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 {-# OPTIONS_GHC -fno-warn-orphans #-}
  12 -- | Expression for 'Applicative'.
  13 module Language.Symantic.Expr.Applicative where
  14
  15 import Control.Applicative (Applicative)
  16 import Data.Proxy (Proxy(..))
  17 import Data.Type.Equality ((:~:)(Refl))
  18 import Prelude hiding (Applicative(..))
  19
  20 import Language.Symantic.Type
  21 import Language.Symantic.Trans.Common
  22 import Language.Symantic.Expr.Common
  23 import Language.Symantic.Expr.Lambda
  24 import Language.Symantic.Expr.Functor
  25
  26 -- * Class 'Sym_Applicative'
  27 -- | Symantic.
  28 class Sym_Applicative repr where
  29         pure  :: Applicative f => repr a -> repr (f a)
  30         -- (*>)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
  31         -- (<*)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
  32
  33         default pure :: (Trans t repr, Applicative f) => t repr a -> t repr (f a)
  34         pure = trans_map1 pure
  35
  36 -- * Class 'Sym_Applicative_Lam'
  37 -- | Symantic requiring a 'Lambda'.
  38 class Sym_Functor lam repr => Sym_Applicative_Lam lam repr where
  39         (<*>) :: Applicative f => repr (f (Lambda lam a b)) -> repr (f a) -> repr (f b)
  40         -- (*>)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
  41         -- (<*)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
  42
  43         default (<*>) :: (Trans t repr, Applicative f) => t repr (f (Lambda lam a b)) -> t repr (f a) -> t repr (f b)
  44         -- default (*>)  :: (Trans t, Applicative f) => t repr (f a) -> t repr (f b) -> t repr (f b)
  45         -- default (<*)  :: (Trans t, Applicative f) => t repr (f a) -> t repr (f b) -> t repr (f a)
  46         (<*>) = trans_map2 (<*>)
  47 infixl 4 <*>
  48
  49 -- * Type 'Expr_Applicative'
  50 -- | Expression.
  51 data Expr_Applicative (lam:: * -> *) (root:: *)
  52 type instance Root_of_Expr      (Expr_Applicative lam root)      = root
  53 type instance Type_of_Expr      (Expr_Applicative lam root)      = No_Type
  54 type instance Sym_of_Expr       (Expr_Applicative lam root) repr = (Sym_Applicative repr, Sym_Applicative_Lam lam repr)
  55 type instance Error_of_Expr ast (Expr_Applicative lam root)      = No_Error_Expr
  56 instance Constraint_Type1 Applicative (Type_Type0 px root)
  57 instance Constraint_Type1 Applicative (Type_Var1 root)
  58 instance Constraint_Type1 Applicative (Type_Type2 px root)
  59
  60 pure_from
  61  :: forall root ty ty_root lam ast hs ret.
  62  ( ty ~ Type_Root_of_Expr (Expr_Applicative lam root)
  63  , ty_root ~ Type_Root_of_Expr root
  64  , Eq_Type (Type_Root_of_Expr root)
  65  , Type1_from ast (Type_Root_of_Expr root)
  66  , Expr_from ast root
  67  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  68                    (Error_of_Expr ast root)
  69  , Root_of_Expr root ~ root
  70  , Constraint_Type1 Applicative ty
  71  ) => ast -> ast
  72  -> Expr_From ast (Expr_Applicative lam root) hs ret
  73 pure_from ast_f ast_a ex ast ctx k =
  74  -- pure :: Applicative f => a -> f a
  75         either (\err -> Left $ error_expr ex $ Error_Expr_Type err ast) id $
  76         type1_from (Proxy::Proxy ty_root) ast_f $ \_f ty_f -> Right $
  77                 expr_from (Proxy::Proxy root) ast_a ctx $
  78                  \(ty_a::Type_Root_of_Expr root h_a) (Forall_Repr_with_Context a) ->
  79                 let ty_fa = ty_f ty_a in
  80                 check_constraint1_type ex (Proxy::Proxy Applicative) ast ty_fa $ \Dict ->
  81                 k ty_fa $ Forall_Repr_with_Context $
  82                  \c -> pure (a c)
  83
  84 ltstargt_from
  85  :: forall root ty lam ast hs ret.
  86  ( ty ~ Type_Root_of_Expr (Expr_Applicative lam root)
  87  , String_from_Type ty
  88  , Eq_Type (Type_Root_of_Expr root)
  89  , Eq_Type1 (Type_Root_of_Expr root)
  90  , Expr_from ast root
  91  , Lift_Type   (Type_Fun lam) (Type_of_Expr root)
  92  , Unlift_Type (Type_Fun lam) (Type_of_Expr root)
  93  , Unlift_Type1 (Type_of_Expr root)
  94  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  95                    (Error_of_Expr ast root)
  96  , Root_of_Expr root ~ root
  97  , Constraint_Type1 Applicative ty
  98  ) => ast -> ast
  99  -> Expr_From ast (Expr_Applicative lam root) hs ret
 100 ltstargt_from ast_fg ast_fa ex ast ctx k =
 101  -- (<*>) :: Applicative f => f (a -> b) -> f a -> f b
 102         expr_from (Proxy::Proxy root) ast_fg ctx $
 103          \(ty_fg::Type_Root_of_Expr root h_fg) (Forall_Repr_with_Context fg) ->
 104         expr_from (Proxy::Proxy root) ast_fa ctx $
 105          \(ty_fa::Type_Root_of_Expr root h_fa) (Forall_Repr_with_Context fa) ->
 106         check_type1 ex ast ty_fg $ \(Type_Type1 _f (ty_g::Type_Root_of_Expr root h_g), _) ->
 107         check_type1 ex ast ty_fa $ \(Type_Type1 f ty_fa_a, Lift_Type1 ty_f) ->
 108         check_eq_type1 ex ast ty_fg ty_fa $ \Refl ->
 109         check_type_fun ex ast ty_g $ \(Type_Type2 Proxy ty_g_a ty_g_b
 110          :: Type_Fun lam (Type_Root_of_Expr root) h_g) ->
 111         check_constraint1_type ex (Proxy::Proxy Applicative) ast ty_fa $ \Dict ->
 112         check_eq_type ex ast ty_g_a ty_fa_a $ \Refl ->
 113         k (Type_Root $ ty_f $ Type_Type1 f ty_g_b) $ Forall_Repr_with_Context $
 114          \c -> (<*>) (fg c) (fa c)