Sorry, this may seem similar to an earlier question but I am still a little confused. Here is the same code I am using as an example:
type Pig = String
type Lion = String
type Feed = [(Char,Char)]
type Visitors = [(Char,Char)]
type Costs = (Int,Int,Int)
data AnimalHome = Farm Pig Pig Pig Feed | Zoo Lion Lion Lion Feed Visitors
orders :: Char -> AnimalHome -> Costs -> Char
orders stuff (Farm p1 p2 p3 feed) (cost1,cost2,cost3) = some code here
But this time I want to execute different functions if the costs are different i.e. (1,3,9) executes a different equation to (0,0,16) etc.
You can adapt the answers to your previos similar questions for this case. Remember that a 3-tuple or triple (i.e. your type Costs) is just another data type. If there were no tuples in Haskell, you could write:
data Triple a b c = Triple a b c
and it would behave exactly as 3-tuples do! The only difference is that Hakell supports a more convenient syntax both for tuple expressions and tuple patterns.
Now for Patterns in general: Simplifying a bit, there are basicall 3 possibilities to write them:
a literal (suitable only for data types that support this, like String, Int, etc.), matches only that value.
a variable, matches any value
a data constructor, applied to patterns. Matches values constructed with that data constructor where the subpatterns match.
Turns out that you already wrote correct patterns in your question:
i.e. (1,3,9) executes a different equation to (0,0,16)
hence
orders stuff (Farm p1 p2 p3 feed) (1,3,9) = some code here
orders stuff (Farm p1 p2 p3 feed) (0,0,16) = some other code here
It probably would help us to help you if we could understand what your specific issues with pattern matching is. i.e. why you couldn't just try to come up with that yourself, as it feels quite natural, does it not?
If you really mean to use different functions with different integers, it's fine to use pattern matching
orders stuff (Farm p1 p2 p3 feed) (1,3,9) = -- one thing
orders stuff (Farm p1 p2 p3 feed) (0,0,16) = -- another thing
but I'd only really use that with 0, not other values. Really what you're after is called guards:
orders stuff (Farm p1 p2 p3 feed) (a,b,c)
| a == 0 && b == 0 = -- one thing
| a*b^2=c = -- another thing
| b < 0 = -- a third thing
and each condition is checked in turn - only the first true condition gets to run its code.
Related
I was playing with musical note names having the goal to not confuse enharmonic equals, i.e. I wanted to get the accidentals (sharps and flats) right. The note a perfect fifth above the note B needs to be Fs and not Gb, even though Fs and Gb are the same key on a piano keyboard.
Also I wanted the convenience of writing e.e. Fs in a haskell program, without spaces, quotes or an extra function.
I ended up defining 35 constructors, ranging from Cbb to Bss. While this worked and did get the accidentals right, I was unhappy about the limitation to at most two accidentals. Internally, the accidentals we represented asInts anyways.
Is there a way to define an infinite number of constructors as indicated in the title, so notes with any number of accidentals (like Cbbbb) could be used? Template haskell maybe?
Or alternatively, can I get the convenience of writing Cbbbb in a haskell program (without quotes, spaces or an extra function) without making Cbbbb a constructor?
I agree with Carsten that actually having lots of disperate constructors like that is a bad idea. It's much more sensible to use data like
data BaseNote = C | D | E | F | G | A | B
data PitchClass = PitchClass
{ baseNote :: BaseNote
, accidentals :: Int }
data Note = Note
{ pitchClass :: PitchClass
, octave :: Int }
As for
Also I wanted the convenience of writing e.e. Fs in a haskell program, without spaces, quotes or an extra function.
you have multiple options.
You could use -XPatternSynonyms. This lets you procure matchable constructors for already-defined data types.
{-# LANGUAGE PatternSynonyms #-}
pattern Cn = PitchClass C 0
pattern Cs = PitchClass C 1
pattern Cb = PitchClass C (-1)
...
These can be provided by a TemplateHaskell macro to avoid code duplication.
You could provide a function that makes it look as compact as single constructor names, but actually isn't.
(♮), (♯), (♭) :: BaseNote -> Int -> Note
bn♮octv = Note (PitchClass bn 0) octv
bn♯octv = Note (PitchClass bn 1) octv
bn♭octv = Note (PitchClass bn (-1)) octv
Now you can write things like
[A♮2, A♮2, C♯3, C♯3, D♮3, D♮3, C♯3]
TBH I don't think either of these is really good though. IMO it makes more sense to specify musical material not in absolute pitches at all, but rather as a sequence of either scale degrees or interval steps.
I'm studying project euler solutions and this is the solution of problem 4, which asks to
Find the largest palindrome made from the product of two 3-digit
numbers
problem_4 =
maximum [x | y<-[100..999], z<-[y..999], let x=y*z, let s=show x, s==reverse s]
I understand that this code creates a list such that x is a product of all possible z and y.
However I'm having a problem understanding what does s do here. Looks like everything after | is going to be executed everytime a new element from this list is needed, right?
I don't think I understand what's happening here. Shouldn't everything to the right of | be constraints?
A list comprehension is a rather thin wrapper around a do expression:
problem_4 = maximum $ do
y <- [100..999]
z <- [y..999]
let x = y*z
let s = show x
guard $ s == reverse s
return x
Most pieces translate directly; pieces that aren't iterators (<-) or let expressions are treated as arguments to the guard function found in Control.Monad. The effect of guard is to short-circuit the evaluation; for the list monad, this means not executing return x for the particular value of x that led to the false argument.
I don't think I understand what's happening here. Shouldn't everything to the right of | be constraints?
No, at the right part you see an expression that is a comma-separated (,) list of "parts", and every part is one of the following tree:
an "generator" of the form somevar <- somelist;
a let statement which is an expression that can be used to for instance introduce a variable that stores a subresult; and
expressions of the type boolean that act like a filter.
So it is not some sort of "constraint programming" where one simply can list some constraints and hope that Haskell figures it out (in fact personally that is the difference between a "programming language" and a "specification language": in a programming language you have "control" how the data flows, in a specification language, that is handled by a system that reads your specifications)
Basically an iterator can be compared to a "foreach" loop in many imperative programming languages. A "let" statement can be seen as introducing a temprary variable (but note that in Haskell you do not assign variable, you declare them, so you can not reassign values). The filter can be seen as an if statement.
So the list comprehension would be equivalent to something in Python like:
for y in range(100, 1000):
for z in range(y, 1000):
x = y * z
s = str(x)
if x == x[::-1]:
yield x
We thus first iterate over two ranges in a nested way, then we declare x to be the multiplication of y and z, with let s = show x, we basically convert a number (for example 15129) to its string counterpart (for example "15129"). Finally we use s == reverse s to reverse the string and check if it is equal to the original string.
Note that there are more efficient ways to test Palindromes, especially for multiplications of two numbers.
I'm learning Haskell by writing an OSC musical sequencer to use it with SuperCollider. But because I'd like to make fairly complex stuff with it, it will work like a programming language where you can declare variables and define functions so you can write music in an algorithmic way. The grammar is unusual in that we're coding sequences and sometimes a bar will reference the last bar (something like "play that last chord again but a fifth above").
I don't feel satisfied with my own explanation, but that's the best I can without getting too technical.
Anyway, what I'm coding now is the parser for that language, stateless so far, but now I need some way to implement a growing list of the declared variables and alikes using a dictionary in the [("key","value")] fashion, so I can add new values as I go parsing bar by bar.
I know this involves monads, which I don't really understand yet, but I need something meaningful enough to start toying with them or else I find the raw theory a bit too raw.
So what would be a clean and simple way to start?
Thanks and sorry if the question was too long.
Edit on how the thing works:
we input a string to the main parsing function, say
"afunction(3) ; anotherone(1) + [3,2,1]"
we identify closures first, then kinds of chars (letters, nums, etc) and group them together, so we get a list like:
[("word","afunction"),("parenth","(3)"),("space"," "),("semicolon",";"),("space"," "),("word","anotherone"),("parenth","(1)"),("space"," "),("opadd","+"),("space"," "),("bracket","[3,2,1]")]
then we use a function that tags all those tuples with the indices of the original string they occupy, like:
[("word","afunction",(0,8)),("parenth","(3)",(9,11)),("space"," ",(12,13)) ...]
then cut it in a list of bars, which in my language are separated using a semicolon, and then in notes, using commas.
And now I'm at the stage where those functions should be executed sequentially, but because some of them are reading or modifying previously declared values, I need to keep track of that change. For example, let's say the function f(x) moves the pitch of the last note by x semitones, so
f(9), -- from an original base value of 0 (say that's an A440) we go to 9
f(-2), -- 9-2 = 7, so a fifth from A
f(-3); -- 9-2-3, a minor third down from the last value.
etc
But sometimes it can get a bit more complicated than that, don't make me explain how cause I could bore you to death.
Adding an item to a list
You can make a new list that contains one more item than an existing list with the : constructor.
("key", "value") : existing
Where existing is a list you've already made
Keeping track of changing state
You can keep track of changing state between functions by passing the state from each function to the next. This is all the State monad is doing. State s a is a value of type a that depends on (and changes) a state s.
{- ┌---- type of the state
v v-- type of the value -}
data State s a = State { runState :: s -> (a, s) }
{- ^ ^ ^ ^
a function ---|--┘ | |
that takes a state ---┘ | |
and returns | |
a value that depends on the state ---┘ |
and a new state ------┘ -}
The bind operation >>= for State takes a value that depends on (and changes) the state and a function to compute another value that depends on (and changes) the state and combines them to make a new value that depends on (and changes) the state.
m >>= k = State $ \s ->
let ~(a, s') = runState m s
in runState (k a) s'
I'm trying to write a function in Haskell that calculates all factors of a given number except itself.
The result should look something like this:
factorlist 15 => [1,3,5]
I'm new to Haskell and the whole recursion subject, which I'm pretty sure I'm suppoused to apply in this example but I don't know where or how.
My idea was to compare the given number with the first element of a list from 1 to n div2
with the mod function but somehow recursively and if the result is 0 then I add the number on a new list. (I hope this make sense)
I would appreciate any help on this matter
Here is my code until now: (it doesn't work.. but somehow to illustrate my idea)
factorList :: Int -> [Int]
factorList n |n `mod` head [1..n`div`2] == 0 = x:[]
There are several ways to handle this. But first of all, lets write a small little helper:
isFactorOf :: Integral a => a -> a -> Bool
isFactorOf x n = n `mod` x == 0
That way we can write 12 `isFactorOf` 24 and get either True or False. For the recursive part, lets assume that we use a function with two arguments: one being the number we want to factorize, the second the factor, which we're currently testing. We're only testing factors lesser or equal to n `div` 2, and this leads to:
createList n f | f <= n `div` 2 = if f `isFactorOf` n
then f : next
else next
| otherwise = []
where next = createList n (f + 1)
So if the second parameter is a factor of n, we add it onto the list and proceed, otherwise we just proceed. We do this only as long as f <= n `div` 2. Now in order to create factorList, we can simply use createList with a sufficient second parameter:
factorList n = createList n 1
The recursion is hidden in createList. As such, createList is a worker, and you could hide it in a where inside of factorList.
Note that one could easily define factorList with filter or list comprehensions:
factorList' n = filter (`isFactorOf` n) [1 .. n `div` 2]
factorList'' n = [ x | x <- [1 .. n`div` 2], x `isFactorOf` n]
But in this case you wouldn't have written the recursion yourself.
Further exercises:
Try to implement the filter function yourself.
Create another function, which returns only prime factors. You can either use your previous result and write a prime filter, or write a recursive function which generates them directly (latter is faster).
#Zeta's answer is interesting. But if you're new to Haskell like I am, you may want a "simple" answer to start with. (Just to get the basic recursion pattern...and to understand the indenting, and things like that.)
I'm not going to divide anything by 2 and I will include the number itself. So factorlist 15 => [1,3,5,15] in my example:
factorList :: Int -> [Int]
factorList value = factorsGreaterOrEqual 1
where
factorsGreaterOrEqual test
| (test == value) = [value]
| (value `mod` test == 0) = test : restOfFactors
| otherwise = restOfFactors
where restOfFactors = factorsGreaterOrEqual (test + 1)
The first line is the type signature, which you already knew about. The type signature doesn't have to live right next to the list of pattern definitions for a function, (though the patterns themselves need to be all together on sequential lines).
Then factorList is defined in terms of a helper function. This helper function is defined in a where clause...that means it is local and has access to the value parameter. Were we to define factorsGreaterOrEqual globally, then it would need two parameters as value would not be in scope, e.g.
factorsGreaterOrEqual 4 15 => [5,15]
You might argue that factorsGreaterOrEqual is a useful function in its own right. Maybe it is, maybe it isn't. But in this case we're going to say it isn't of general use besides to help us define factorList...so using the where clause and picking up value implicitly is cleaner.
The indentation rules of Haskell are (to my tastes) weird, but here they are summarized. I'm indenting with two spaces here because it grows too far right if you use 4.
Having a list of boolean tests with that pipe character in front are called "guards" in Haskell. I simply establish the terminal condition as being when the test hits the value; so factorsGreaterOrEqual N = [N] if we were doing a call to factorList N. Then we decide whether to concatenate the test number into the list by whether dividing the value by it has no remainder. (otherwise is a Haskell keyword, kind of like default in C-like switch statements for the fall-through case)
Showing another level of nesting and another implicit parameter demonstration, I added a where clause to locally define a function called restOfFactors. There is no need to pass test as a parameter to restOfFactors because it lives "in the scope" of factorsGreaterOrEqual...and as that lives in the scope of factorList then value is available as well.
Classic way to define Haskell functions is
f1 :: String -> Int
f1 ('-' : cs) -> f1 cs + 1
f1 _ = 0
I'm kinda unsatisfied writing function name at every line. Now I usually write in the following way, using pattern guards extension and consider it more readable and modification friendly:
f2 :: String -> Int
f2 s
| '-' : cs <- s = f2 cs + 1
| otherwise = 0
Do you think that second example is more readable, modifiable and elegant? What about generated code? (Haven't time to see desugared output yet, sorry!). What are cons? The only I see is extension usage.
Well, you could always write it like this:
f3 :: String -> Int
f3 s = case s of
('-' : cs) -> f3 cs + 1
_ -> 0
Which means the same thing as the f1 version. If the function has a lengthy or otherwise hard-to-read name, and you want to match against lots of patterns, this probably would be an improvement. For your example here I'd use the conventional syntax.
There's nothing wrong with your f2 version, as such, but it seems a slightly frivolous use of a syntactic GHC extension that's not common enough to assume everyone will be familiar with it. For personal code it's not a big deal, but I'd stick with the case expression for anything you expect other people to be reading.
I prefer writing function name when I am pattern matching on something as is shown in your case. I find it more readable.
I prefer using guards when I have some conditions on the function arguments, which helps avoiding if else, which I would have to use if I was to follow the first pattern.
So to answer your questions
Do you think that second example is more readable, modifiable and elegant?
No, I prefer the first one which is simple and readable. But more or less it depends on your personal taste.
What about generated code?
I dont think there will be any difference in the generated code. Both are just patternmatching.
What are cons?
Well patternguards are useful to patternmatch instead of using let or something more cleanly.
addLookup env var1 var2
| Just val1 <- lookup env var1
, Just val2 <- lookup env var2
= val1 + val2
Well the con is ofcourse you need to use an extension and also it is not Haskell98 (which you might not consider much of a con)
On the other hand for trivial pattern matching on function arguments I will just use the first method, which is simple and readable.