Gary MarsdenSlide 1University of Cape Town Functional programming in Clean Gary Marsden Semester 2 – 2000

Gary MarsdenSlide 2University of Cape Town What the heck is functional programming  Functional languages are so called because they require code to be written as functions (in the mathematical sense)  Note that everything is a function – there is no notion of “state”  This is radically different from other non- functional (dis-functional?) imperative languages

Gary MarsdenSlide 3University of Cape Town So what the heck is imperative programming?  The languages you are used to (C++, Java, C etc.) are all based on the Von Neumann computer architecture  Simply put,the VN model has a CPU which accesses a piece of memory. That memory contains data and instructions to perform on the data CPU Data Instructions Data Instructions (Bottleneck)

Gary MarsdenSlide 4University of Cape Town Should programming follow Von Neumann?  The Von Neumann architecture worked so well for low level hardware, that the idea was carried over into programming languages  Over time, it has become clear that some of the low level ideas lead to problems in writing good software – GOTO statements and global variables being two culprits.  Functional languages aim to rid us of the last anachronism – the assignment statement

Gary MarsdenSlide 5University of Cape Town No assignment statement! a=5

Gary MarsdenSlide 6University of Cape Town Reasons for ditching assignment even = TRUE; int calc (int x) { even = !even; if (even) x++ else x-- ; }.... if (calc(6) == calc(6)) {....  Look at the last ‘if’ statement  Shouldn’t the expression always evaluate to true?  Having explicit state results in side effects

Gary MarsdenSlide 7University of Cape Town More reasons  Because of side effects, it is impossible to reason about the correctness of a program  Proving a program correct becomes important if software reliability is to improve  One response to this was strongly types OO languages (Java)  Another response is the creation of functional languages, where programs can be proven correct

Gary MarsdenSlide 8University of Cape Town How do we remove assignment?  One way to remove assignments (and therefore explicit state) is to make everything a function (even data values)  One can program “functionally” in imperative languages, but there is a temptation to the dark side  By making everything a function we can ensure that our program calculates using functions whose results can be determined through parameters alone – referential transparency

Gary MarsdenSlide 9University of Cape Town So can we keep variables?  Kind of – a variable should be thought of as an undefined constant  As a variable can never be altered through a direct assignment, the value of the variable can be taken as constant at any given point in the execution of a function  This has important consequences for serialisation and parallel tasks

Gary MarsdenSlide 10University of Cape Town Can functional languages be used for any program?  Yes!  You should be familiar with the notion of a Turing machine and Turing computability  Functional languages are based on - calculus  Church (who invented -calculus) and Turing managed to show that anything definable in -calculus was Turing computable

Gary MarsdenSlide 11University of Cape Town What is the catch  Functional languages have two main problems –Efficiency Underlying architectures optimised for imperative style Not as much experience in compiler technology –Coding inherently imperative tasks Highly interactive programs rely on a non-functional human Operating systems deal with machine hardware; i.e. state

Gary MarsdenSlide 12University of Cape Town Some terminology  Before we look at a functional program we need to learn some functional terms –A function maps values from a domain to a range –Independent values are taken from the domain and converted to a dependent value in the range  y = f(x) where –f: X  Y –y  {Y} (the range) –x  {X} (the domain)

Gary MarsdenSlide 13University of Cape Town Defining functions inc:: Int -> Int square x = x * x alwaysthree:: Int -> Int alwaysthree x = 3 Start:: Int Start = square 5 Points to note  First line is type definition of function  No ‘;’  Case sensitive  ‘main’ program

Gary MarsdenSlide 14University of Cape Town Evaluating functions  Before getting into Clean, it is worth considering how these programs are evaluated –Evaluation proceeds by re-writing the program to a reduced form –Each reduction is called a redex (reducible expression) –When there are no more redexs available, the program is in its simplest (normal) form and the result is printed out –This leads to a very recursive style of programming

Gary MarsdenSlide 15University of Cape Town Redex in action “ -> “ denotes a redex step square (1+2)-> (1+2) * (1+2) -> 3 * (1+2) -> 3 * 3 -> 9 (normal form) –In the second step, there was a choice about which bracket to evaluate –Choice does not matter as no side effects – parallel execution? –Order of evaluation is called the reduction strategy

Gary MarsdenSlide 16University of Cape Town Finding a result  There is one warning about evaluation order – some orders may result in no answer being found  Consider an infinitely recursive function (inf = inf)  What is the reduction of this call alwaysthree inf -> alwaysthree inf ->... or alwaysthree inf -> 3

Gary MarsdenSlide 17University of Cape Town Laziness  In some languages (e.g. ML), the parameters to a function are evaluated before the function body is executed –eager evaluation  In newer languages (like Clean) function parameters are only calculated when needed –lazy evaluation

Gary MarsdenSlide 18University of Cape Town Benefits of laziness  Lazy evaluation will always find a normal form, if it is possible to find one  Functions written in a lazy language can also deal with infinitely long lists (should this be needed) –this is a typical way to deal with user input

Gary MarsdenSlide 19University of Cape Town The ubiquitous factorial function  Calculating a factorial is the “hello world” for functional languages –probably because the algorithm is elegantly expressed recursively fac:: Int -> Int fac 0 = 1 fac n = n * fac (n-1) –Try redexing this by hand

Gary MarsdenSlide 20University of Cape Town What we can learn from fac  First off, it looks like we have two declarations of fac –In a sense we do. This is called pattern matching, where the most appropriate form of the function is used to evaluate the given parameter  There is a propagation part to the function, which includes a recursive call (the last line)  There is a termination line in the function (the line matching to 0)  Make sure there is always a termination clause!

Gary MarsdenSlide 21University of Cape Town Guards!  An alternative to pattern matching is the guard mechanisim  More flexible than pattern matching, but harder (perhaps) to read fac:: Int -> Int fac n |n == 0 = 1 = n * (n-1)

Gary MarsdenSlide 22University of Cape Town Data structures  Data structures in functional languages can only be read, once they have been created –remember no assignment (no destructive update)  There is no global state, so all structures must be passed as a parameter  Common to all functional languages is the list data structure (like a linked list)  Just as with arrays in imperative languages, list operators are built in to the language

Gary MarsdenSlide 23University of Cape Town List definition  Lists are ordered and can contain any data type, provided every element is of the same type  The list is built using a constructor (or cons) operation. In early languages, this was a prefix operator – more recent languages (including Clean) use the ‘:’ infix operator  Lists end with the ‘empty list’ or ‘Nil’ symbol – usually ‘[]’

Gary MarsdenSlide 24University of Cape Town List creation  Lists in Clean are conceptually like this:  And can be written as –1:(2:(3:[])) –1:2:3:[] –[1,2,3] – shorthand form, most popular 23:: 1: [ ]

Gary MarsdenSlide 25University of Cape Town List manipulation – head and tail  There are many functions which work on lists, but the most common are hd and tl hd:: [a] -> a hd [x:xs] -> x tl:: [a] -> [a] tl [x:xs] -> xs

Gary MarsdenSlide 26University of Cape Town Notes on hd and tl  The notation [a] is used to denote a list of some type ‘a’  Therefore, hd takes a list of ‘a’ and returns the first element from that list (that element being of type ‘a’)  tl takes a list of type ‘a’, removes the first element and returns the rest of the list  Note how we use the cons operator to pattern match

Gary MarsdenSlide 27University of Cape Town Sample list function  How would we write a length function?  Type length:: [a] -> Int  Code – Hint: think about termination first length [] = 0 length [x:xs] = 1 + length xs

Gary MarsdenSlide 28University of Cape Town Sorting  Quicksort is a recursive algorithm – can we write a functional language equivalent? qsort:: [Int] -> [Int] qsort [] = [] qsort [x:xs] =qsort(seq x xs)++[x]++qsort(gt x xs) seq:: Int [Int] -> [Int] seq a [] = [] seq a [x:xs] |x<=a = [x:seq a xs] = seq a xs gt:: Int [Int] -> [Int] gt a [] = [] gt a [x:xs] |x>a = [x:gt a xs] = gt a xs

Gary MarsdenSlide 29University of Cape Town Tuples  Besides lists, functional languages have the equivalent of records – i.e. Tuples  Tuples are denoted by normal brackets ( ) –(1,’a’):: (Int,Char) –(“hi”,True,2):: (String,Bool,Int) –([1,2],sqrt):: ([Int], Real->Real) –(1,(2,3)):: (Int,(Int,Int)) –[(1,’a’)]:: [(Int,Char)]  Actually, Clean has a Record type, where fields can be named

Gary MarsdenSlide 30University of Cape Town Higher order functions  The final thing to look at (for now) is sending functions as parameters: map:: (a->b) [a] -> [b] map f [] -> [] map f [x:xs] -> [f x: map f xs]  So, we can pass a function to map which it can apply to every element of the list

Gary MarsdenSlide 31University of Cape Town Applicative programming  Another name for functional programming is applicative programming  This idea is that you state the solution you want, not the means to calculate it (as in imperative programming)  Applicative languages are thought to be easier to use, so most 4GL’s are built in this way  The proponents of FL’s say they represent the highest level programming available

Gary MarsdenSlide 32University of Cape Town Some parting thoughts  These extracts are taken from a XEROX PARC paper on FL’s –“Even if they never become useful for real programmers, functional languages are useful objects of study. Functional languages are entirely mathematical, so the places where they don’t work show where computing is not mathematics and help to illuminate both fields.”James H. Morris