Coming from Haskell, I struggle finding an easy way to look up type definitions in Purescript's REPL. In Haskell, I can do the following inside GHCI:
-- type class
:info Monad
-- shortcut
:i Monad
-- concrete types
:i []
:i (->)
-- type constructors work as well with a minimized output
:i Just
type Monad :: (* -> *) -> Constraint
class Applicative m => Monad m where
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
{-# MINIMAL (>>=) #-}
-- Defined in ‘GHC.Base’
instance Monad (Either e) -- Defined in ‘Data.Either’
instance Monad [] -- Defined in ‘GHC.Base’
instance Monad Maybe -- Defined in ‘GHC.Base’
instance Monad IO -- Defined in ‘GHC.Base’
instance Monad ((->) r) -- Defined in ‘GHC.Base’
instance (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c)
-- Defined in ‘GHC.Base’
instance (Monoid a, Monoid b) => Monad ((,,) a b)
-- Defined in ‘GHC.Base’
instance Monoid a => Monad ((,) a) -- Defined in ‘GHC.Base’
I can't find anything similar in spago. Is there a way to get this information without searching it online, for instance in Pursuit?
To get the type signatures, use :type
> :type (1 + _)
> Int -> Int
To display the kind of a type, use :kind
> :kind Maybe
> Type -> Type
To See all the functions, types, and type classes that a module exports, you can use browse
> :browse Data.Maybe
data Maybe a
= Nothing
| Just a
fromJust :: forall (a :: Type). Partial => Maybe a -> a
......
......
For more info, you can refer this
Related
Well, just simplified as possible:
There is a function that takes functor and does whatever
sToInt :: ∀ a s. Functor s => s a -> Int
sToInt val = unsafeCoerce val
Usage of this function with functor S which param (v) is functor too.
-- declare date type S that is functor
data S (v :: Type -> Type) a = S (v a)
instance functorS :: Functor v => Functor (S v) where
map f (S a) = S (map f a)
sV :: ∀ v a. S v a
sV = unsafeCoerce 1
sss :: Int
sss = sToInt sV -- get the error here
No type class instance was found for
Data.Functor.Functor t2
The instance head contains unknown type variables. Consider adding a type annotation.
while applying a function sToInt
of type Functor t0 => t0 t1 -> Int
to argument sV
while checking that expression sToInt sV
has type Int
in value declaration sss
where t0 is an unknown type
t1 is an unknown type
t2 is an unknown type
So it doesn't like S Functor instance has v param Functor constraint, I wonder why getting this error and how to fix it for this case.
This doesn't have to do with v or with the specific shape of S. Try this instead:
sV :: forall f a. Functor f => f a
sV = unsafeCoerce 1
sss :: Int
sss = sToInt sV
You get a similar error.
Or here's an even more simplified version:
sV :: forall a. a
sV = unsafeCoerce 1
sss :: Int
sss = sToInt sV
Again, same error.
The problem is that sToInt must get a Functor instance as a parameter (that's what the Functor s => bit in its type signature says), and in order to pick which Functor instance to pass, the compiler needs to know the type of the value. Like, if it's Maybe a, it will pass the Functor Maybe instance, and if it's Array a, it will pass the Functor Array instance, and so on.
Usually the type can be inferred from the context. For example when you say map show [1,2,3], the compiler knows that map should come from Functor Array, because [1,2,3] :: Array Int.
But in your case there is nowhere to get that information: sV can return S v for any v, and sToInt can also take any functor type. There is nothing to tell the compiler what the type should be.
And the way to fix this is obvious: if there is no context information for the compiler to get the type from, you have to tell it what the type is yourself:
sss :: Int
sss = sToInt (sV :: S Maybe _)
This will be enough for the compiler to know that v ~ Maybe, and it will be able to construct a Functor (S Maybe) instance and pass it to sToInt.
Alternatively, if you want the consumer of sss to decide what v is, you can add an extra dummy parameter to capture the type, and require that the consumer pass in a Functor v instance:
sss :: forall v. Functor v => FProxy v -> Int
sss _ = sToInt (sV :: S v _)
ddd :: Int
ddd = sss (FProxy :: FProxy Maybe)
In Haskell you can do this with visible type applications instead of FProxy, but PureScript, sadly, doesn't support that yet.
Even more alternatively, if sToInt doesn't actually care for a Functor instance, you can remove that constraint from it, and everything will work as-is:
sToInt :: forall s a. s a -> Int
sToInt a = unsafeCoerce a
sV :: forall v a. S v a
sV = unsafeCoerce 1
sss :: Int
sss = sToInt sV
This works because PureScript allows for ambiguous (aka "unknown") types to exist as long as they're not used for selecting instances.
Scala has a very nice support of partial functions, mainly because in Scala when you define a partial function it also defines an isDefinedAt function for it. And also Scala has orElse and andThen functions to work with partial functions.
Haskell does support partial functions by simply non-exhaustively defining a function (though they are strongly discouraged in Haskell community). But to define isDefinedAt function in general you have to use some sort of exception handling, which I'm not being able to figure out. Once isDefinedAt function is defined then it can be used to define orElse and andThen function is already there as (.).
In short, I want to define a function,
isDefinedAt :: (a -> b) -> a -> Bool
isDefinedAt f x = -- returns True if f is defined at x else False
Can anyone please tell me how such a function can be written.
Note, I can define a function with signature
isDefinedAt :: (a -> b) -> a -> IO Bool
for generic b. But I want a function without IO in co-domain.
A nice article on Scala's Partial Functions is - How to create and use partial functions in Scala By Alvin Alexander
I recommend that, like in Scala, you use a separate type for partial functions.
import Control.Arrow
import Data.Maybe
type Partial = Kleisli Maybe
isDefinedAt :: Partial a b -> a -> Bool
isDefinedAt f x = isJust $ runKleisli f x
-- laziness should save some of the work, if possible
orElse :: Partial a b -> Partial a b -> Partial a b
orElse = (<+>)
andThen :: Partial a b -> Partial b c -> Partial a c
andThen = (>>>)
Your versions of isDefinedAt are not what Scala does (even in signature); it's very possible (though discouraged) for a PartialFunction to throw an exception when isDefinedAt is true. Or, when you define one explicitly (not using a literal), vice versa: apply doesn't have to throw when isDefinedAt is false, it's user responsibility not to call it then. So the direct equivalent would just be
data PartialFunction a b = PartialFunction { apply :: a -> b, isDefinedAt :: a -> Boolean }
which isn't particularly useful.
apply and isDefinedAt are only really linked in Scala for PartialFunction literals which requires compiler support:
A PartialFunction's value receives an additional isDefinedAt member, which is derived from the pattern match in the function literal, with each case's body being replaced by true, and an added default (if none was given) that evaluates to false.
You can emulate this by using Template Haskell, I believe, but I honestly think using the more Haskell-like approach as described in Daniel Wagner's answer is better. As he mentions, laziness helps.
Though it works even better if you make sure runKleisli f x is executed only once; optimizing cases where you have both isDefinedAt and runKleisli requires Common Subexpression Elimination, and the compiler is cautious about doing that, see Under what circumstances could Common Subexpression Elimination affect the laziness of a Haskell program?
You could do something like this (DISCLAIMER: I have not checked the laws of the relevant typeclasses, and the presence of a string in the constructor for the exception in Alternative makes me wonder if it is lawful). Scala's heterogeneous andThen is covered by fmap; its homogeneous andThen / compose are covered by the >>> / <<< from Category; orElse is covered by <|>; lift is runToMaybe.
However, without a deep compiler integration such as exists in Scala, the pattern incompleteness warnings will interact poorly with this. Haskell only has module-level pragmas for these things, and you won't want to just indiscriminately turn them off in any module where you declare inexhaustive functions, or you may get nasty surprises. Depending on your usecase, you may find optics more idiomatic and less problematic; you can have the boilerplate generated for you through Template Haskell.
(Note: I called it Inexhaustive because PartialFunction is something of a misnomer, in that it implies that Function is total. But Scala has no termination or positivity checkers, so the compiler is not actually able to talk about totality; so you get this weird situation where a function that is not a partial function is just a "regular" Function, whereas you should be able to call it a "total Function". The question here is not partially or totality, which is a broader idea, but inexhaustivity of pattern matches.)
{-# LANGUAGE TypeApplications #-}
module Inexhaustive
( Inexhaustive, inexhaustive
, runToMaybe, isDefinedAt
) where
import Prelude hiding ((.), id)
import Control.Applicative
import Control.Exception
import Control.Category
import Data.Maybe
import System.IO.Unsafe (unsafePerformIO)
newtype Inexhaustive a b = Inexhaustive (a -> b)
inexhaustive :: (a -> b) -> Inexhaustive a b
inexhaustive = Inexhaustive
runToMaybe :: Inexhaustive a b -> a -> Maybe b
runToMaybe (Inexhaustive f) x =
let io = fmap Just $ evaluate $ f x
in unsafePerformIO $ catch #PatternMatchFail io (\_ -> return Nothing)
isDefinedAt :: Inexhaustive a b -> a -> Bool
isDefinedAt f = isJust . runToMaybe f
instance Functor (Inexhaustive z) where
fmap f (Inexhaustive g) = inexhaustive (f . g)
instance Applicative (Inexhaustive z) where
pure x = inexhaustive (const x)
(Inexhaustive zab) <*> (Inexhaustive za) = Inexhaustive (\z -> zab z $ za z)
instance Alternative (Inexhaustive z) where
empty = inexhaustive (\_ -> throw $ PatternMatchFail "inexhaustive empty")
f <|> g =
inexhaustive $ \x ->
case runToMaybe f x <|> runToMaybe g x of
Just y -> y
instance Category Inexhaustive where
id = inexhaustive id
(Inexhaustive f) . (Inexhaustive g) = Inexhaustive (f . g)
Suppose you are using the FlexibleInstances extension and have the class
class C a where
f :: a b -> Maybe b
how would you implement it for a list of lists of a datatype. In particular, how would the type be written. The only thing I could find is how to do it for a single list, but not a list of lists or lists of any other datatypes.
This works:
instance C [] where
...
But this doesn't
data D = ...
instance C [[D]] where
...
How can I express something like this?
You need a newtype
class C a where
f :: a b -> b -- the class before the OP edited
newtype LL a = LL [[a]]
instance C LL where
f (LL xss) = ...
However, it is impossible to write a completely meaningful instance, since if the lists-of-lists is empty, it is impossible to extract an element. the best we could do is
instance C LL where
f (LL xss) = case concat xss of
(x:_) -> x
_ -> error "f: no elements"
I'm not sure if that is a good idea.
As an alternative, you could use type families or functional dependencies. Here's a solution with type families.
{-# LANGUAGE TypeFamilies, FlexibleInstances #-}
class C a where
type T a
f :: a -> Maybe (T a)
instance C [[b]] where
type T [[b]] = b
f xss = case concat xss of
[] -> Nothing
(x:_) -> Just x
Existentially quantified types explains:
any use of a lowercase type implicitly begins with a forall keyword, so the two type declarations for map are equivalent, as are the declarations below:
id :: a -> a
id :: forall a . a -> a
Given Scala's scala.Predef#identity, is there a forall equivalent, i.e. per Haskell's above second function?
There is no explicit forall in Scala, but it has equivalents to the different ways explicit foralls are used in Haskell:
To enable ScopedTypeVariables: not necessary, as Scala type variables are scoped by default.
For existential types: Scala supports them directly.
For higher-rank types, i.e. ones which have a forall nested under function arrows: consider this example:
f2 :: (forall a. a->a) -> Int -> Int
f2 f x = f x
In Scala [A](A => A) can't be used directly, but
trait Poly1 {
def apply[A](x: A): A
}
is equivalent to it, so you can implement f2:
def f2(p: Poly1, x: Int) = p(x)
I am not a Scala expert, but my understanding is that all Scala type parameters are universally quantified (i.e. declared with a forall) unless they are explicitly quantified with forSome. See, for instance:
What is the forSome keyword in Scala for?
In Haskell we use the forall keyword to declare existential types. It may seem counter-intuitive to use forall when we mean for some, but it can be done using the logical equivalence of the following statements:
(forSome x. P(x)) implies Q
(forall x. P(x) implies Q)
Here Q is a statement not containing x.
In the process of writing a simple RPN calculator, I have the following type aliases:
type Stack = List[Double]
type Operation = Stack => Option[Stack]
... and I have written a curious-looking line of Scala code:
val newStack = operations.foldLeft(Option(stack)) { _ flatMap _ }
This takes an initial stack of values and applies a list of operations to that stack. Each operation may fail (i.e. yields an Option[Stack]) so I sequence them with flatMap. The thing that's somewhat unusual about this (in my mind) is that I'm folding over a list of monadic functions, rather than folding over a list of data.
I want to know if there's a standard function that captures this "fold-bind" behavior. When I'm trying to play the "Name That Combinator" game, Hoogle is usually my friend, so I tried the same mental exercise in Haskell:
foldl (>>=) (Just stack) operations
The types here are:
foldl :: (a -> b -> a) -> a -> [b] -> a
(>>=) :: Monad m => m a -> (a -> m b) -> m b
So the type of my mystery foldl (>>=) combinator, after making the types of foldl and (>>=) line up, should be:
mysteryCombinator :: Monad m => m a -> [a -> m a] -> m a
... which is again what we'd expect. My problem is that searching Hoogle for a function with that type yields no results. I tried a couple other permutations that I thought might be reasonable: a -> [a -> m a] -> m a (i.e. starting with a non-monadic value), [a -> m a] -> m a -> m a (i.e. with arguments flipped), but no luck there either. So my question is, does anybody know a standard name for my mystery "fold-bind" combinator?
a -> m a is just a Kleisli arrow with the argument and result types both being a. Control.Monad.(>=>) composes two Kleisli arrows:
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
Think flip (.), but for Kleisli arrows instead of functions.
So we can split this combinator into two parts, the composition and the "application":
composeParts :: (Monad m) => [a -> m a] -> a -> m a
composeParts = foldr (>=>) return
mysteryCombinator :: (Monad m) => m a -> [a -> m a] -> m a
mysteryCombinator m fs = m >>= composeParts fs
Now, (>=>) and flip (.) are related in a deeper sense than just being analogous; both the function arrow, (->), and the data type wrapping a Kleisli arrow, Kleisli, are instances of Control.Category.Category. So if we were to import that module, we could in fact rewrite composeParts as:
composeParts :: (Category cat) => [cat a a] -> cat a a
composeParts = foldr (>>>) id
(>>>) (defined in Control.Category) is just a nicer way of writing as flip (.).
So, there's no standard name that I know of, but it's just a generalisation of composing a list of functions. There's an Endo a type in the standard library that wraps a -> a and has a Monoid instance where mempty is id and mappend is (.); we can generalise this to any Category:
newtype Endo cat a = Endo { appEndo :: cat a a }
instance (Category cat) => Monoid (Endo cat a) where
mempty = Endo id
mappend (Endo f) (Endo g) = Endo (f . g)
We can then implement composeParts as:
composeParts = appEndo . mconcat . map Endo . reverse
which is just mconcat . reverse with some wrapping. However, we can avoid the reverse, which is there because the instance uses (.) rather than (>>>), by using the Dual a Monoid, which just transforms a monoid into one with a flipped mappend:
composeParts :: (Category cat) => [cat a a] -> cat a a
composeParts = appEndo . getDual . mconcat . map (Dual . Endo)
This demonstrates that composeParts is a "well-defined pattern" in some sense :)
The one starting with a non-monadic value is (modulo flip)
Prelude> :t foldr (Control.Monad.>=>) return
foldr (Control.Monad.>=>) return
:: Monad m => [c -> m c] -> c -> m c
(or foldl)
(Yes, I know this doesn't answer the question, but the code layout in comments isn't satisfactory.)