[Haskell-cafe] Typeclasses question in "Real World Haskell" book

[Richard O'Keefe]

On Jul 27, 2010, at 1:16 AM, Angel de Vicente wrote:
> data JValue = JString String
>             | JNumber Double
>             | JBool Bool
>             | JNull
>             | JObject [(String, JValue)]
>             | JArray [JValue]
>             deriving (Eq, Ord, Show)
> 
> type JSONError = String
> 
> class JSON a where
>    toJValue :: a -> JValue
>    fromJValue :: JValue -> Either JSONError a

The type class JSON is the class of types (a)
that have been provided with functions functions to
convert between (a) and JValue.

	toJValue	converts an (a) to a JValue.
	fromJValue	tries to convert a JValue to
			an (a), returning Right x if
			it succeeds, or Left ".." if
			it fails, for some error message.

So the JSON type class is useful when every value of
type (a) can be faithfully represented by some JValue,
but not every JValue represents an (a).

For example, we might say
	instance (JSON a, JSON b) => JSON (a,b)
	  where

	    toJValue (x,y) = JArray [toJValue x, toJValue y]

	    fromJValue (JArray [u,v]) =
		case (fromJValue u, fromJValue v) of
		  (Right x, Right y) -> Right (x,y)
		  (Right _, Left er) -> Left er
		  (Left er, _)       -> Left er
	    fromJValue _ = Left "not a 2-element array"

> instance JSON JValue where
>    toJValue = id
>    fromJValue = Right

A JValue can be converted to a JValue by doing nothing.
A JValue can be converted back to a JValue again by doing
nothing, BUT we must say that the conversion succeeded by
wrapping the result in Right.
> 
> instance JSON Bool where
>    toJValue = JBool
>    fromJValue (JBool b) = Right b
>    fromJValue _ = Left "not a JSON boolean"

A Bool can be converted to a JValue by wrapping it in JBool.
A JBool can be converted back to a Bool by unwrapping it
and then wrapping the result in Right.
But any JValue other than a JBool cannot be converted to a
Bool.  (Actually, this is was a choice; other choices could
have been made.)  Since we can't do it, we have to say _that_
we didn't (Left) and _why_ ("not a JSON boolean").

> I don't understand how the JSON typeclass is defined, in particular the
> fromJValue definition.

There's a simple pattern for "communication" types like XML or
JSON or UBF or for that matter byte strings.  Roughly speaking

	class Communicable t
	  where
	    to_exchange_format   :: t -> Maybe Exchange
	    from_exchange_format :: Exchange -> Maybe t

Variations on this are
 - where one direction of conversion must never fail,
   so the "Maybe" disappears
 - where the designer chose to require reasons for failure,
   so that Maybe is replaced by Either String.

> For instance, when defining the instance for Bool types, then I
> understand that both functions (toJValue and fromJValue) will be called
> upon when we supply a Bool type, but then the (JBool b) type in function fromJValue doesn't match....

Ah.  What you may be missing here is that Haskell resolves the
types of functions taking into account ALL information about
them,
	>>> INCLUDING THE RESULT <<<

So if we do
	let boo = True
	    jay = toJValue boo
	    lea = fromJValue jay
	...
then the call of toJValue is resolved thanks to the type of its
*argument* and the call to fromJValue is not resolved.  But if
we do
	let boo = True
	    jay = toJValue boo
	    lea :: Bool
	    lea = fromJValue jay
then the call of fromJValue is resolved thanks to the (now!) known
type of its *result*.

> toJValue is no problem, but I cannot understand how fromJValue is
> supposed to work, and the comments in the online book
> (http://book.realworldhaskell.org/read/using-typeclasses.html) don't
> help with this either.
> 
> *Main> :load ch6
> [1 of 1] Compiling Main             ( ch6.hs, interpreted )
> Ok, modules loaded: Main.
> *Main> toJValue False
> JBool False
> *Main> :type it
> it :: JValue
> *Main> fromJValue False
> 
> <interactive>:1:11:
>    Couldn't match expected type `JValue' against inferred type `Bool'
>    In the first argument of `fromJValue', namely `False'

This is hardly surprising, because you have an explicit declaration
that says

	fromJValue :: JValue -> Either JSONError a

so the argument of fromJValue may only be a JValue, and False is
not a JValue.

> *Main> fromJValue (JBool False)
> 
> <interactive>:1:0:
>    Ambiguous type variable `a' in the constraint:
>      `JSON a' arising from a use of `fromJValue' at <interactive>:1:0-23
>    Probable fix: add a type signature that fixes these type variable(s)
> *Main>
> 
> 
> 
> Any pointers?

Yes.  That last error message you quoted told you exactly what to
do.  It said, in effect, that the only thing wrong with
fromJValue (JBool False)
is that it doesn't know what the result type (a) should be,
except that it must involve *some* instance of JSON,
and it recommended that you add a type signature (:: t for some t)
to something that might tell it.

*Main> (fromJValue (JBool False)) :: (Either JSONError Bool)
Right False

Or you could have asked whether

*Main> fromJValue (JBool False) == Right False
True