map2 list_cons
  34         list l     = trans_lift $ list (trans_apply <$> l)
  35 -- | Symantic requiring a 'Lambda'.
  36 class Sym_List_Lam lam repr where
  37         list_filter
  38          :: repr (Lambda lam a Bool)
  39          -> repr [a]
  40          -> repr [a]
  41
  42         default list_filter
  43          :: Trans t repr
  44          => t repr (Lambda lam a Bool)
  45          -> t repr [a]
  46          -> t repr [a]
  47         list_filter = trans_map2 list_filter
  48
  49 instance -- Sym_List Dup
  50  ( Sym_List r1
  51  , Sym_List r2
  52  ) => Sym_List (Dup r1 r2) where
  53         list_empty = list_empty `Dup` list_empty
  54         list_cons (a1 `Dup` a2) (l1 `Dup` l2) = list_cons a1 l1 `Dup` list_cons a2 l2
  55         list l =
  56                 let (l1, l2) =
  57                         foldr (\(x1 `Dup` x2) (xs1, xs2) ->
  58                                 (x1:xs1, x2:xs2)) ([], []) l in
  59                 list l1 `Dup` list l2
  60 instance -- Sym_List_Lam Dup
  61  ( Sym_List_Lam lam r1
  62  , Sym_List_Lam lam r2
  63  ) => Sym_List_Lam lam (Dup r1 r2) where
  64         list_filter (f1 `Dup` f2) (l1 `Dup` l2) =
  65                 list_filter f1 l1 `Dup` list_filter f2 l2
  66
  67 -- * Type 'Expr_List'
  68 -- | Expression.
  69 data Expr_List (lam:: * -> *) (root:: *)
  70 type instance Root_of_Expr      (Expr_List lam root)      = root
  71 type instance Type_of_Expr      (Expr_List lam root)      = Type_List
  72 type instance Sym_of_Expr       (Expr_List lam root) repr = (Sym_List repr, Sym_List_Lam lam repr)
  73 type instance Error_of_Expr ast (Expr_List lam root)      = No_Error_Expr
  74
  75 instance Constraint1_Type Functor_with_Lambda (Type_Type1 [] root) where
  76         constraint1_type _c (Type_Type1 _ _) = Just Dict
  77
  78 -- | Parsing utility to check that the given type is a 'Type_List'
  79 -- or raise 'Error_Expr_Type_mismatch'.
  80 check_type_list
  81  :: forall ast ex root ty h ret.
  82  ( root ~ Root_of_Expr ex
  83  , ty ~ Type_Root_of_Expr ex
  84  , Type_Lift   Type_List (Type_of_Expr root)
  85  , Type_Unlift Type_List (Type_of_Expr root)
  86  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
  87                    (Error_of_Expr ast root)
  88  )
  89  => Proxy ex -> ast -> ty h
  90  -> (Type_List ty h -> Either (Error_of_Expr ast root) ret)
  91  -> Either (Error_of_Expr ast root) ret
  92 check_type_list ex ast ty k =
  93         case type_unlift $ unType_Root ty of
  94          Just ty_l -> k ty_l
  95          Nothing -> Left $
  96                 error_expr ex $
  97                 Error_Expr_Type_mismatch ast
  98                  (Exists_Type (type_list $ type_var SZero
  99                  :: Type_Root_of_Expr ex [Zero]))
 100                  (Exists_Type ty)
 101
 102 -- | Parse 'list_empty'.
 103 list_empty_from
 104  :: forall root lam ty ty_root ast hs ret.
 105  ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 106  , ty_root ~ Type_Root_of_Expr root
 107  , Type_from ast ty_root
 108  , Type_Root_Lift Type_List ty_root
 109  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 110                    (Error_of_Expr ast root)
 111  , Root_of_Expr root ~ root
 112  ) => ast
 113  -> Expr_From ast (Expr_List lam root) hs ret
 114 list_empty_from ast_ty_a ex ast _ctx k =
 115         case type_from (Proxy::Proxy ty_root)
 116          ast_ty_a (Right . Exists_Type) of
 117          Left err -> Left $ error_expr ex $ Error_Expr_Type err ast
 118          Right (Exists_Type ty_a) ->
 119                 k (type_list ty_a) $ Forall_Repr_with_Context $
 120                         const list_empty
 121
 122 -- | Parse 'list_cons'.
 123 list_cons_from
 124  :: forall root lam ty ast hs ret.
 125  ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 126  , Eq_Type (Type_Root_of_Expr root)
 127  , Expr_from ast root
 128  , Type_Lift   Type_List (Type_of_Expr root)
 129  , Type_Unlift Type_List (Type_of_Expr root)
 130  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 131                    (Error_of_Expr ast root)
 132  , Root_of_Expr root ~ root
 133  ) => ast -> ast
 134  -> Expr_From ast (Expr_List lam root) hs ret
 135 list_cons_from ast_a ast_l ex ast ctx k =
 136         expr_from (Proxy::Proxy root) ast_a ctx $
 137          \(ty_a::Type_Root_of_Expr root h_a) (Forall_Repr_with_Context a) ->
 138         expr_from (Proxy::Proxy root) ast_l ctx $
 139          \(ty_l::Type_Root_of_Expr root h_l) (Forall_Repr_with_Context l) ->
 140         check_type_list ex ast ty_l $ \(Type_Type1 _ ty_l_a) ->
 141         check_eq_type ex ast ty_a ty_l_a $ \Refl ->
 142         k (type_list ty_a) $ Forall_Repr_with_Context $
 143                 \c -> list_cons (a c) (l c)
 144
 145 -- | Parse 'list'.
 146 list_from
 147  :: forall root lam ex ty ty_root ast hs ret.
 148  ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 149  , ty_root ~ Type_Root_of_Expr root
 150  , ex ~ Expr_List lam root
 151  , Eq_Type (Type_Root_of_Expr root)
 152  , Type_from ast ty_root
 153  , Expr_from ast root
 154  , Type_Lift   Type_List (Type_of_Expr root)
 155  , Type_Unlift Type_List (Type_of_Expr root)
 156  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 157                    (Error_of_Expr ast root)
 158  , Root_of_Expr root ~ root
 159  , Root_of_Type ty_root ~ ty_root
 160  ) => ast -> [ast]
 161  -> Expr_From ast ex hs ret
 162 list_from ast_ty_a ast_as =
 163         case type_from (Proxy::Proxy ty_root)
 164          ast_ty_a (Right . Exists_Type) of
 165          Left err -> \ex ast _ctx _k -> Left $ error_expr ex $ Error_Expr_Type err ast
 166          Right (Exists_Type ty_a) -> go ty_a [] ast_as
 167         where
 168         go :: Type_Root_of_Expr root ty_a
 169            -> [Forall_Repr_with_Context root hs ty_a]
 170            -> [ast]
 171            -> Expr_From ast (Expr_List lam root) hs ret
 172         go ty_a as [] _ex _ast _ctx k =
 173                 k (type_list ty_a) $ Forall_Repr_with_Context $
 174                         \c -> list ((\(Forall_Repr_with_Context a) -> a c) <$> reverse as)
 175         go ty_a as (ast_x:ast_xs) ex ast ctx k =
 176                 expr_from (Proxy::Proxy root) ast_x ctx $
 177                  \(ty_x::Type_Root_of_Expr root h_x) x ->
 178                 check_eq_type ex ast ty_a ty_x $ \Refl ->
 179                 go ty_a (x:as) ast_xs ex ast ctx k
 180
 181 -- | Parse 'list_filter'.
 182 list_filter_from
 183  :: forall root lam ty ty_root ast hs ret.
 184  ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 185  , ty_root ~ Type_of_Expr root
 186  , Eq_Type (Type_Root_of_Expr root)
 187  , Expr_from ast root
 188  , Type_Lift   Type_Bool      ty_root
 189  , Type_Lift   (Type_Fun lam) ty_root
 190  , Type_Unlift (Type_Fun lam) ty_root
 191  , Type_Lift   Type_List      ty_root
 192  , Type_Unlift Type_List      ty_root
 193  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 194                    (Error_of_Expr ast root)
 195  , Root_of_Expr root ~ root
 196  ) => ast -> ast
 197  -> Expr_From ast (Expr_List lam root) hs ret
 198 list_filter_from ast_f ast_l ex ast ctx k =
 199         expr_from (Proxy::Proxy root) ast_f ctx $
 200          \(ty_f::Type_Root_of_Expr root h_f) (Forall_Repr_with_Context f) ->
 201         expr_from (Proxy::Proxy root) ast_l ctx $
 202          \(ty_l::Type_Root_of_Expr root h_l) (Forall_Repr_with_Context l) ->
 203         check_type_fun ex ast ty_f $ \(ty_f_a `Type_Fun` ty_f_b
 204          :: Type_Fun lam (Type_Root_of_Expr root) h_f) ->
 205         check_eq_type ex ast type_bool ty_f_b $ \Refl ->
 206         check_type_list ex ast ty_l $ \(Type_Type1 _ ty_l_a) ->
 207         check_eq_type ex ast ty_f_a ty_l_a $ \Refl ->
 208         k ty_l $ Forall_Repr_with_Context $
 209          \c -> list_filter (f c) (l c)