Language/Symantic/Expr/Applicative.hs

   1 {-# LANGUAGE DefaultSignatures #-}
   2 {-# LANGUAGE GADTs #-}
   3 {-# LANGUAGE FlexibleContexts #-}
   4 {-# LANGUAGE FlexibleInstances #-}
   5 {-# LANGUAGE MultiParamTypeClasses #-}
   6 {-# LANGUAGE Rank2Types #-}
   7 {-# LANGUAGE ScopedTypeVariables #-}
   8 {-# LANGUAGE TypeFamilies #-}
   9 {-# LANGUAGE TypeOperators #-}
  10 {-# LANGUAGE UndecidableInstances #-}
  11 -- | Expression for 'Applicative'.
  12 module Language.Symantic.Expr.Applicative where
  13
  14 import Control.Applicative (Applicative)
  15 import Data.Proxy (Proxy(..))
  16 import Data.Type.Equality ((:~:)(Refl))
  17 import Prelude hiding (Applicative(..))
  18
  19 import Language.Symantic.Type
  20 import Language.Symantic.Trans.Common
  21 import Language.Symantic.Expr.Common
  22 import Language.Symantic.Expr.Lambda
  23 import Language.Symantic.Expr.Functor
  24
  25 -- * Class 'Sym_Applicative'
  26 -- | Symantic.
  27 class Sym_Applicative repr where
  28         pure  :: Applicative f => repr a -> repr (f a)
  29         -- (*>)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
  30         -- (<*)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
  31
  32         default pure :: (Trans t repr, Applicative f) => t repr a -> t repr (f a)
  33         pure = trans_map1 pure
  34
  35 -- * Class 'Sym_Applicative_Lam'
  36 -- | Symantic requiring a 'Lambda'.
  37 class Sym_Functor lam repr => Sym_Applicative_Lam lam repr where
  38         (<*>) :: Applicative_with_Lambda f => repr (f (Lambda lam a b)) -> repr (f a) -> repr (f b)
  39         -- (*>)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
  40         -- (<*)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
  41
  42         default (<*>) :: (Trans t repr, Applicative_with_Lambda f) => t repr (f (Lambda lam a b)) -> t repr (f a) -> t repr (f b)
  43         -- default (*>)  :: (Trans t, Applicative f) => t repr (f a) -> t repr (f b) -> t repr (f b)
  44         -- default (<*)  :: (Trans t, Applicative f) => t repr (f a) -> t repr (f b) -> t repr (f a)
  45         (<*>) = trans_map2 (<*>)
  46 infixl 4 <*>
  47
  48 -- ** Class 'Applicative_with_Lambda'
  49 -- | A class alias to join 'Traversable' to 'Applicative'.
  50 --
  51 -- NOTE: see comment of 'Functor_with_Lambda'.
  52 class    (Applicative f, Traversable f) => Applicative_with_Lambda f
  53 instance (Applicative f, Traversable f) => Applicative_with_Lambda f
  54 instance Constraint_Type1 Applicative_with_Lambda (Type_Bool     root)
  55 instance Constraint_Type1 Applicative_with_Lambda (Type_Fun lam  root)
  56 instance Constraint_Type1 Applicative_with_Lambda (Type_Int      root)
  57 instance Constraint_Type1 Applicative_with_Lambda (Type_Ordering root)
  58 instance Constraint_Type1 Applicative_with_Lambda (Type_Unit     root)
  59 instance Constraint_Type1 Applicative_with_Lambda (Type_Var0     root)
  60 instance Constraint_Type1 Applicative_with_Lambda (Type_Var1     root)
  61
  62 -- * Type 'Expr_Applicative'
  63 -- | Expression.
  64 data Expr_Applicative (lam:: * -> *) (root:: *)
  65 type instance Root_of_Expr      (Expr_Applicative lam root)      = root
  66 type instance Type_of_Expr      (Expr_Applicative lam root)      = No_Type
  67 type instance Sym_of_Expr       (Expr_Applicative lam root) repr = (Sym_Applicative repr, Sym_Applicative_Lam lam repr)
  68 type instance Error_of_Expr ast (Expr_Applicative lam root)      = No_Error_Expr
  69
  70 pure_from
  71  :: forall root ty ty_root lam ast hs ret.
  72  ( ty ~ Type_Root_of_Expr (Expr_Applicative lam root)
  73  , ty_root ~ Type_Root_of_Expr root
  74  , Eq_Type (Type_Root_of_Expr root)
  75  , Type1_from ast (Type_Root_of_Expr root)
  76  , Expr_from ast root
  77  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  78                    (Error_of_Expr ast root)
  79  , Root_of_Expr root ~ root
  80  , Constraint_Type1 Applicative_with_Lambda ty
  81  ) => ast -> ast
  82  -> Expr_From ast (Expr_Applicative lam root) hs ret
  83 pure_from ast_f ast_a ex ast ctx k =
  84  -- pure :: Applicative f => a -> f a
  85         either (\err -> Left $ error_expr ex $ Error_Expr_Type err ast) id $
  86         type1_from (Proxy::Proxy ty_root) ast_f $ \_f ty_f -> Right $
  87                 expr_from (Proxy::Proxy root) ast_a ctx $
  88                  \(ty_a::Type_Root_of_Expr root h_a) (Forall_Repr_with_Context a) ->
  89                 let ty_fa = ty_f ty_a in
  90                 check_constraint1_type ex (Proxy::Proxy Applicative_with_Lambda) ast ty_fa $ \Dict ->
  91                 k ty_fa $ Forall_Repr_with_Context $
  92                  \c -> pure (a c)
  93
  94 ltstargt_from
  95  :: forall root ty lam ast hs ret.
  96  ( ty ~ Type_Root_of_Expr (Expr_Applicative lam root)
  97  , String_from_Type ty
  98  , Eq_Type (Type_Root_of_Expr root)
  99  , Eq_Type1 (Type_Root_of_Expr root)
 100  , Expr_from ast root
 101  , Lift_Type   (Type_Fun lam) (Type_of_Expr root)
 102  , Unlift_Type (Type_Fun lam) (Type_of_Expr root)
 103  , Unlift_Type1 (Type_of_Expr root)
 104  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 105                    (Error_of_Expr ast root)
 106  , Root_of_Expr root ~ root
 107  , Constraint_Type1 Applicative_with_Lambda ty
 108  ) => ast -> ast
 109  -> Expr_From ast (Expr_Applicative lam root) hs ret
 110 ltstargt_from ast_fg ast_fa ex ast ctx k =
 111  -- (<*>) :: Applicative f => f (a -> b) -> f a -> f b
 112         expr_from (Proxy::Proxy root) ast_fg ctx $
 113          \(ty_fg::Type_Root_of_Expr root h_fg) (Forall_Repr_with_Context fg) ->
 114         expr_from (Proxy::Proxy root) ast_fa ctx $
 115          \(ty_fa::Type_Root_of_Expr root h_fa) (Forall_Repr_with_Context fa) ->
 116         check_type1 ex ast ty_fg $ \(Type_Type1 _f (ty_g::Type_Root_of_Expr root h_g), _) ->
 117         check_type1 ex ast ty_fa $ \(Type_Type1 f ty_fa_a, Lift_Type1 ty_f) ->
 118         check_eq_type1 ex ast ty_fg ty_fa $ \Refl ->
 119         check_type_fun ex ast ty_g $ \(Type_Type2 Proxy ty_g_a ty_g_b
 120          :: Type_Fun lam (Type_Root_of_Expr root) h_g) ->
 121         check_constraint1_type ex (Proxy::Proxy Applicative_with_Lambda) ast ty_fa $ \Dict ->
 122         check_eq_type ex ast ty_g_a ty_fa_a $ \Refl ->
 123         k (Type_Root $ ty_f $ Type_Type1 f ty_g_b) $ Forall_Repr_with_Context $
 124          \c -> (<*>) (fg c) (fa c)