Partial application of operators - function

If I want to add a space at the end of a character to return a list, how would I accomplish this with partial application if I am passing no arguments?
Also would the type be?
space :: Char -> [Char]
I'm having trouble adding a space at the end due to a 'parse error' by using the ++ and the : operators.
What I have so far is:
space :: Char -> [Char]
space = ++ ' '
Any help would be much appreciated! Thanks

Doing what you want is so common in Haskell it's got its own syntax, but being Haskell, it's extraordinarily lightweight. For example, this works:
space :: Char -> [Char]
space = (:" ")
so you weren't far off a correct solution. ([Char] is the same as String. " " is the string containing the character ' '.) Let's look at using a similar function first to get the hang of it. There's a function in a library called equalFilePath :: FilePath -> FilePath -> Bool, which is used to test whether two filenames or folder names represent the same thing. (This solves the problem that on unix, mydir isn't the same as MyDir, but on Windows it is.) Perhaps I want to check a list to see if it's got the file I want:
isMyBestFile :: FilePath -> Bool
isMyBestFile fp = equalFilePath "MyBestFile.txt" fp
but since functions gobble their first argument first, then return a new function to gobble the next, etc, I can write that shorter as
isMyBestFile = equalFilePath "MyBestFile.txt"
This works because equalFilePath "MyBestFile.txt" is itself a function that takes one argument: it's type is FilePath -> Bool. This is partial application, and it's super-useful. Maybe I don't want to bother writing a seperate isMyBestFile function, but want to check whether any of my list has it:
hasMyBestFile :: [FilePath] -> Bool
hasMyBestFile fps = any (equalFilePath "MyBestFile.txt") fps
or just the partially applied version again:
hasMyBestFile = any (equalFilePath "MyBestFile.txt")
Notice how I need to put brackets round equalFilePath "MyBestFile.txt", because if I wrote any equalFilePath "MyBestFile.txt", then filter would try and use just equalFilePath without the "MyBestFile.txt", because functions gobble their first argument first. any :: (a -> Bool) -> [a] -> Bool
Now some functions are infix operators - taking their arguments from before and after, like == or <. In Haskell these are just regular functions, not hard-wired into the compiler (but have precedence and associativity rules specified). What if I was a unix user who never heard of equalFilePath and didn't care about the portability problem it solves, then I would probably want to do
hasMyBestFile = any ("MyBestFile.txt" ==)
and it would work, just the same, because == is a regular function. When you do that with an operator function, it's called an operator section.
It can work at the front or the back:
hasMyBestFile = any (== "MyBestFile.txt")
and you can do it with any operator you like:
hassmalls = any (< 5)
and a handy operator for lists is :. : takes an element on the left and a list on the right, making a new list of the two after each other, so 'Y':"es" gives you "Yes". (Secretly, "Yes" is actually just shorthand for 'Y':'e':'s':[] because : is a constructor/elemental-combiner-of-values, but that's not relevant here.) Using : we can define
space c = c:" "
and we can get rid of the c as usual
space = (:" ")
which hopefully make more sense to you now.

What you want here is an operator section. For that, you'll need to surround the application with parentheses, i.e.
space = (: " ")
which is syntactic sugar for
space = (\x -> x : " ")
(++) won't work here because it expects a string as the first argument, compare:
(:) :: a -> [a] -> [a]
(++) :: [a] -> [a] -> [a]

Related

Unable to define a parser in Haskell: Not in scope: type variable ‘a’

I am trying to define a parser in Haskell. I am a total beginner and somehow didn't manage to find any solution to my problem at all.
For the first steps I tried to follow the instructions on the slides of a powerpoint presentation. But I constantly get the error "Not in scope: type variable ‘a’":
type Parser b = a -> [(b,a)]
item :: Parser Char
item = \inp -> case inp of
[] -> []
(x:xs) -> [(x:xs)]
error: Not in scope: type variable ‘a’
|
11 | type Parser b = a -> [(b,a)]
| ^
I don't understand the error but moreover I don't understand the first line of the code as well:
type Parser b = a -> [(b,a)]
What is this supposed to do? On the slide it just tells me that in Haskell, Parsers can be defined as functions. But that doesn't look like a function definition to me. What is "type" doing here? If it s used to specify the type, why not use "::" like in second line above? And "Parser" seems to be a data type (because we can use it in the type definition of "item"). But that doesn't make sense either.
The line derives from:
type Parser = String -> (String, Tree)
The line I used in my code snippet above is supposed to be a generalization of that.
Your help would be much appreciated. And please bear in mind that I hardly know anything about Haskell, when you write an answer :D
There is a significant difference between the type alias type T = SomeType and the type annotation t :: SomeType.
type T = Int simply states that T is just another name for the type Int. From now on, every time we use T, it will be replaced with Int by the compiler.
By contrast, t :: Int indicates that t is some value of type Int. The exact value is to be specified by an equation like t = 42.
These two concepts are very different. On one hand we have equations like T = Int and t = 42, and we can replace either side with the other side, replacing type with types and values with values. On the other hand, the annotation t :: Int states that a value has a given type, not that the value and the type are the same thing (which is nonsensical: 42 and Int have a completely different nature, a value and a type).
type Parser = String -> (String, Tree)
This correctly defines a type alias. We can make it parametric by adding a parameter:
type Parser a = String -> (String, a)
In doing so, we can not use variables in the right hand side that are not parameters, for the same reason we can not allow code like
f x = x + y -- error: y is not in scope
Hence you need to use the above Parser type, or some variation like
type Parser a = String -> [(String, a)]
By contrast, writing
type Parser a = b -> [(b, a)] -- error
would use an undeclared type b, and is an error. At best, we could have
type Parser a b = b -> [(b, a)]
which compiles. I wonder, though, is you really need to make the String type even more general than it is.
So, going back to the previous case, a possible way to make your code run is:
type Parser a = String -> [(a, String)]
item :: Parser Char
item = \inp -> case inp of
[] -> []
(x:xs) -> [(x, xs)]
Note how [(x, xs)] is indeed of type [(Char, String)], as needed.
If you really want to generalize String as well, you need to write:
type Parser a b = b -> [(b, a)]
item :: Parser Char String
item = \inp -> case inp of
[] -> []
(x:xs) -> [(xs, x)]

Understanding the use of brackets in the all function in Haskell?

I'm trying to wrap my head around the conventions and rules of programming in Haskell. One thing that I find confusing or difficult to understand is the use of brackets (). Can anyone explain to me what it does in the case of the all function?
all :: (a -> Bool) -> [a] -> Bool
all p xs = and [ p x | x <- xs ]
As I understand it, the type of a function shows the type constraints, inputs and outputs. Wouldn't having
all :: [a] -> Bool
Be enough?
What parentheses do here
Parentheses in Haskell serve a purpose that is very similar to most other programming languages: changing precedence of operations and/or grouping terms.
In your case, the fact that (a -> Bool) is wrapped in parentheses shows that the type of the function's first parameter is a -> Bool. If there was no parentheses (i.e. if the signature was all :: a -> Bool -> [a] -> Bool), then the meaning would be that the type of the function's first parameter is a, and the type of the function's second parameter is Bool.
Wouldn't it be enough to have all :: [a] -> Bool?
If that was the signature, then the question would be: what does such function mean? Does it return True when the list is not empty? Or when it's empty? Or when it contains precisely 42 elements? A bad name for a function. Should have named it has42Elements instead of all.
On the other hand, if the function takes the first parameter of type a -> Bool (that is, a function that takes an a and returns a Bool), then the meaning of all would be "check if this function is True for all elements in this list".

Difference between let, fun and function in F#

I'm learning F# and I cannot figure out what the difference between let, fun and function is, and my text book doesn't really explain that either. As an example:
let s sym = function
| V x -> Map.containsKey x sym
| A(f, es) -> Map.containsKey f sym && List.forall (s sym) es;;
Couldn't I have written this without the function keyword? Or could I have written that with fun instead of function? And why do I have to write let when I've seen some examples where you write
fun s x =
...
What's the difference really?
I guess you should really ask MSDN, but in a nutshell:
let binds a value with a symbol. The value can be a plain type like an int or a string, but it can also be a function. In FP functions are values and can be treated in the same way as those types.
fun is a keyword that introduces an anonymous function - think lambda expression if you're familiar with C#.
Those are the two important ones, in the sense that all the others usages you've seen can be thought as syntax sugar for those two. So to define a function, you can say something like this:
let myFunction =
fun firstArg secondArg ->
someOperation firstArg secondArg
And that's very clear way of saying it. You declare that you have a function and then bind it to the myFunction symbol.
But you can save yourself some typing by just conflating anonymous function declaration and binding it to a symbol with let:
let myFunction firstArg secondArg =
someOperation firstArg secondArg
What function does is a bit trickier - you combine an anonymous single-argument function declaration with a match expression, by matching on an implicit argument. So these two are equivalent:
let myFunction firstArg secondArg =
match secondArg with
| "foo" -> firstArg
| x -> x
let myFunction firstArg = function
| "foo" -> firstArg
| x -> x
If you're just starting on F#, I'd steer clear of that one. It has its uses (mainly for providing succinct higher order functions for maps/filters etc.), but results in code less readable at a glance.
These things are sort of shortcuts to each other.
The most fundamental thing is let. This keyword gives names to stuff:
let name = "stuff"
Speaking more technically, the let keyword defines an identifier and binds it to a value:
let identifier = "value"
After this, you can use words name and identifier in your program, and the compiler will know what they mean. Without the let, there wouldn't be a way to name stuff, and you'd have to always write all your stuff inline, instead of referring to chunks of it by name.
Now, values come in different flavors. There are strings "some string", there are integer numbers 42, floating point numbers 5.3, Boolean values true, and so on. One special kind of value is function. Functions are also values, in most respects similar to strings and numbers. But how do you write a function? To write a string, you use double quotes, but what about function?
Well, to write a function, you use the special word fun:
let squareFn = fun x -> x*x
Here, I used the let keyword to define an identifier squareFn, and bind that identifier to a value of the function kind. Now I can use the word squareFn in my program, and the compiler will know that whenever I use it I mean a function fun x -> x*x.
This syntax is technically sufficient, but not always convenient to write. So in order to make it shorter, the let binding takes an extra responsibility upon itself and provides a shorter way to write the above:
let squareFn x = x*x
That should do it for let vs fun.
Now, the function keyword is just a short form for fun + match. Writing function is equivalent to writing fun x -> match x with, period.
For example, the following three definitions are equivalent:
let f = fun x ->
match x with
| 0 -> "Zero"
| _ -> "Not zero"
let f x = // Using the extra convenient form of "let", as discussed above
match x with
| 0 -> "Zero"
| _ -> "Not zero"
let f = function // Using "function" instead of "fun" + "match"
| 0 -> "Zero"
| _ -> "Not zero"

Use list cons operator (a :: b) as a function

F# lets you turn operators into functions by surrounding them with ( ): for instance, (+) is of type int -> int -> int.
Is it possible to do this with the list cons operator, ::?
It doesn't behave like a normal binary operator:
FSI> (::);;
(::);;
-^^
c:\temp\stdin(3,2): error FS0010: Unexpected symbol '::' in expression.
Expected ')' or other token.
And the List.Cons method takes a tuple; it's not curried.
(It's useful to be able to do this. For instance, you can use it to implement map in terms of fold).
Paraphrased from http://cs.hubfs.net/forums/permalink/11713/11713/ShowThread.aspx#11713
(::) is a discriminated union 'constructor' for the list<'a> type, and so raised the question of whether as a function value its arguments should be curried (like +) or tupled (like all DU constructors). Either way seems fishy/unexpected to some people, so F# simply disallows the construct.
Of course you can always write e.g.
let cons x y = x :: y
and use cons, or just use a lambda fun x y -> x::y, if you want a "curried prefix function of two args" for this.
Unfortunately, no, you can't. :: is not an operator, but a "symbolic keyword" according to the language grammar (see section 3.6 of the spec), as are :?> and a few others. The language doesn't seem completely consistent here, though, since there are a few symbolic keywords which can be treated as though they were operators (at least (*) and (<# #>)).
:: and [] can both be represented by List<_>.Cons and List<_>.Empty respectively. Keep in mind though that the former takes a tuple as an argument. These are here so lists can be created in languages other than F#.
> List.Cons(4, List.Empty);;
val it : int list = [4]
> 4::[];;
val it : int list = [4]
> List<int>.Cons(4, List<int>.Empty);;
val it : int list = [4]
> List.Cons;;
val it : 'a * 'a list -> 'a list = <fun:clo#24-7> //'
> List<int>.Empty;;
val it : int list = []

Haskell IO Passes to Another Function

This question here is related to
Haskell Input Return Tuple
I wonder how we can passes the input from monad IO to another function in order to do some computation.
Actually what i want is something like
-- First Example
test = savefile investinput
-- Second Example
maxinvest :: a
maxinvest = liftM maximuminvest maxinvestinput
maxinvestinput :: IO()
maxinvestinput = do
str <- readFile "C:\\Invest.txt"
let cont = words str
let mytuple = converttuple cont
let myint = getint mytuple
putStrLn ""
-- Convert to Tuple
converttuple :: [String] -> [(String, Integer)]
converttuple [] = []
converttuple (x:y:z) = (x, read y):converttuple z
-- Get Integer
getint :: [(String, Integer)] -> [Integer]
getint [] = []
getint (x:xs) = snd (x) : getint xs
-- Search Maximum Invest
maximuminvest :: (Ord a) => [a] -> a
maximuminvest [] = error "Empty Invest Amount List"
maximuminvest [x] = x
maximuminvest (x:xs)
| x > maxTail = x
| otherwise = maxTail
where maxTail = maximuminvest xs
In the second example, the maxinvestinput is read from file and convert the data to the type maximuminvest expected.
Please help.
Thanks.
First, I think you're having some basic issues with understanding Haskell, so let's go through building this step by step. Hopefully you'll find this helpful. Some of it will just arrive at the code you have, and some of it will not, but it is a slowed-down version of what I'd be thinking about as I wrote this code. After that, I'll try to answer your one particular question.
I'm not quite sure what you want your program to do. I understand that you want a program which reads as input a file containing a list of people and their investments. However, I'm not sure what you want to do with it. You seem to (a) want a sensible data structure ([(String,Integer)]), but then (b) only use the integers, so I'll suppose that you want to do something with the strings too. Let's go through this. First, you want a function that can, given a list of integers, return the maximum. You call this maximuminvest, but this function is more general that just investments, so why not call it maximum? As it turns out, this function already exists. How could you know this? I recommend Hoogle—it's a Haskell search engine which lets you search both function names and types. You want a function from lists of integers to a single integer, so let's search for that. As it turns out, the first result is maximum, which is the more general version of what you want. But for learning purposes, let's suppose you want to write it yourself; in that case, your implementation is just fine.
Alright, now we can compute the maximum. But first, we need to construct our list. We're going to need a function of type [String] -> [(String,Integer)] to convert our formattingless list into a sensible one. Well, to get an integer from a string, we'll need to use read. Long story short, your current implementation of this is also fine, though I would (a) add an error case for the one-item list (or, if I were feeling nice, just have it return an empty list to ignore the final item of odd-length lists), and (b) use a name with a capital letter, so I could tell the words apart (and probably a different name):
tupledInvestors :: [String] -> [(String, Integer)]
tupledInvestors [] = []
tupledInvestors [_] = error "tupledInvestors: Odd-length list"
tupledInvestors (name:amt:rest) = (name, read amt) : tupledInvestors rest
Now that we have these, we can provide ourselves with a convenience function, maxInvestment :: [String] -> Integer. The only thing missing is the ability to go from the tupled list to a list of integers. There are several ways to solve this. One is the one you have, though that would be unusual in Haskell. A second would be to use map :: (a -> b) -> [a] -> [b]. This is a function which applies a function to every element of a list. Thus, your getint is equivalent to the simpler map snd. The nicest way would probably be to use Data.List.maximumBy :: :: (a -> a -> Ordering) -> [a] -> a. This is like maximum, but it allows you to use a comparison function of your own. And using Data.Ord.comparing :: Ord a => (b -> a) -> b -> b -> Ordering, things become nice. This function allows you to compare two arbitrary objects by converting them to something which can be compared. Thus, I would write
maxInvestment :: [String] -> Integer
maxInvestment = maximumBy (comparing snd) . tupledInvestors
Though you could also write maxInvestment = maximum . map snd . tupledInvestors.
Alright, now on to the IO. Your main function, then, wants to read from a specific file, compute the maximum investment, and print that out. One way to represent that is as a series of three distinct steps:
main :: IO ()
main = do dataStr <- readFile "C:\\Invest.txt"
let maxInv = maxInvestment $ words dataStr
print maxInv
(The $ operator, if you haven't seen it, is just function application, but with more convenient precedence; it has type (a -> b) -> a -> b, which should make sense.) But that let maxInv seems pretty pointless, so we can get rid of that:
main :: IO ()
main = do dataStr <- readFile "C:\\Invest.txt"
print . maxInvestment $ words dataStr
The ., if you haven't seen it yet, is function composition; f . g is the same as \x -> f (g x). (It has type (b -> c) -> (a -> b) -> a -> c, which should, with some thought, make sense.) Thus, f . g $ h x is the same as f (g (h x)), only easier to read.
Now, we were able to get rid of the let. What about the <-? For that, we can use the =<< :: Monad m => (a -> m b) -> m a -> m b operator. Note that it's almost like $, but with an m tainting almost everything. This allows us to take a monadic value (here, the readFile "C:\\Invest.txt" :: IO String), pass it to a function which turns a plain value into a monadic value, and get that monadic value. Thus, we have
main :: IO ()
main = print . maxInvestment . words =<< readFile "C:\\Invest.txt"
That should be clear, I hope, especially if you think of =<< as a monadic $.
I'm not sure what's happening with testfile; if you edit your question to reflect that, I'll try to update my answer.
One more thing. You said
I wonder how we can passes the input from monad IO to another function in order to do some computation.
As with everything in Haskell, this is a question of types. So let's puzzle through the types here. You have some function f :: a -> b and some monadic value m :: IO a. You want to use f to get a value of type b. This is impossible, as I explained in my answer to your other question; however, you can get something of type IO b. Thus, you need a function which takes your f and gives you a monadic version. In other words, something with type Monad m => (a -> b) -> (m a -> m b). If we plug that into Hoogle, the first result is Control.Monad.liftM, which has precisely that type signature. Thus, you can treat liftM as a slightly different "monadic $" than =<<: f `liftM` m applies f to the pure result of m (in accordance with whichever monad you're using) and returns the monadic result. The difference is that liftM takes a pure function on the left, and =<< takes a partially-monadic one.
Another way to write the same thing is with do-notation:
do x <- m
return $ f x
This says "get the x out of m, apply f to it, and lift the result back into the monad." This is the same as the statement return . f =<< m, which is precisely liftM again. First f performs a pure computation; its result is passed into return (via .), which lifts the pure value into the monad; and then this partially-monadic function is applied, via =<,, to m.
It's late, so I'm not sure how much sense that made. Let me try to sum it up. In short, there is no general way to leave a monad. When you want to perform computation on monadic values, you lift pure values (including functions) into the monad, and not the other way around; that could violate purity, which would be Very Bad™.
I hope that actually answered your question. Let me know if it didn't, so I can try to make it more helpful!
I'm not sure I understand your question, but I'll answer as best I can. I've simplified things a bit to get at the "meat" of the question, if I understand it correctly.
maxInvestInput :: IO [Integer]
maxInvestInput = liftM convertToIntegers (readFile "foo")
maximumInvest :: Ord a => [a] -> a
maximumInvest = blah blah blah
main = do
values <- maxInvestInput
print $ maximumInvest values
OR
main = liftM maximumInvest maxInvestInput >>= print