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Comp 205: Comparative Programming Languages

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/. Tuple Types. Haskell allows composite types to be built up by "tupling", e.g.

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Comp 205: Comparative Programming Languages

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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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