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GC16/3011 Functional Programming Lecture 5 Miranda

GC16/3011 Functional Programming Lecture 5 Miranda. patterns, functions, recursion and lists. Contents. Offside rule / where blocks / evaluation Partial / polymorphic functions Patterns and pattern-matching Recursive functions Lists Functions using lists Recursive functions using lists.

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GC16/3011 Functional Programming Lecture 5 Miranda

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  1. GC16/3011 Functional ProgrammingLecture 5Miranda patterns, functions, recursion and lists

  2. Contents • Offside rule / where blocks / evaluation • Partial / polymorphic functions • Patterns and pattern-matching • Recursive functions • Lists • Functions using lists • Recursive functions using lists

  3. Functions • The offside rule and “where” blocks • Mapping from source to target type domains • Application associates to the left! • Function evaluation • normal order, lazy • main = fst (34, (23 / 0) )

  4. Functions • Partial functions • those which have no result (i.e. return an error) for some valid values of valid input type • f (x,y) = x / y • Polymorphic functions • fst, snd • g (x,y) = (-y, x) • three x = 3

  5. Patterns • Tuple patterns • (x,y,z) = (3, “hello”, (34,True,[3])) • as a test • as a definition • Patterns for function definitions not True = False not False = True • Top-down evaluation semantics f 3 = 45 f 489 = 3 f any = 345*219

  6. Patterns • Non-exhaustive patterns f True = False • Patterns can destroy laziness fst (x,0) = x fst (x,y) = x • Can a pattern contain a redex? • No! A pattern must be a constant expression • (special exception – “(n + 1)” in Miranda) • Duplicate parameter names (Miranda only)

  7. Recursive Functions • Recursion is the ONLY way to program loops in a functional language • Function calls itself inside its own body • Very powerful – very flexible • In imperative languages, can be slow • In functional languages, highly optimised

  8. Recursive Functions • Beware: loop_forever x = loop_forever x • Must have: • Terminating condition • Changing argument • …that converges on the terminating condition! f :: num -> [char] f 0 = “” f n = “X” ++ (f (n – 1))

  9. Recursive Functions • Stack recursion • f 3 • è “X” ++ (f (3 – 1)) • è “X” ++ (f 2) • è “X” ++ (“X” ++ (f (2-1))) • è “X” ++ (“X” ++ (f 1)) • è “X” ++ (“X” ++ (“X” ++ (f (1-1)))) • è “X” ++ (“X” ++ (“X” ++ “”)) • è “X” ++ (“X” ++ “X”) • è “X” ++ “XX” • è “XXX”

  10. Recursive Functions • Accumulative recursion plus :: (num, num) -> num plus (x, 0) = x plus (x, y) = plus (x+1, y-1)

  11. Type Synonyms • f :: (([char],num,[char]),(num,num,num)) -> bool • str = = [char] • coord = = (num, num, num) • f :: ((str,num,str), coord) -> bool

  12. LISTS • Lists are another way to collect together related data • But lists are special - they are RECURSIVE • Data can be recursive, just like functions!

  13. LISTS • A list of type a is either: • Empty, or • An element of type a together with a list of elements of the same type • List of num: • [] • (34: []) [34] • (34: (13: [])) [34, 13]

  14. Functions using lists bothempty :: ([*],[**]) -> bool bothempty ([], []) = True bothempty anything = False myhd :: [*] -> * myhd [] = error “take head of empty list” myhd (x : rest) = x

  15. Recursive functions using lists sumlist :: [num] -> num sumlist [] = 0 sumlist (x : rest) = x + (sumlist rest) length :: [*] -> num length [] = 0 length (x : rest) = 1 + (length rest)

  16. Exercise • Can you write a function “threes” which takes as input a list of whole numbers and produces as output a count of how many 3s occur in the input?

  17. Summary • Offside rule / where blocks / evaluation • Partial / polymorphic functions • Patterns and pattern-matching • Recursive functions • Lists • Functions using lists • Recursive functions using lists

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