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[haskell/symantic.git] / Language / Symantic / Expr / Applicative.hs
1 {-# LANGUAGE DefaultSignatures #-}
2 {-# LANGUAGE GADTs #-}
3 {-# LANGUAGE FlexibleContexts #-}
4 {-# LANGUAGE FlexibleInstances #-}
5 {-# LANGUAGE MultiParamTypeClasses #-}
6 {-# LANGUAGE OverloadedStrings #-}
7 {-# LANGUAGE Rank2Types #-}
8 {-# LANGUAGE ScopedTypeVariables #-}
9 {-# LANGUAGE TypeFamilies #-}
10 {-# LANGUAGE TypeOperators #-}
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 qualified Control.Applicative as Applicative
17 import Control.Monad
18 import qualified Data.Function as Fun
19 import Data.Proxy (Proxy(..))
20 import Data.Type.Equality ((:~:)(Refl))
21 import Prelude hiding (Functor(..), (<$>), Applicative(..), id, const)
22
23 import Language.Symantic.Type
24 import Language.Symantic.Repr
25 import Language.Symantic.Trans.Common
26 import Language.Symantic.Expr.Root
27 import Language.Symantic.Expr.Error
28 import Language.Symantic.Expr.From
29 import Language.Symantic.Expr.Lambda
30 import Language.Symantic.Expr.Functor
31
32 -- * Class 'Sym_Applicative'
33 -- | Symantic.
34 class Sym_Functor repr => Sym_Applicative repr where
35 pure :: Applicative f => repr a -> repr (f a)
36 (<*>) :: Applicative f => repr (f ((->) a b)) -> repr (f a) -> repr (f b)
37
38 default pure :: (Trans t repr, Applicative f) => t repr a -> t repr (f a)
39 default (<*>) :: (Trans t repr, Applicative f)
40 => t repr (f ((->) a b)) -> t repr (f a) -> t repr (f b)
41
42 pure = trans_map1 pure
43 (<*>) = trans_map2 (<*>)
44 (*>) :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
45 (<*) :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
46 x *> y = (lam Fun.id <$ x) <*> y
47 x <* y = (lam (lam . Fun.const) <$> x) <*> y
48
49 infixl 4 *>
50 infixl 4 <*
51 infixl 4 <*>
52
53 instance Sym_Applicative Repr_Host where
54 pure = liftM Applicative.pure
55 (<*>) = liftM2 (Applicative.<*>)
56 instance Sym_Applicative Repr_Text where
57 pure = repr_text_app1 "pure"
58 (<*>) = repr_text_infix "<*>" (Precedence 4)
59 (<* ) = repr_text_infix "<*" (Precedence 4)
60 ( *>) = repr_text_infix "*>" (Precedence 4)
61 instance (Sym_Applicative r1, Sym_Applicative r2) => Sym_Applicative (Repr_Dup r1 r2) where
62 pure (a1 `Repr_Dup` a2) =
63 pure a1 `Repr_Dup` pure a2
64 (<*>) (f1 `Repr_Dup` f2) (m1 `Repr_Dup` m2) =
65 (<*>) f1 m1 `Repr_Dup` (<*>) f2 m2
66
67 -- * Type 'Expr_Applicative'
68 -- | Expression.
69 data Expr_Applicative (root:: *)
70 type instance Root_of_Expr (Expr_Applicative root) = root
71 type instance Type_of_Expr (Expr_Applicative root) = No_Type
72 type instance Sym_of_Expr (Expr_Applicative root) repr = (Sym_Applicative repr)
73 type instance Error_of_Expr ast (Expr_Applicative root) = No_Error_Expr
74
75 -- | Parse 'pure'.
76 pure_from
77 :: forall root ty ast hs ret.
78 ( ty ~ Type_Root_of_Expr (Expr_Applicative root)
79 , Type0_Eq ty
80 , Type1_From ast ty
81 , Expr_From ast root
82 , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
83 (Error_of_Expr ast root)
84 , Root_of_Expr root ~ root
85 , Type1_Constraint Applicative ty
86 ) => ast -> ast
87 -> ExprFrom ast (Expr_Applicative root) hs ret
88 pure_from ast_f ast_a ex ast ctx k =
89 -- pure :: Applicative f => a -> f a
90 either (\err -> Left $ error_expr ex $ Error_Expr_Type err ast) Fun.id $
91 type1_from (Proxy::Proxy ty) ast_f $ \_f ty_f -> Right $
92 expr_from (Proxy::Proxy root) ast_a ctx $
93 \(ty_a::ty h_a) (Forall_Repr_with_Context a) ->
94 let ty_fa = ty_f ty_a in
95 check_type1_constraint ex (Proxy::Proxy Applicative) ast ty_fa $ \Dict ->
96 k ty_fa $ Forall_Repr_with_Context $
97 \c -> pure (a c)
98
99 -- | Parse '<*>'.
100 ltstargt_from
101 :: forall root ty ast hs ret.
102 ( ty ~ Type_Root_of_Expr (Expr_Applicative root)
103 , Expr_From ast root
104 , Type0_Eq ty
105 , Type1_Eq ty
106 , Type0_Lift Type_Fun (Type_of_Expr root)
107 , Type0_Unlift Type_Fun (Type_of_Expr root)
108 , Type1_Unlift (Type_of_Expr 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 , Type1_Constraint Applicative ty
113 ) => ast -> ast
114 -> ExprFrom ast (Expr_Applicative root) hs ret
115 ltstargt_from ast_fg ast_fa ex ast ctx k =
116 -- (<*>) :: Applicative f => f (a -> b) -> f a -> f b
117 expr_from (Proxy::Proxy root) ast_fg ctx $
118 \(ty_fg::ty h_fg) (Forall_Repr_with_Context fg) ->
119 expr_from (Proxy::Proxy root) ast_fa ctx $
120 \(ty_fa::ty h_fa) (Forall_Repr_with_Context fa) ->
121 check_type1 ex ast ty_fg $ \(Type1 _f (ty_g::ty h_g), _) ->
122 check_type1 ex ast ty_fa $ \(Type1 f ty_fa_a, Type1_Lift ty_f) ->
123 check_type1_eq ex ast ty_fg ty_fa $ \Refl ->
124 check_type_fun ex ast ty_g $ \(Type2 Proxy ty_g_a ty_g_b) ->
125 check_type1_constraint ex (Proxy::Proxy Applicative) ast ty_fa $ \Dict ->
126 check_type0_eq ex ast ty_g_a ty_fa_a $ \Refl ->
127 k (Type_Root $ ty_f $ Type1 f ty_g_b) $ Forall_Repr_with_Context $
128 \c -> (<*>) (fg c) (fa c)