Monad class contains declaration *fail* :: String -> m a and provides default implementation for 'fail' as: fail s = error s On the other hand Prelude defines: * error* :: String -> a which stops execution and displays an error message. Questions: 1) What value and type 'error' actually returns in: error "some message" ? 2) How declaration String -> m a matches with String -> a ? 3) In Maybe monad: fail = Nothing When and how 'fail' is used in Maybe monad? Thanks! -- Dmitri O. Kondratiev dokondr@gmail.com http://www.geocities.com/dkondr
On Wed, Jun 06, 2007 at 01:39:32PM +0400, Dmitri O.Kondratiev wrote:
Monad class contains declaration
*fail* :: String -> m a
and provides default implementation for 'fail' as:
fail s = error s
On the other hand Prelude defines: * error* :: String -> a
which stops execution and displays an error message.
Questions: 1) What value and type 'error' actually returns in: error "some message" ? 'a' here is a type variable, therefore 'error' is a polymorphic function which can return value of any type.
2) How declaration String -> m a matches with String -> a ? as I said above, 'String->a' means that the return value can have any type. 'String-> m a' means that return value may be of type 'm a' where 'a' can be any type.
3) In Maybe monad: fail = Nothing 'Nothing' is constructor which returns value of type 'Maybe a' where 'a' is any type.
When and how 'fail' is used in Maybe monad? Values of type 'Maybe a' can be either 'Just x' where x is value of type 'a' or 'Nothing'. The Maybe monad is used to represent computations which may fail, 'Just x' represents successful computation yielding value x, and 'Nothing' represents failing computation.
Thanks!
-- Dmitri O. Kondratiev dokondr@gmail.com http://www.geocities.com/dkondr
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Dmitri O.Kondratiev wrote:
Monad class contains declaration
*fail* :: String -> m a
and provides default implementation for 'fail' as:
fail s = error s
On the other hand Prelude defines: * error* :: String -> a
which stops execution and displays an error message.
Questions: 1) What value and type 'error' actually returns in: error "some message" ?
For practical purposes: typechecking: every type the context asks for. execution: no value, because execution stops. For theoretical purposes, error could be implemented by error :: String -> a error msg = error msg with the extra-semantical magical side effect of printing msg and aborting execution.
2) How declaration String -> m a matches with String -> a ?
Alpha renaming to fresh variables yields String -> b c String -> d wich unifies by taking d := b c.
3) In Maybe monad: fail = Nothing
When and how 'fail' is used in Maybe monad?
The default fail implementation is not very clever. If something fails, execution is aborted and the user is confronted with some error message. Some monads support richer error handling schemes. The maybe monad encodes a succeeding computation with Just it's result, and a failed computation with Nothing. An example: -- divBy is a possible failing computation in some monad divBy :: Monad m => Int -> Int -> m Int divBy a 0 = fail "div by zero" divBy a b = return (a `div` b) -- div by three succeeds 15 `divBy` 3 :: Maybe Int ~~> Just 5 -- div by zero fails 15 `divBy` 0 :: Maybe Int ~~> Nothing -- divByAll is a shortcut for a list of divBy's divByAll :: Monad m => Int -> [Int] -> [m Int] divByAll a bs = map (divBy a) bs -- div by all returns a list of computations 15 `divByAll` [3, 0] :: [Maybe Int] ~~> [Just 5, Nothing] -- sequence succeeds if all computations in a list succeeds sequence (15 `divByAll` [3, 0]) :: Maybe [Int] ~~> Nothing sequence (15 `divByAll` [3, 5]) :: Maybe [Int] ~~> Just [5, 3] divBy, divByAll, sequence do not know anything about Maybe, they work for all monads, because they only use >>=, fail and return. The idea is that Monad defines some general interface for computations, and the various Monad instances define the exact behaviour. Maybe's behaviour is: if a subcomputation fails, the whole computation fails. There are other monads. consider the list monad, and it's behaviour: if a subcomputation fails, backtrack and try some other alternative. Tillmann
Thanks for excellent explanation! Examples really help.
So, in general 'fail' behavior will differ from monad to monad.
In this example:
divBy :: Monad m => Int -> Int -> m Int
divBy a 0 = fail "div by zero"
divBy a b = return (a `div` b)
Default 'fail' implementation in Monad class will be:
*DivBy> divBy 5 0
Loading package haskell98-1.0 ... linking ... done.
*** Exception: user error (div by zero)
And when explicitly defining monad as Maybe it will be different:
*DivBy> divBy 5 0::Maybe Int
Nothing
I am curious if it is possible to 'cast' divBy to List, Identity, other
monads? How?
On 6/6/07, Tillmann Rendel
Dmitri O.Kondratiev wrote:
Monad class contains declaration
*fail* :: String -> m a
and provides default implementation for 'fail' as:
fail s = error s
On the other hand Prelude defines: * error* :: String -> a
which stops execution and displays an error message.
Questions: 1) What value and type 'error' actually returns in: error "some message" ?
For practical purposes:
typechecking: every type the context asks for. execution: no value, because execution stops.
For theoretical purposes, error could be implemented by
error :: String -> a error msg = error msg
with the extra-semantical magical side effect of printing msg and aborting execution.
2) How declaration String -> m a matches with String -> a ?
Alpha renaming to fresh variables yields
String -> b c String -> d
wich unifies by taking d := b c.
3) In Maybe monad: fail = Nothing
When and how 'fail' is used in Maybe monad?
The default fail implementation is not very clever. If something fails, execution is aborted and the user is confronted with some error message. Some monads support richer error handling schemes. The maybe monad encodes a succeeding computation with Just it's result, and a failed computation with Nothing.
An example:
-- divBy is a possible failing computation in some monad divBy :: Monad m => Int -> Int -> m Int divBy a 0 = fail "div by zero" divBy a b = return (a `div` b)
-- div by three succeeds 15 `divBy` 3 :: Maybe Int ~~> Just 5
-- div by zero fails 15 `divBy` 0 :: Maybe Int ~~> Nothing
-- divByAll is a shortcut for a list of divBy's divByAll :: Monad m => Int -> [Int] -> [m Int] divByAll a bs = map (divBy a) bs
-- div by all returns a list of computations 15 `divByAll` [3, 0] :: [Maybe Int] ~~> [Just 5, Nothing]
-- sequence succeeds if all computations in a list succeeds sequence (15 `divByAll` [3, 0]) :: Maybe [Int] ~~> Nothing sequence (15 `divByAll` [3, 5]) :: Maybe [Int] ~~> Just [5, 3]
divBy, divByAll, sequence do not know anything about Maybe, they work for all monads, because they only use >>=, fail and return.
The idea is that Monad defines some general interface for computations, and the various Monad instances define the exact behaviour. Maybe's behaviour is: if a subcomputation fails, the whole computation fails.
There are other monads. consider the list monad, and it's behaviour: if a subcomputation fails, backtrack and try some other alternative.
Tillmann
On Wed, 06 Jun 2007 09:29:09 -0700, Dmitri O.Kondratiev
Default 'fail' implementation in Monad class will be: *DivBy> divBy 5 0 Loading package haskell98-1.0 ... linking ... done. *** Exception: user error (div by zero)
And when explicitly defining monad as Maybe it will be different: *DivBy> divBy 5 0::Maybe Int Nothing
I am curious if it is possible to 'cast' divBy to List, Identity, other monads? How?
It just works, and you already did it for Maybe. Just provide the type: *Main> divBy 5 0::[Int] [] *Main> divBy 5 1::[Int] [5] Identity fails with a stack overflow, though (GHC 6.6): *Main> divBy 5 0::Identity Int *** Exception: stack overflow *Main> fail "KK" :: Identity () *** Exception: stack overflow *Main> divBy 5 1::Identity Int *** Exception: stack overflow Anyway... JCAB
"Dmitri O.Kondratiev"
1) What value and type 'error' actually returns in: error "some message" ?
For the purpose of type checking, error returns whatever value is expected for that expression by whatever is 'using' the value. In practice, 'error' terminates programme execution so that it evades the trouble of figuring out how to construct a return value of the correct type.
2) How declaration String -> m a matches with String -> a ?
'a' can be any type, including 'm a'. (Those are different 'a's! So I should really rename 'm a' to 'm b' when I use them in the same sentence.)
3) In Maybe monad: fail = Nothing
When and how 'fail' is used in Maybe monad?
A common way to think of the Maybe monad is that it represents a thing that works only if all the parts worked. If any of the parts (bound with
=) fail, then the Nothing is contagious across bind, as the >>= doesn't have a value to feed in to the next function as its argument, and the return value of the whole thing is Nothing.
-- Mark
participants (5)
-
Dmitri O.Kondratiev -
Ilya Tsindlekht -
Juan Carlos Arevalo Baeza -
mark＠ixod.org -
Tillmann Rendel