Language/Symantic/Expr/Integral.hs

   1 {-# LANGUAGE DefaultSignatures #-}
   2 {-# LANGUAGE FlexibleContexts #-}
   3 {-# LANGUAGE ScopedTypeVariables #-}
   4 {-# LANGUAGE TypeFamilies #-}
   5 {-# LANGUAGE TypeOperators #-}
   6 -- | Expression for 'Integral'.
   7 module Language.Symantic.Expr.Integral where
   8
   9 import Data.Proxy (Proxy(..))
  10 import Data.Type.Equality ((:~:)(Refl))
  11 import Prelude hiding (quot, rem, div, mod, quotRem, divMod, toInteger)
  12
  13 import Language.Symantic.Type
  14 import Language.Symantic.Expr.Root
  15 import Language.Symantic.Expr.Error
  16 import Language.Symantic.Expr.From
  17 import Language.Symantic.Trans.Common
  18
  19 -- * Class 'Sym_Integral'
  20 -- | Symantic.
  21 class Sym_Integral repr where
  22         quot      :: Integral i => repr i -> repr i -> repr i
  23         rem       :: Integral i => repr i -> repr i -> repr i
  24         div       :: Integral i => repr i -> repr i -> repr i
  25         mod       :: Integral i => repr i -> repr i -> repr i
  26         quotRem   :: Integral i => repr i -> repr i -> repr (i, i)
  27         divMod    :: Integral i => repr i -> repr i -> repr (i, i)
  28         toInteger :: Integral i => repr i -> repr Integer
  29
  30         default quot      :: (Trans t repr, Integral i) => t repr i -> t repr i -> t repr i
  31         default rem       :: (Trans t repr, Integral i) => t repr i -> t repr i -> t repr i
  32         default div       :: (Trans t repr, Integral i) => t repr i -> t repr i -> t repr i
  33         default mod       :: (Trans t repr, Integral i) => t repr i -> t repr i -> t repr i
  34         default quotRem   :: (Trans t repr, Integral i) => t repr i -> t repr i -> t repr (i, i)
  35         default divMod    :: (Trans t repr, Integral i) => t repr i -> t repr i -> t repr (i, i)
  36         default toInteger :: (Trans t repr, Integral i) => t repr i -> t repr Integer
  37
  38         quot      = trans_map2 quot
  39         rem       = trans_map2 rem
  40         div       = trans_map2 div
  41         mod       = trans_map2 mod
  42         quotRem   = trans_map2 quotRem
  43         divMod    = trans_map2 divMod
  44         toInteger = trans_map1 toInteger
  45
  46 infixl 7 `quot`
  47 infixl 7 `rem`
  48 infixl 7 `div`
  49 infixl 7 `mod`
  50
  51 -- * Type 'Expr_Integral'
  52 -- | Expression.
  53 data Expr_Integral (root:: *)
  54 type instance Root_of_Expr      (Expr_Integral root)      = root
  55 type instance Type_of_Expr      (Expr_Integral root)      = No_Type
  56 type instance Sym_of_Expr       (Expr_Integral root) repr = Sym_Integral repr
  57 type instance Error_of_Expr ast (Expr_Integral root)      = No_Error_Expr
  58
  59 -- | Parse 'quotRem'.
  60 quotRem_from
  61  :: forall root ty ast hs ret.
  62  ( ty ~ Type_Root_of_Expr (Expr_Integral root)
  63  , Eq_Type ty
  64  , Expr_from ast root
  65  , Lift_Type Type_Tuple2 (Type_of_Expr root)
  66  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  67                    (Error_of_Expr ast root)
  68  , Root_of_Expr root ~ root
  69  , Constraint_Type Integral ty
  70  ) => ast -> ast
  71  -> Expr_From ast (Expr_Integral root) hs ret
  72 quotRem_from ast_x ast_y ex ast ctx k =
  73  -- quotRem :: a -> a -> (a, a)
  74         expr_from (Proxy::Proxy root) ast_x ctx $
  75          \(ty_x::ty h_x) (Forall_Repr_with_Context x) ->
  76         expr_from (Proxy::Proxy root) ast_y ctx $
  77          \(ty_y::ty h_y) (Forall_Repr_with_Context y) ->
  78         check_eq_type ex ast ty_x ty_y $ \Refl ->
  79         check_constraint_type ex (Proxy::Proxy Integral) ast ty_x $ \Dict ->
  80         k (type_tuple2 ty_x ty_x) $ Forall_Repr_with_Context $
  81          \c -> quotRem (x c) (y c)
  82
  83 -- | Parse 'divMod'.
  84 divMod_from
  85  :: forall root ty ast hs ret.
  86  ( ty ~ Type_Root_of_Expr (Expr_Integral root)
  87  , Eq_Type ty
  88  , Expr_from ast root
  89  , Lift_Type Type_Tuple2 (Type_of_Expr root)
  90  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  91                    (Error_of_Expr ast root)
  92  , Root_of_Expr root ~ root
  93  , Constraint_Type Integral ty
  94  ) => ast -> ast
  95  -> Expr_From ast (Expr_Integral root) hs ret
  96 divMod_from ast_x ast_y ex ast ctx k =
  97  -- divMod :: a -> a -> (a, a)
  98         expr_from (Proxy::Proxy root) ast_x ctx $
  99          \(ty_x::ty h_x) (Forall_Repr_with_Context x) ->
 100         expr_from (Proxy::Proxy root) ast_y ctx $
 101          \(ty_y::ty h_y) (Forall_Repr_with_Context y) ->
 102         check_eq_type ex ast ty_x ty_y $ \Refl ->
 103         check_constraint_type ex (Proxy::Proxy Integral) ast ty_x $ \Dict ->
 104         k (type_tuple2 ty_x ty_x) $ Forall_Repr_with_Context $
 105          \c -> divMod (x c) (y c)