repr-0.2: Repr.hs
{-# LANGUAGE OverloadedStrings #-}
module Repr
( Repr
, value
, renderer
, Renderer
, Precedence
, Fixity(..)
, render
, (<?>)
) where
--------------------------------------------------------------------------------
-- Imports
--------------------------------------------------------------------------------
import Data.String ( IsString, fromString )
import Data.String.ToString ( ToString, toString )
import Data.String.Combinators ( (<>)
, (<+>)
, between
, paren
, thenParen
, fromShow
, integer
, int
, hsep
)
import Data.DString ( DString, fromShowS )
import Control.Applicative ( liftA2 )
--------------------------------------------------------------------------------
-- Repr
--------------------------------------------------------------------------------
{-| @Repr a@ is a value of type @a@ paired with a way to render that
value to a string which will contain a representation of the value.
Note that @Repr a@ is overloaded for all the numeric classes provided that
@a@ has instances for the respected classes. This allows you to write a
numeric expression of type @Repr a@. For example:
@
*Repr> let r = 1.5 + 2 + (3 + (-4) * (5 - pi / sqrt 6)) :: Repr Double
@
You can extract the value of @r@:
@
*Repr> value r
17.281195923884734
@
And you can than render @r@ to its textual representation:
@
*Repr> render r
\"fromRational (3 % 2) + fromInteger 2 + (fromInteger 3 + negate (fromInteger 4) * (fromInteger 5 - pi / sqrt (fromInteger 6)))\"
@
-}
data Repr a = S { value :: a -- ^ Extract the value of the @Repr@.
, renderer :: Renderer -- ^ Extrac the renderer of the @Repr@.
}
{-| To render you need to supply the precedence and fixity of the
enclosing context.
(For rendering /top-level/ values see 'render'.)
For more documentation about precedence and fixity see:
<http://haskell.org/onlinereport/decls.html#sect4.4.2>
The reason the renderer returns a 'DString', instead of a 'String' for example,
is that the rendering of numeric expression involves lots of left-factored
appends i.e.: @((a ++ b) ++ c) ++ d@. A 'DString' has a O(1) append operation
while a 'String' just has a O(n) append. So choosing a 'DString' is more
efficient.
-}
type Renderer = Precedence -> Fixity -> DString
{-| The precedence of operators and function application.
* Operators usually have a precedence in the range of 0 to 9.
* Function application always has precedence 10.
-}
type Precedence = Int
-- | Precedence of function application.
funAppPrec :: Precedence
funAppPrec = 10
-- | Fixity of operators.
data Fixity = Non -- ^ No fixity information.
| L -- ^ Left associative operator.
| R -- ^ Right associative operator.
deriving Eq
{-| Render a /top-level/ value to a 'String'. Note that:
@
render r = 'toString' $ 'renderer' r 0 'Non'
@
-}
render :: Repr a -> String
render r = toString $ renderer r 0 Non
{-| @x \<?\> s@ annotates the rendering with the given string.
The rendering wil look like: @\"({\- s -\} ...)\"@ where @...@ is the rendering
of @x@.
This combinator is handy when you want to render the ouput of a
function and you want to see how the parameters of the function
contribute to the result. For example, suppose you defined the
following function @f@:
@
f p0 p1 p2 = p0 ^ 2 + sqrt p1 * ([p2..] !! 10)
@
You can then apply @f@ to some parameters annotated with some descriptive
strings (the name of the parameter is usally a good idea):
@
f (1 \<?\> \"p0\") (2 \<?\> \"p1\") (3 \<?\> \"p2\")
@
The rendering will then look like:
@
\"({\- p0 -\} fromInteger 1) * ({\- p0 -\} fromInteger 1) + sqrt ({\- p1 -\} (fromInteger 2)) * enumFrom ({\- p2 -\} (fromInteger 3)) !! 10\"
@
-}
(<?>) :: Repr a -> DString -> Repr a
(S x rx) <?> s =
S x $ \_ _ -> paren (between "{- " " -}" s <+> rx 0 Non)
--------------------------------------------------------------------------------
-- Instances
--------------------------------------------------------------------------------
instance Show (Repr a) where
show = render
instance Num a => Num (Repr a) where
fromInteger = from fromInteger "fromInteger"
(+) = infx L 6 (+) "+"
(-) = infx L 6 (-) "-"
(*) = infx L 7 (*) "*"
negate = app negate "negate"
abs = app abs "abs"
signum = app signum "signum"
instance Real a => Real (Repr a) where
toRational = to toRational
instance Integral a => Integral (Repr a) where
quot = app2 quot "quot"
rem = app2 rem "rem"
div = app2 div "div"
mod = app2 mod "mod"
quotRem = tup quotRem "quotRem"
divMod = tup divMod "divMod"
toInteger = to toInteger
instance Fractional a => Fractional (Repr a) where
(/) = infx L 7 (*) "/"
recip = app recip "recip"
fromRational = from fromRational "fromRational"
instance Floating a => Floating (Repr a) where
pi = constant pi "pi"
(**) = infx R 8 (**) "**"
logBase = app2 logBase "logBase"
exp = app exp "exp"
sqrt = app sqrt "sqrt"
log = app log "log"
sin = app sin "sin"
tan = app tan "tan"
cos = app cos "cos"
asin = app asin "asin"
atan = app atan "atan"
acos = app acos "acos"
sinh = app sinh "sinh"
tanh = app tanh "tanh"
cosh = app cosh "cosh"
asinh = app asinh "asinh"
atanh = app atanh "atanh"
acosh = app acosh "acosh"
instance RealFrac a => RealFrac (Repr a) where
properFraction (S x rx) =
let (n, f) = properFraction x
in (n, S f $ "snd" `apply` paren ("properFraction" <+> args [rx]))
instance RealFloat a => RealFloat (Repr a) where
floatRadix = to floatRadix
floatDigits = to floatDigits
floatRange = to floatRange
decodeFloat = to decodeFloat
encodeFloat = from2 encodeFloat "encodeFloat"
exponent = to exponent
significand = app significand "significand"
scaleFloat i = app (scaleFloat i) ("scaleFloat" <+> int i)
isNaN = to isNaN
isInfinite = to isInfinite
isDenormalized = to isDenormalized
isNegativeZero = to isNegativeZero
isIEEE = to isIEEE
atan2 = app2 atan2 "atan2"
instance Enum a => Enum (Repr a) where
succ = app succ "succ"
pred = app pred "pred"
toEnum = from toEnum "toEnum"
fromEnum = to fromEnum
enumFrom (S x rx) = enum "From" (enumFrom x) [rx]
enumFromThen (S x rx)
(S y ry) = enum "FromThen" (enumFromThen x y) [rx, ry]
enumFromTo (S x rx)
(S y ry) = enum "FromTo" (enumFromTo x y) [rx, ry]
enumFromThenTo (S x rx)
(S y ry)
(S z rz) = enum "FromThenTo" (enumFromThenTo x y z) [rx, ry, rz]
enum :: DString -> [a] -> [Renderer] -> [Repr a]
enum enumStr xs rxs = zipWith combine [0..] xs
where
combine i y = S y $ bin L 9 "!!" ("enum" <> enumStr <+> args rxs) (integer i)
instance Ord a => Ord (Repr a) where
compare = to2 compare
(<) = to2 (<)
(>=) = to2 (>=)
(>) = to2 (>)
(<=) = to2 (<=)
max = app2 max "max"
min = app2 min "min"
instance Eq a => Eq (Repr a) where
(==) = to2 (==)
(/=) = to2 (/=)
instance IsString a => IsString (Repr a) where
fromString = liftA2 constant fromString fromShow
--------------------------------------------------------------------------------
-- Utility functions
--------------------------------------------------------------------------------
-- | Construct a 'Repr' from a given value and string.
constant :: a -> DString -> Repr a
constant x xStr = S x $ \_ _ -> xStr
{-| Given a function @f@ and the name of that function @fStr@ return
a function that takes a 'Show'able argument @x@ and returns a 'Repr'
that has @f x@ as value and @fStr@ prepended to the showed @x@ as
renderer .
For example:
@
*Repr> let r = from fromRational "fromRational" 13.4
*Repr> value r
13.4 -- fromRational (67 % 5)
*Repr> render r
"fromRational (67 % 5)"
@
-}
from :: Show a => (a -> b) -> DString -> (a -> Repr b)
from f fStr =
\x -> S (f x) $ fStr `apply` fromShowS (showsPrec funAppPrec x)
-- | Same as 'from' with the difference that the given function has two arguments.
from2 :: (Show a, Show b) => (a -> b -> c) -> DString -> (a -> b -> Repr c)
from2 f fStr =
\x y -> S (f x y) $ fStr `apply`( fromShowS (showsPrec funAppPrec x)
<+> fromShowS (showsPrec funAppPrec y)
)
-- | Return the converted value of the 'Repr'.
to :: (a -> b) -> (Repr a -> b)
to f = f . value
-- | Return the combined values of the 'Repr's.
to2 :: (a -> b -> c) -> (Repr a -> Repr b -> c)
to2 f = \x y -> f (value x) (value y)
{-| Given a function @f@ and the name of that function @fStr@ return
a function that takes a @Repr@ and returns a @Repr@ that has as value
@f@ applied to the value of the given @Repr@ and as renderer @fStr@
prepended to the renderer of the given @Repr@.
For example:
@
*Repr> let r = app sqrt "sqrt" 4
*Repr> value r
2.0 -- sqrt (fromInteger 4)
*Repr> render r
"sqrt (fromInteger 4)"
@
-}
app :: (a -> b) -> DString -> (Repr a -> Repr b)
app f fStr =
\(S x rx) -> S (f x) $ fStr `apply` args [rx]
{-| Like 'app' but works for binary functions.
For example:
@
*Repr> let r = app2 quot "quot" 4 2
*Repr> value r
2 -- quot (fromInteger 4) (fromInteger 2)
*Repr> render r
"quot (fromInteger 4) (fromInteger 2)"
@
-}
app2 :: (a -> b -> c) -> DString -> (Repr a -> Repr b -> Repr c)
app2 f fStr =
\(S x rx) (S y ry) -> S (f x y) $ fStr `apply` args [rx, ry]
{-| Given the fixity, precedence, the actual operator @op@ and the name of the
operator @opStr@ return a function that takes two @Repr@s: @rx@ and @ry@ and
returns a @Repr@ that has as value @value rx `op` value ry@ and as renderer
@opStr@ in between the rendering of @rx@ and @ry@.
For example:
@
*Repr> let r = infx L 6 (+) "+" 2 3
*Repr> value r
5 -- fromInteger 2 + fromInteger 3
*Repr> render r
"fromInteger 2 + fromInteger 3"
@
-}
infx :: Fixity -> Precedence -> (a -> b -> c) -> DString
-> (Repr a -> Repr b -> Repr c)
infx opFix opPrec op opStr =
\(S x rx) (S y ry) ->
S (x `op` y) $ bin opFix opPrec opStr (rx opPrec L) (ry opPrec R)
bin :: Fixity -> Precedence -> DString -> DString -> DString -> Renderer
bin opFix opPrec opStr l r = \prec fixity -> (prec > opPrec ||
(prec == opPrec &&
fixity /= Non &&
fixity /= opFix))
`thenParen`
(l <+> opStr <+> r)
apply :: DString -> DString -> Renderer
funStr `apply` argsStr = \prec _ -> (prec >= funAppPrec)
`thenParen`
(funStr <+> argsStr)
args :: [Renderer] -> DString
args = hsep . map (\rx -> rx funAppPrec Non)
tup :: (a -> b -> (c, d)) -> DString
-> (Repr a -> Repr b -> (Repr c, Repr d))
tup f fStr =
\(S x rx) (S y ry) -> let (q, r) = f x y
s = paren (fStr <+> args [rx, ry])
in ( S q $ "fst" `apply` s
, S r $ "snd" `apply` s
)
-- The End ---------------------------------------------------------------------