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.Trans.Common
  17 import Language.Symantic.Expr.Root
  18 import Language.Symantic.Expr.Error
  19 import Language.Symantic.Expr.From
  20 import Language.Symantic.Expr.Lambda
  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 Prelude.<$> 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 -- * Type 'Expr_List'
  50 -- | Expression.
  51 data Expr_List (lam:: * -> *) (root:: *)
  52 type instance Root_of_Expr      (Expr_List lam root)      = root
  53 type instance Type_of_Expr      (Expr_List lam root)      = Type_List
  54 type instance Sym_of_Expr       (Expr_List lam root) repr = (Sym_List repr, Sym_List_Lam lam repr)
  55 type instance Error_of_Expr ast (Expr_List lam root)      = No_Error_Expr
  56
  57 instance Constraint_Type1 Functor (Type_List root) where
  58         constraint_type1 _c Type_Type1{} = Just Dict
  59 instance Constraint_Type1 Applicative (Type_List root) where
  60         constraint_type1 _c Type_Type1{} = Just Dict
  61 instance Constraint_Type1 Traversable (Type_List root) where
  62         constraint_type1 _c Type_Type1{} = Just Dict
  63
  64 -- | Parsing utility to check that the given type is a 'Type_List'
  65 -- or raise 'Error_Expr_Type_mismatch'.
  66 check_type_list
  67  :: forall ast ex root ty h ret.
  68  ( root ~ Root_of_Expr ex
  69  , ty ~ Type_Root_of_Expr ex
  70  , Lift_Type   Type_List (Type_of_Expr root)
  71  , Unlift_Type Type_List (Type_of_Expr root)
  72  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  73                    (Error_of_Expr ast root)
  74  )
  75  => Proxy ex -> ast -> ty h
  76  -> (Type_List ty h -> Either (Error_of_Expr ast root) ret)
  77  -> Either (Error_of_Expr ast root) ret
  78 check_type_list ex ast ty k =
  79         case unlift_type $ unType_Root ty of
  80          Just ty_l -> k ty_l
  81          Nothing -> Left $
  82                 error_expr ex $
  83                 Error_Expr_Type_mismatch ast
  84                  (Exists_Type (type_list $ type_var0 SZero
  85                  :: Type_Root_of_Expr ex [Var0]))
  86                  (Exists_Type ty)
  87
  88 -- | Parse 'list_empty'.
  89 list_empty_from
  90  :: forall root lam ty ty_root ast hs ret.
  91  ( ty ~ Type_Root_of_Expr (Expr_List lam root)
  92  , ty_root ~ Type_Root_of_Expr root
  93  , Type_from ast ty_root
  94  , Lift_Type_Root Type_List ty_root
  95  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  96                    (Error_of_Expr ast root)
  97  , Root_of_Expr root ~ root
  98  ) => ast
  99  -> Expr_From ast (Expr_List lam root) hs ret
 100 list_empty_from ast_ty_a ex ast _ctx k =
 101         either (\err -> Left $ error_expr ex $ Error_Expr_Type err ast) id $
 102         type_from (Proxy::Proxy ty_root) ast_ty_a $ \ty_a -> Right $
 103         k (type_list ty_a) $ Forall_Repr_with_Context $
 104                 const list_empty
 105
 106 -- | Parse 'list_cons'.
 107 list_cons_from
 108  :: forall root lam ty ast hs ret.
 109  ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 110  , Eq_Type (Type_Root_of_Expr root)
 111  , Expr_from ast root
 112  , Lift_Type   Type_List (Type_of_Expr root)
 113  , Unlift_Type Type_List (Type_of_Expr root)
 114  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 115                    (Error_of_Expr ast root)
 116  , Root_of_Expr root ~ root
 117  ) => ast -> ast
 118  -> Expr_From ast (Expr_List lam root) hs ret
 119 list_cons_from ast_a ast_l ex ast ctx k =
 120         expr_from (Proxy::Proxy root) ast_a ctx $
 121          \(ty_a::Type_Root_of_Expr root h_a) (Forall_Repr_with_Context a) ->
 122         expr_from (Proxy::Proxy root) ast_l ctx $
 123          \(ty_l::Type_Root_of_Expr root h_l) (Forall_Repr_with_Context l) ->
 124         check_type_list ex ast ty_l $ \(Type_Type1 _ ty_l_a) ->
 125         check_eq_type ex ast ty_a ty_l_a $ \Refl ->
 126         k (type_list ty_a) $ Forall_Repr_with_Context $
 127                 \c -> list_cons (a c) (l c)
 128
 129 -- | Parse 'list'.
 130 list_from
 131  :: forall root lam ex ty ty_root ast hs ret.
 132  ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 133  , ty_root ~ Type_Root_of_Expr root
 134  , ex ~ Expr_List lam root
 135  , Eq_Type (Type_Root_of_Expr root)
 136  , Type_from ast ty_root
 137  , Expr_from ast root
 138  , Lift_Type   Type_List (Type_of_Expr root)
 139  , Unlift_Type Type_List (Type_of_Expr root)
 140  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 141                    (Error_of_Expr ast root)
 142  , Root_of_Expr root ~ root
 143  , Root_of_Type ty_root ~ ty_root
 144  ) => ast -> [ast]
 145  -> Expr_From ast ex hs ret
 146 list_from ast_ty_a ast_as =
 147         case type_from (Proxy::Proxy ty_root)
 148          ast_ty_a (Right . Exists_Type) of
 149          Left err -> \ex ast _ctx _k -> Left $ error_expr ex $ Error_Expr_Type err ast
 150          Right (Exists_Type ty_a) -> go ty_a [] ast_as
 151         where
 152         go :: Type_Root_of_Expr root ty_a
 153            -> [Forall_Repr_with_Context root hs ty_a]
 154            -> [ast]
 155            -> Expr_From ast (Expr_List lam root) hs ret
 156         go ty_a as [] _ex _ast _ctx k =
 157                 k (type_list ty_a) $ Forall_Repr_with_Context $
 158                         \c -> list ((\(Forall_Repr_with_Context a) -> a c) Prelude.<$> reverse as)
 159         go ty_a as (ast_x:ast_xs) ex ast ctx k =
 160                 expr_from (Proxy::Proxy root) ast_x ctx $
 161                  \(ty_x::Type_Root_of_Expr root h_x) x ->
 162                 check_eq_type ex ast ty_a ty_x $ \Refl ->
 163                 go ty_a (x:as) ast_xs ex ast ctx k
 164
 165 -- | Parse 'list_filter'.
 166 list_filter_from
 167  :: forall root lam ty ty_root ast hs ret.
 168  ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 169  , ty_root ~ Type_of_Expr root
 170  , Eq_Type (Type_Root_of_Expr root)
 171  , Expr_from ast root
 172  , Lift_Type   Type_Bool      ty_root
 173  , Lift_Type   (Type_Fun lam) ty_root
 174  , Unlift_Type (Type_Fun lam) ty_root
 175  , Lift_Type   Type_List      ty_root
 176  , Unlift_Type Type_List      ty_root
 177  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 178                    (Error_of_Expr ast root)
 179  , Root_of_Expr root ~ root
 180  ) => ast -> ast
 181  -> Expr_From ast (Expr_List lam root) hs ret
 182 list_filter_from ast_f ast_l ex ast ctx k =
 183         expr_from (Proxy::Proxy root) ast_f ctx $
 184          \(ty_f::Type_Root_of_Expr root h_f) (Forall_Repr_with_Context f) ->
 185         expr_from (Proxy::Proxy root) ast_l ctx $
 186          \(ty_l::Type_Root_of_Expr root h_l) (Forall_Repr_with_Context l) ->
 187         check_type_fun ex ast ty_f $ \(Type_Type2 Proxy ty_f_a ty_f_b
 188          :: Type_Fun lam (Type_Root_of_Expr root) h_f) ->
 189         check_eq_type ex ast type_bool ty_f_b $ \Refl ->
 190         check_type_list ex ast ty_l $ \(Type_Type1 _ ty_l_a) ->
 191         check_eq_type ex ast ty_f_a ty_l_a $ \Refl ->
 192         k ty_l $ Forall_Repr_with_Context $
 193          \c -> list_filter (f c) (l c)