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Exploring Tuples and Currying in Haskell Programming

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This document covers key concepts in Haskell's functional programming paradigm, focusing on tuple types and currying. It explains how composite types can be created using tuples, exemplified by types like (Integer, Char). The section also illustrates pattern matching, where constructors are applied, and demonstrates currying, showing how functions can be transformed from a multi-argument format to a series of single-argument functions. Additional topics include local definitions with the `where` keyword, and a brief exploration of the Fibonacci sequence calculation.

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Exploring Tuples and Currying in Haskell Programming

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  1. Comp 205:Comparative Programming Languages • Functional Programming Languages: • More Haskell • Lecture notes, exercises, etc., can be found at: • www.csc.liv.ac.uk/~grant/Teaching/COMP205/

  2. Tuple Types • Haskell allows composite types to be built up by • "tupling", e.g. • (Integer,Integer)is the type of pairs of Integers; similarly • (Integer,Char,Bool),etc. • In general, (A,B) represents the type of pairs whose first component has type A and whose second component has type B.

  3. Tuples • Elements of tuple types are also written using • the (_,_) notation; • for example, (24,'a')is of type (Integer,Char). • The (_,_) notation is an example of a special kind • of operator called a constructor: • all tuples can be built using this operator, and • the operator is not evaluated: Prelude> (24,'a') (24,'a')

  4. Pattern-Matching #2 Constructors can be used in patterns: -- add a pair of numbers add :: (Integer,Integer) -> Integer add (x,y) = x + y fst (x,y) = x snd (x,y) = y

  5. Hot Stuff: Currying curriedAdd :: Integer -> Integer -> Integer curriedAdd m n = m + n Prelude>:l arithmetic ... Main>:t curriedAdd curriedAdd :: Integer -> Integer -> Integer Main>:t curriedAdd 3 curriedAdd 3 :: Integer -> Integer Main> curriedAdd 3 5 8

  6. Currying There is a one-to-one correspondence between the types (A,B) -> C and A -> (B -> C). Given a function f :: (A,B) -> C , its curried equivalent is the function curriedF :: A -> B -> C curriedF a b = f (a,b)

  7. Curried Max maxOf2 :: Integer -> Integer -> Integer A possible definition of maxOf2 is: maxOf2 m n | m >= n = m | m < n = n

  8. Or... Another possible (equivalent) definition of maxOf2 is: maxOf2 m n | m >= n = m | otherwise = n

  9. Or Even... Another possible (equivalent) definition of maxOf2 is: maxOf2 m n | m >= n = m | m <= n = n

  10. Nested Definitions "Local" definitions can be made using the where keyword: maxOf3 :: Int -> Int -> Int -> Int maxOf3 x y z = maxOf2 u z where u = maxOf2 x y which is equivalent to: maxOf3 x y z = maxOf2 (maxOf2 x y) z

  11. The Fibonnacci Sequence -- nth number in the Fibonnacci sequence fib n = fib1 where (fib1, fib2) = fibs n -- (nth, (n+1)th) in Fib. seq. fibs 0 = (1,1) fibs n = (f2, f1 + f2) where (f1,f2) = fibs (n-1)

  12. ... Or fib n = fib1 where (fib1, fib2) = fibs n fibs n | n <= 0 = (1,1) | n > 0 = (f2, f1 + f2) where (f1,f2) = fibs (n-1)

  13. TheFsequence whereF = Fibonacci -- file: fib.hs fib n = fib1 where (fib1, fib2) = fibs n fibs m | m < 1 = (1,1) | 0 < m = (f2, f1 + f2) where (f1,f2) = fibs (m-1),

  14. TheFsequence whereF = Fibonacci -- file: fib.hs fib n = f1 where (f1, f2) = fibs n fibs n | n < 1 = (1,1) | 0 < n = (f2, f1 + f2) where (f1,f2) = fibs (n-1),

  15. Local is Hidden Main>:l fib.hs ... Main>fibs 5 ERROR - Undefined variable "fibs" Main>

  16. Summary • Key topics: • Tuples and Currying • Guards (| <Test> = …) • Local definitions (where) • Next: Lists

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