Language/Symantic/Expr/Maybe.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 'Maybe'.
  10 module Language.Symantic.Expr.Maybe where
  11
  12 import Data.Proxy (Proxy(..))
  13 import Data.Type.Equality ((:~:)(Refl))
  14 import Prelude hiding (maybe)
  15
  16 import Language.Symantic.Type
  17 import Language.Symantic.Trans.Common
  18 import Language.Symantic.Expr.Root
  19 import Language.Symantic.Expr.Error
  20 import Language.Symantic.Expr.From
  21 import Language.Symantic.Expr.Lambda
  22
  23 -- * Class 'Sym_Maybe_Lam'
  24 -- | Symantic.
  25 class Sym_Maybe repr where
  26         nothing :: repr (Maybe a)
  27         just    :: repr a -> repr (Maybe a)
  28
  29         default nothing :: Trans t repr => t repr (Maybe a)
  30         default just    :: Trans t repr => t repr a -> t repr (Maybe a)
  31         nothing = trans_lift nothing
  32         just    = trans_map1 just
  33 -- | Symantic requiring a 'Lambda'.
  34 class Sym_Maybe_Lam lam repr where
  35         maybe
  36          :: repr b
  37          -> repr (Lambda lam a b)
  38          -> repr (Maybe a)
  39          -> repr b
  40
  41         default maybe
  42          :: Trans t repr
  43          => t repr b
  44          -> t repr (Lambda lam a b)
  45          -> t repr (Maybe a)
  46          -> t repr b
  47         maybe = trans_map3 maybe
  48
  49 -- * Type 'Expr_Maybe'
  50 -- | Expression.
  51 data Expr_Maybe (lam:: * -> *) (root:: *)
  52 type instance Root_of_Expr      (Expr_Maybe lam root)      = root
  53 type instance Type_of_Expr      (Expr_Maybe lam root)      = Type_Maybe
  54 type instance Sym_of_Expr       (Expr_Maybe lam root) repr = (Sym_Maybe repr, Sym_Maybe_Lam lam repr)
  55 type instance Error_of_Expr ast (Expr_Maybe lam root)      = No_Error_Expr
  56
  57 instance Constraint_Type1 Functor (Type_Maybe root) where
  58         constraint_type1 _c (Type_Type1 _ _) = Just Dict
  59 instance Constraint_Type1 Applicative (Type_Maybe root) where
  60         constraint_type1 _c (Type_Type1 _ _) = Just Dict
  61
  62 -- | Parsing utility to check that the given type is a 'Type_Maybe'
  63 -- or raise 'Error_Expr_Type_mismatch'.
  64 check_type_maybe
  65  :: forall ast ex root ty h ret.
  66  ( root ~ Root_of_Expr ex
  67  , ty ~ Type_Root_of_Expr ex
  68  , Lift_Type   Type_Maybe (Type_of_Expr root)
  69  , Unlift_Type Type_Maybe (Type_of_Expr root)
  70  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  71                    (Error_of_Expr ast root)
  72  )
  73  => Proxy ex -> ast -> ty h
  74  -> (Type_Maybe ty h -> Either (Error_of_Expr ast root) ret)
  75  -> Either (Error_of_Expr ast root) ret
  76 check_type_maybe ex ast ty k =
  77         case unlift_type $ unType_Root ty of
  78          Just ty_l -> k ty_l
  79          Nothing -> Left $
  80                 error_expr ex $
  81                 Error_Expr_Type_mismatch ast
  82                  (Exists_Type (type_maybe $ type_var0 SZero
  83                  :: Type_Root_of_Expr ex (Maybe Var0)))
  84                  (Exists_Type ty)
  85
  86 -- | Parse 'maybe'.
  87 maybe_from
  88  :: forall root lam ty ty_root ast hs ret.
  89  ( ty ~ Type_Root_of_Expr (Expr_Maybe lam root)
  90  , ty_root ~ Type_of_Expr root
  91  , Eq_Type ty
  92  , Expr_from ast root
  93  , Lift_Type   (Type_Fun lam) ty_root
  94  , Unlift_Type (Type_Fun lam) ty_root
  95  , Lift_Type   Type_Maybe     ty_root
  96  , Unlift_Type Type_Maybe     ty_root
  97  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  98                    (Error_of_Expr ast root)
  99  , Root_of_Expr root ~ root
 100  ) => ast -> ast -> ast
 101  -> Expr_From ast (Expr_Maybe lam root) hs ret
 102 maybe_from ast_n ast_j ast_m ex ast ctx k =
 103         expr_from (Proxy::Proxy root) ast_n ctx $
 104          \(ty_n::Type_Root_of_Expr root h_n) (Forall_Repr_with_Context n) ->
 105         expr_from (Proxy::Proxy root) ast_j ctx $
 106          \(ty_j::Type_Root_of_Expr root h_j) (Forall_Repr_with_Context j) ->
 107         expr_from (Proxy::Proxy root) ast_m ctx $
 108          \(ty_m::Type_Root_of_Expr root h_m) (Forall_Repr_with_Context m) ->
 109         check_type_fun ex ast ty_j $ \(Type_Type2 Proxy ty_j_a ty_j_b
 110          :: Type_Fun lam (Type_Root_of_Expr root) h_j) ->
 111         check_type_maybe ex ast ty_m $ \(Type_Type1 _ ty_m_a) ->
 112         check_eq_type ex ast ty_n   ty_j_b $ \Refl ->
 113         check_eq_type ex ast ty_m_a ty_j_a $ \Refl ->
 114                 k ty_n $ Forall_Repr_with_Context $
 115                  \c -> maybe (n c) (j c) (m c)
 116
 117 -- | Parse 'nothing'.
 118 nothing_from
 119  :: forall root lam ty ty_root ast hs ret.
 120  ( ty ~ Type_Root_of_Expr (Expr_Maybe lam root)
 121  , ty_root ~ Type_Root_of_Expr root
 122  , Type_from ast ty_root
 123  , Lift_Type_Root Type_Maybe ty_root
 124  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 125                    (Error_of_Expr ast root)
 126  , Root_of_Expr root ~ root
 127  ) => ast
 128  -> Expr_From ast (Expr_Maybe lam root) hs ret
 129 nothing_from ast_ty_a ex ast _ctx k =
 130         case type_from (Proxy::Proxy ty_root)
 131          ast_ty_a (Right . Exists_Type) of
 132          Left err -> Left $ error_expr ex $ Error_Expr_Type err ast
 133          Right (Exists_Type ty_a) ->
 134                 k (type_maybe ty_a) $ Forall_Repr_with_Context $
 135                         const nothing
 136
 137 -- | Parse 'just'.
 138 just_from
 139  :: forall root lam ty ast hs ret.
 140  ( ty ~ Type_Root_of_Expr (Expr_Maybe lam root)
 141  , Expr_from ast root
 142  , Lift_Type_Root Type_Maybe (Type_Root_of_Expr root)
 143  , Root_of_Expr root ~ root
 144  ) => ast
 145  -> Expr_From ast (Expr_Maybe lam root) hs ret
 146 just_from ast_a _ex _ast ctx k =
 147         expr_from (Proxy::Proxy root) ast_a ctx $
 148          \(ty_a::Type_Root_of_Expr root h_a) (Forall_Repr_with_Context a) ->
 149                 k (type_maybe ty_a) $ Forall_Repr_with_Context $
 150                         \c -> just (a c)