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GC16/3011 Functional ProgrammingLecture 5

Mirandapatterns, functions, recursion and listspatterns, functions, recursion and lists

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Contents

Offside rule / where blocks / evaluationOffside rule / where blocks / evaluation Partial / polymorphic functionsPartial / polymorphic functions Patterns and pattern-matchingPatterns and pattern-matching Recursive functionsRecursive functions ListsLists

Functions using listsFunctions using lists Recursive functions using listsRecursive functions using lists

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Functions

The offside rule and “where” blocksThe offside rule and “where” blocks

Mapping from source to target type domainsMapping from source to target type domains

Application associates to the left!Application associates to the left!

Function evaluationFunction evaluation normal order, lazynormal order, lazy main = fst (34, (23 / 0) )main = fst (34, (23 / 0) )

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Functions

Partial functionsPartial functions those which have no result (i.e. return an error) for those which have no result (i.e. return an error) for

some valid values of valid input typesome valid values of valid input type f (x,y) = x / yf (x,y) = x / y

Polymorphic functionsPolymorphic functions fst, sndfst, snd g (x,y) = (-y, x)g (x,y) = (-y, x) three x = 3three x = 3

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Patterns

Tuple patternsTuple patterns (x,y,z) = (3, “hello”, (34,True,[3]))(x,y,z) = (3, “hello”, (34,True,[3]))

as a testas a test as a definitionas a definition

Patterns for function definitionsPatterns for function definitionsnot True = Falsenot True = Falsenot False = Truenot False = True

Top-down evaluation semanticsTop-down evaluation semanticsf 3 = 45f 3 = 45f 489 = 3f 489 = 3f any = 345*219f any = 345*219

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Patterns

Non-exhaustive patternsNon-exhaustive patternsf True = Falsef True = False

Patterns can destroy lazinessPatterns can destroy lazinessfst (x,0) = xfst (x,0) = xfst (x,y) = xfst (x,y) = x

Can a pattern contain a redex?Can a pattern contain a redex? No! A pattern must be a constant expressionNo! A pattern must be a constant expression (special exception – “(n + 1)” in Miranda)(special exception – “(n + 1)” in Miranda)

Duplicate parameter names (Miranda only)Duplicate parameter names (Miranda only)

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Recursive Functions

Recursion is the ONLY way to program loops in a Recursion is the ONLY way to program loops in a functional languagefunctional language Function calls itself inside its own bodyFunction calls itself inside its own body

Very powerful – very flexibleVery powerful – very flexible

In imperative languages, can be slow In imperative languages, can be slow

In functional languages, highly optimisedIn functional languages, highly optimised

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Recursive Functions

Beware:Beware:loop_forever x = loop_forever xloop_forever x = loop_forever x

Must have:Must have: Terminating conditionTerminating condition Changing argumentChanging argument ……that converges on the terminating condition!that converges on the terminating condition!

f :: num -> [char]f :: num -> [char]f 0 = “”f 0 = “”f n = “X” ++ (f (n – 1))f n = “X” ++ (f (n – 1))

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Recursive Functions

Stack recursion Stack recursion f 3f 3 “ “X” ++ (f (3 – 1))X” ++ (f (3 – 1)) “ “X” ++ (f 2)X” ++ (f 2) “ “X” ++ (“X” ++ (f (2-1)))X” ++ (“X” ++ (f (2-1))) “ “X” ++ (“X” ++ (f 1))X” ++ (“X” ++ (f 1)) “ “X” ++ (“X” ++ (“X” ++ (f (1-1))))X” ++ (“X” ++ (“X” ++ (f (1-1)))) “ “X” ++ (“X” ++ (“X” ++ “”))X” ++ (“X” ++ (“X” ++ “”)) “ “X” ++ (“X” ++ “X”)X” ++ (“X” ++ “X”) “ “X” ++ “XX”X” ++ “XX” “ “XXX”XXX”

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Recursive Functions

Accumulative recursion Accumulative recursion plus :: (num, num) -> numplus :: (num, num) -> num

plus (x, 0) = xplus (x, 0) = x

plus (x, y) = plus (x+1, y-1)plus (x, y) = plus (x+1, y-1)

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Type Synonyms

f :: (([char],num,[char]),(num,num,num)) -> boolf :: (([char],num,[char]),(num,num,num)) -> bool

str = = [char]str = = [char] coord = = (num, num, num)coord = = (num, num, num)

f :: ((str,num,str), coord) -> boolf :: ((str,num,str), coord) -> bool

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LISTS

Lists are another way to collect together Lists are another way to collect together related datarelated data

But lists are special - they are RECURSIVEBut lists are special - they are RECURSIVE Data can be recursive, just like functions!Data can be recursive, just like functions!

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LISTS

A list of type A list of type is either: is either: Empty, orEmpty, or An element of type An element of type together with a list of together with a list of

elements of the same typeelements of the same type List of num:List of num:

[][] (34: []) [34](34: []) [34] (34: (13: [])) [34, 13](34: (13: [])) [34, 13]

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Functions using lists

bothempty :: ([*],[**]) -> boolbothempty :: ([*],[**]) -> bool

bothempty ([], []) = Truebothempty ([], []) = True

bothempty anything = Falsebothempty anything = False

myhd :: [*] -> *myhd :: [*] -> *

myhd [] = error “take head of empty list”myhd [] = error “take head of empty list”

myhd (x : rest) = xmyhd (x : rest) = x

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Recursive functions using lists

sumlist :: [num] -> numsumlist :: [num] -> num

sumlist [] = 0sumlist [] = 0

sumlist (x : rest) = x + (sumlist rest)sumlist (x : rest) = x + (sumlist rest)

length :: [*] -> numlength :: [*] -> num

length [] = 0length [] = 0

length (x : rest) = 1 + (length rest)length (x : rest) = 1 + (length rest)

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Exercise

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

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Summary

Offside rule / where blocks / evaluationOffside rule / where blocks / evaluation Partial / polymorphic functionsPartial / polymorphic functions Patterns and pattern-matchingPatterns and pattern-matching Recursive functionsRecursive functions ListsLists

Functions using listsFunctions using lists Recursive functions using listsRecursive functions using lists