SLIDE 1
CS302: Paradigms of Programming Functional Programming with Haskell
Manas Thakur
Spring 2020
Last Two Weeks of PoP
- Culmination of whatever we have been learning
- Recall this slide?
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CS302: Paradigms of Programming Functional Programming with Haskell - - PowerPoint PPT Presentation
CS302: Paradigms of Programming Functional Programming with Haskell - - PowerPoint PPT Presentation
CS302: Paradigms of Programming Functional Programming with Haskell Manas Thakur Spring 2020 Last Two Weeks of PoP Culmination of whatever we have been learning Recall this slide? 2 Whats a function? A map from values in a
SLIDE 2
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What’s a function?
- A map from values in a domain D to values in a range R.
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f :: D -> R
- Examples:
sin :: Float -> Float age :: Person -> Int add :: (Integer,Integer) -> Integer
- Applying a function:
f(x) sin OR sin( )? Haskell: f x
θ θ
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Function composition
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f :: Y -> Z g :: X -> Y
- What is f . g?
f . g :: X -> Z (f . g) x :: f (g x)
- All this is Haskell code!
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haskell.org
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Common Words
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the: 154
- f : 50
a : 18 and: 12 in : 11 … … n entries
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Type declaration
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- What’s the type of input?
- An integer
- A list of characters
- What’s the type of output?
- List of characters again!
- What’s the type of commonWords?
Int, [Char] [Char] commonWords :: Int -> ([Char] -> [Char])
Functions in Haskell are curried!
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Possible algorithm
- Get words from text
- Count occurrence of each word
- Sort in decreasing order
- Display
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Type synonyms
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words :: [Char] -> [[Char]] type Text = [Char] type Word = [Char] words :: Text -> [Word]
- Get words from text
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Higher order functions
- Should “The” and “the” be counted as same or different?
- Solution: Convert each letter to lowercase!
- Can you identify a function just by looking at its type signature?
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What? :: (a -> b) -> [a] -> [b] map :: (a -> b) -> [a] -> [b] map toLower :: Text -> Text
Currying again!
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One of the most remarkable ideas in programming
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sortWords [“to”, “be”, “or”, “not”, “to”, “be”] = [“be”, “be”, “not”, “or”, “to”, “to”] sortWords :: [Word] -> [Word]
- Count occurrence of each word
- Sort first?
- Count adjacent runs of each word:
countRuns [“be”, “be”, “not”, “or”, “to”, “to”] = [(2,“be”), (1,“not”), (1,“or”), (2,“to”)] countRuns :: [Word] -> [(Int,Word)]
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I told you sorting is remarkable
- Sort in decreasing order:
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sortRuns [(2,“be”), (1,“not”), (1,“or”), (2,“to”)] = [(2,“be”), (2,“to”), (1,“not”), (1,“or”)] sortRuns :: [(Int,Word)] -> [(Int,Word)]
- But we wanted to take only first n entries:
take 2 [(2,“be”), (2,“to”), (1,“not”), (1,“or”)] = [(2,“be”), (2,“to”)] take :: Int -> [a] -> [a]
Reminder: Every function is curried by default in Haskell!
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I only want to see the output
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showRun :: (Int,Word) -> String showRun (2,”be”) = “be: 2\n”
- We want to do this for each entry in the list:
map showRun :: [(Int,Word)] -> [String] String is a type synonym for [Char].
- Finally, concatenate the list of Strings into one:
concat :: [[a]] -> [a]
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Common Words in a Nutshell
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commonWords :: Int -> Text -> String commonWords n = concat . map showRun . take n . sortRuns . countRuns . sortWords . words . map toLower
- This is how typical Haskell programs look!!
- Mathematics is definitely something you didn’t study unnecessarily
in school!
- But none of those functions was defined?
- Some of them are predefined (concat, words, take, map, toLower).
- Rest (showRun, sortRuns, countRuns, sortWords) we can define.
- Does the implementation matter much? :-)