Right understanding about F# pre-computation logic - functional-programming

This question is extended from my previous question, about mutable value. I'm pretty sure that the main topic of this question, pre-computation has many things to do with the linked question.
Please see below examples, which I have brought from the book I'm studying with:
let isWord (words : string list) =
let wordTable = Set.ofList words // Expensive computation!
fun w -> wordTable.Contains(w)
val isWord : words:string list -> (string -> bool)
Which accept an string list, and returns function which checkes whether input string is in the list. With this tiny cute helper function, here are two examples:
let isCapital = isWord ["London"; "Paris"; "Warsaw"; "Tokyo"];;
val isCapital : (string -> bool)
let isCapitalSlow word = isWord ["London"; "Paris"; "Warsaw"; "Tokyo"] word
val isCapitalSlow : (string -> bool)
I thought these two function do excatly the same thing, but it was not the case. The book says while first one pre-computes the set from the given list, the second one will compute the set whenever the function has called.
As I learned in PL class, in order to evaluate a lambda calculus expression, every parameter should be given to the body. Lacking only one will not allow an expression to be evaulated.
Based on this, I've concluded that the first one has no parameter, so it can immidiately start evaluating when the list is given, but the second one can't start evaluating until parameter word is given. It's fine until here, but after thinking about it with the above linked question, I've become not sure whether I'm correctly understanding it or not.
Thinking from it and the answer of linked question, it seems like the evaluation continues until it becomes not able to evaluate, possibly because the lack of information, parameters, or anything. Then, is it OK to think that every situation-free part of expression will be evaluated only once and pre-computed, just like the first example?
It seems like this part may heavily affect to optimization and performance, so I want to make my understanding about this topic clear.

I've concluded that the first one has no parameter, so it can immidiately start evaluating when the list is given, but the second one can't start evaluating until parameter word is given.
This is exactly right.
It seems like the evaluation continues until it becomes not able to evaluate, possibly because the lack of information, parameters, or anything.
This is essentially also right, but it is simpler than your formulation make it sound. The "lack of information" is not something very sophisticated - it is simply the fact that lambda functions are values and cannot be evaluated until their parameters are specified.
It may be a bit easier to understand this if we rewrite everything using the fun x -> .. notation:
let isWord = fun (words : string list) =
let wordTable = Set.ofList words
fun w -> wordTable.Contains(w)
let isCapital =
isWord ["London"; "Paris"; "Warsaw"; "Tokyo"]
let isCapitalSlow = fun word ->
isWord ["London"; "Paris"; "Warsaw"; "Tokyo"] word
The evaluation proceeds from top to bottom.
The expression assigned to isWord is a function, so the body cannot be evaluated.
The expression assigned to isCapital is a function application, so it can be evaluated. This in turn evaluates the value of wordTable and returns a function - which is a function and cannot be evaluated.
The expression assigned to isCapitalSlow is a function and cannot be evaluated.
If you later call isCapitalSlow "Prague", this will be a function application and so it can be evaluated. It will then invoke isWord with a list of cities as an argument, which will, in turn, invoke Set.ofList to build wordTable and produce a function which is then evaluated with word as an argument.

Since you seem to be familiar with C#, we can rewrite this as a C# class:
class IsWord
{
HashSet<string> set;
public IsWord(string[] words) => set = new HashSet<string>(words);
public bool Contains(string word) => set.Contains(word);
}
What would the equivalent functions look like?
Func<string, bool> isCapital =
new IsWord(new[] { "London", "Paris", "Warsaw", "Tokyo" }).Contains;
Func<string, bool> isCapitalSlow =
(word) => new IsWord(new[] { "London", "Paris", "Warsaw", "Tokyo" }).Contains(word);
Note that isCapital creates an instance of the class once, and returns its contains method. So every time you call isCapital, you're actually only calling HashSet.Contains.
In isCapitalSlow you're creating an instance of IsWord, and in turn a HashSet every single time you call the method. This would naturally be slower.
In idiomatic F#, you would write this as:
let isWord words =
let wordTable = Set.ofList words
let contains word = wordTable |> Set.contains word
contains

Related

Hiding a System.Random instance by returning a function

The following code comes from Stylish F# 6: Crafting Elegant Functional Code for .NET 6 listing 9-13:
let randomByte =
let r = System.Random()
fun () ->
r.Next(0, 255) |> byte
// E.g. A3-52-31-D2-90-E6-6F-45-1C-3F-F2-9B-7F-58-34-44-
for _ in 0..15 do
printf "%X-" (randomByte())
printfn ""
The author states, "Although we call randomByte() multiple times, only one System.Random() instance is created."
I understand randomByte returns a function that does not create a System.Random() instance, but it seems to me multiple System.Random() instances would be created each time through the for-do-loop anyway.
I would appreciate an explanation of how multiple instances of System.Random() are not created in this case.
The key point is that randomByte is not a function. It's a value with some complex initialization logic. Like, for example, I could write:
let x = 5
Or I could write:
let x =
let fourtyTwo = 42
let thirtySeven = 37
fourtyTwo - thirtySeven
And these would be equivalent. Both declare a value named x and equal to 5. I hope you can see how the expression fourtyTwo - thirtySeven is evaluated only once, not every time somebody gets the value of x.
And so it works with randomByte too: it's a value with non-trivial initialization logic. During that value's initialization, first it creates an instance of System.Random, and then it creates an anonymous function that closes over that instance, and this anonymous function becomes the value of randomByte.

currying multiple functions in parallel in F#

I'm trying to learn F# at the moment and have come up on a problem I can't solve and can't find any answers for on google.
Initially I wanted a log function that would work like the printf family of functions whereby I could provide a format string and a number of arguments (statically checked) but which would add a little metadata before printing it out. With googling, I found this was possible using a function like the following:
let LogToConsole level (format:Printf.TextWriterFormat<'T>) =
let extendedFormat = (Printf.TextWriterFormat<string->string->'T> ("%s %s: " + format.Value))
let date = DateTime.UtcNow.ToString "yyyy-MM-dd HH:mm:ss.fff"
let lvl = string level
printfn extendedFormat date lvl
having the printfn function as the last line of this function allows the varargs-like magic of the printf syntax whereby the partially-applied printfn method is returned to allow the caller to finish applying arguments.
However, if I have multiple such functions with the same signature, say LogToConsole, LogToFile and others, how could I write a function that would call them all keeping this partial-application magic?
Essential I'm looking for how I could implement a function MultiLog
that would allow me to call multiple printf-like functions from a single function call Such as in the ResultIWant function below:
type LogFunction<'T> = LogLevel -> Printf.TextWriterFormat<'T> -> 'T
let MultiLog<'T> (loggers:LogFunction<'T>[]) level (format:Printf.TextWriterFormat<'T>) :'T =
loggers
|> Seq.map (fun f -> f level format)
|> ?????????
let TheResultIWant =
let MyLog = MultiLog [LogToConsole; LogToFile]
MyLog INFO "Text written to %i outputs" 2
Perhaps the essence of this question can be caught more succintly: given a list of functions of the same signature how can I partially apply them all with the same arguments?
type ThreeArg = string -> int -> bool -> unit
let funcs: ThreeArg seq = [func1; func2; func3]
let MagicFunction = ?????
// I'd like this to be valid
let partiallyApplied = MagicFunction funcs "string"
// I'd also like this to be valid
let partiallyApplied = MagicFunction funcs "string" 255
// and this (fullyApplied will be `unit`)
let fullyApplied = MagicFunction funcs "string" 255 true
To answer the specific part of the question regarding string formatting, there is a useful function Printf.kprintf which lets you do what you need in a very simple way - the first parameter of the function is a continuation that gets called with the formatted string as an argument. In this continuation, you can just take the formatted string and write it to all the loggers you want. Here is a basic example:
let Loggers = [printfn "%s"]
let LogEverywhere level format =
Printf.kprintf (fun s ->
let date = DateTime.UtcNow.ToString "yyyy-MM-dd HH:mm:ss.fff"
let lvl = string level
for logger in Loggers do logger (sprintf "%s %s %s" date lvl s)) format
LogEverywhere "BAD" "hi %d" 42
I don't think there is a nice and simple way to do what you wanted to do in the more general case - I suspect you might be able to use some reflection or static member constraints magic, but fortunately, you don't need to in this case!
There is almost nothing to add to a perfect #TomasPetricek answer as he is basically a "semi-god" in F#. Another alternative, which comes to mind, is to use a computation expression (see, for example: https://fsharpforfunandprofit.com/series/computation-expressions.html). When used properly it does look like magic :) However, I have a feeling that it is a little bit too heavy for the problem, which you described.

In functional programming, can a function call another function that was declared outside of it's scope and not passed as a parameter?

Does using a function declared outside the scope of the function it is being used in violate a Functional principle like immutability? Or is that referring specifically to data like arrays, strings, etc.
For example:
var data ["cat", "dog", "bird"];
function doThing (val) {
return val + ", go away!"
}
function alterData (data) {
return data.map(doThing);
}
alterData(data);
Would the above code be acceptable? or would the "doThing" function need to be passed into the alterData function as an argument?
The reason I am confused is because in Functional Programming examples I often see functions native to the language being used without being first passed to the function. However, the examples are never complicated enough to show how one would work with a library of functions.
Regards
Functional programming is no different from procedural in that regard—you write definitions that you can reuse anywhere that they are in scope. You control what's in scope where with a variety of mechanisms, for example with module definitions, module export lists and module imports. So for example (in Haskell):
module My.Module
-- List of definitions exported from this module
( doThing
, alterData
) where
-- Any definitions exported from `My.Other.Module` will be in scope
-- in this one
import My.Other.Module
-- Can't name this `data` because it's a reserved word in Haskell
yourData :: [String]
yourData = ["cat", "dog", "bird"]
doThing :: String -> String
doThing val = val ++ ", go away!"
alterData :: [String] -> [String]
alterData strings = map doThings strings
TL;DR
It's fine to rely on scoping in FP code.
Immutability means that something represented by a name can't change its value. I wouldn't call it a "principle" of functional programming, though.
Anyway, this is not related to scoping at all. Passing things as arguments makes sense if you want to parametrize a function over another function - essentially making it a Higher-Order function. A good example of such is fold (also known as reduce) - but map is also one.
In your case alterData function isn't adding much value, though. mapping something over something is so common, that it's typically better to provide only the one-element function, as it's fundamentally more reusable.
If you've passed doThing to alterData, you'd make that function essentially useless; why would I use it, if I could simply use map? However, packing the operation together with the mapping can sometimes be an useful abstraction.
It is fine have doThing the way it is.
You need to do this :
var data = ["cat", "dog", "bird"];
var doThing = function (val) {
return val + ", go away!"
}
function alterData (data) {
return data.map(doThing);
}
alterData(data);

Pulling out a column in all records in a Sqlite table into a concatenated string in Haskell with Persist

I'm trying to learn Haskell, specifically Snap, Blaze HTML5 and Persist. I would like to take every row in a table, select a single column from it, and then concatenate the values into a single string.
I've previously worked with C#'s LINQ quite extensively and under Entity Framework I could do it like this:
String.Join(", ", dbContext.People.Select(p => p.Name));
This would compile down to SELECT Name FROM People, with C# then concatenating those rows into a string with ", " in between.
To try and get the concatenation part right, I put this together, which seems to work:
intercalate ", " $ map show [1..10]
(it counts 1-9, concatenates with ", " in between the items)
However, I can't get this to work with Database.Persist.Sqlite. I'm not sure I quite understand the syntax here in Haskell. To contact the DB and retrieve the rows, I have to call: (as far as I understand)
runSqlite "TestDB" $ selectList ([] :: [Filter Person]) [] 0 0
The problem is that I'm not sure how to get the list out of runSqlite. runSqlite doesn't return the type I'm after, so I can't use the return value of runSqlite. How would I do this?
Thank you for reading.
To clarify:
Snap requires that I define a function to return the HTML I wish to send back to the client making the HTTP request. This means that:
page = runSqlite "TestDB" $ do
{pull data from the DB)
Is no-go as I can't return the data via the runSqlite call, and as far as I know I can't have a variable in the page function which is set within the runSqlite do block. All examples I can find just write to IO in the runSqlite do block, which is not what needs to be done here.
The type of runSqlite is:
runSqlite :: (MonadBaseControl IO m, MonadIO m) => Text -> SqlPersistT (NoLoggingT (ResourceT m)) a -> m a
And the type of selectList is:
[Filter val] -> [SelectOpt val] -> m [Entity val]
So, you can actually, use the nice do notation of Monad, to extract it:
runSqlite "TestDB" $ do
myData <- selectList ([] :: [Filter Person]) [] 0 0
-- Now do stuff with myData
The <- thing gets the list out of the monad. I would suggest you to go through this chapter to get an idea of how Persistent is used. Note that the chapters in the book assume a basic Haskell understanding.
The issue is that I want to use the selectList outside of runSqlite as
I need to pass the concatenated string to a Blaze HTML5 tag builder:
body $ do p (concatenated list...)
For this case, just define a function that does your intended task:
myLogic :: [SqlColumnData] -> String -- Note that SqlColumnData is hypothetical
myLogic xs = undefined
And then just call them appropriately in your main function:
main = runSqlite "TestDB" $ do
myData <- selectList ([] :: [Filter Person]) [] 0 0
let string = myLogic myData
-- do any other remaining stuff
It hadn't clicked that if I didn't use a do block with runSqlite, the result of the last call in the statement was the return value of the statement - this makes total sense.
https://gist.github.com/egonSchiele/5400694
In this example (not mine) the readPosts function does exactly what I'm after and cleared up some Haskell syntax confusion.
Thank you for your help #Sibi.

What is 'Pattern Matching' in functional languages?

I'm reading about functional programming and I've noticed that Pattern Matching is mentioned in many articles as one of the core features of functional languages.
Can someone explain for a Java/C++/JavaScript developer what does it mean?
Understanding pattern matching requires explaining three parts:
Algebraic data types.
What pattern matching is
Why its awesome.
Algebraic data types in a nutshell
ML-like functional languages allow you define simple data types called "disjoint unions" or "algebraic data types". These data structures are simple containers, and can be recursively defined. For example:
type 'a list =
| Nil
| Cons of 'a * 'a list
defines a stack-like data structure. Think of it as equivalent to this C#:
public abstract class List<T>
{
public class Nil : List<T> { }
public class Cons : List<T>
{
public readonly T Item1;
public readonly List<T> Item2;
public Cons(T item1, List<T> item2)
{
this.Item1 = item1;
this.Item2 = item2;
}
}
}
So, the Cons and Nil identifiers define simple a simple class, where the of x * y * z * ... defines a constructor and some data types. The parameters to the constructor are unnamed, they're identified by position and data type.
You create instances of your a list class as such:
let x = Cons(1, Cons(2, Cons(3, Cons(4, Nil))))
Which is the same as:
Stack<int> x = new Cons(1, new Cons(2, new Cons(3, new Cons(4, new Nil()))));
Pattern matching in a nutshell
Pattern matching is a kind of type-testing. So let's say we created a stack object like the one above, we can implement methods to peek and pop the stack as follows:
let peek s =
match s with
| Cons(hd, tl) -> hd
| Nil -> failwith "Empty stack"
let pop s =
match s with
| Cons(hd, tl) -> tl
| Nil -> failwith "Empty stack"
The methods above are equivalent (although not implemented as such) to the following C#:
public static T Peek<T>(Stack<T> s)
{
if (s is Stack<T>.Cons)
{
T hd = ((Stack<T>.Cons)s).Item1;
Stack<T> tl = ((Stack<T>.Cons)s).Item2;
return hd;
}
else if (s is Stack<T>.Nil)
throw new Exception("Empty stack");
else
throw new MatchFailureException();
}
public static Stack<T> Pop<T>(Stack<T> s)
{
if (s is Stack<T>.Cons)
{
T hd = ((Stack<T>.Cons)s).Item1;
Stack<T> tl = ((Stack<T>.Cons)s).Item2;
return tl;
}
else if (s is Stack<T>.Nil)
throw new Exception("Empty stack");
else
throw new MatchFailureException();
}
(Almost always, ML languages implement pattern matching without run-time type-tests or casts, so the C# code is somewhat deceptive. Let's brush implementation details aside with some hand-waving please :) )
Data structure decomposition in a nutshell
Ok, let's go back to the peek method:
let peek s =
match s with
| Cons(hd, tl) -> hd
| Nil -> failwith "Empty stack"
The trick is understanding that the hd and tl identifiers are variables (errm... since they're immutable, they're not really "variables", but "values" ;) ). If s has the type Cons, then we're going to pull out its values out of the constructor and bind them to variables named hd and tl.
Pattern matching is useful because it lets us decompose a data structure by its shape instead of its contents. So imagine if we define a binary tree as follows:
type 'a tree =
| Node of 'a tree * 'a * 'a tree
| Nil
We can define some tree rotations as follows:
let rotateLeft = function
| Node(a, p, Node(b, q, c)) -> Node(Node(a, p, b), q, c)
| x -> x
let rotateRight = function
| Node(Node(a, p, b), q, c) -> Node(a, p, Node(b, q, c))
| x -> x
(The let rotateRight = function constructor is syntax sugar for let rotateRight s = match s with ....)
So in addition to binding data structure to variables, we can also drill down into it. Let's say we have a node let x = Node(Nil, 1, Nil). If we call rotateLeft x, we test x against the first pattern, which fails to match because the right child has type Nil instead of Node. It'll move to the next pattern, x -> x, which will match any input and return it unmodified.
For comparison, we'd write the methods above in C# as:
public abstract class Tree<T>
{
public abstract U Match<U>(Func<U> nilFunc, Func<Tree<T>, T, Tree<T>, U> nodeFunc);
public class Nil : Tree<T>
{
public override U Match<U>(Func<U> nilFunc, Func<Tree<T>, T, Tree<T>, U> nodeFunc)
{
return nilFunc();
}
}
public class Node : Tree<T>
{
readonly Tree<T> Left;
readonly T Value;
readonly Tree<T> Right;
public Node(Tree<T> left, T value, Tree<T> right)
{
this.Left = left;
this.Value = value;
this.Right = right;
}
public override U Match<U>(Func<U> nilFunc, Func<Tree<T>, T, Tree<T>, U> nodeFunc)
{
return nodeFunc(Left, Value, Right);
}
}
public static Tree<T> RotateLeft(Tree<T> t)
{
return t.Match(
() => t,
(l, x, r) => r.Match(
() => t,
(rl, rx, rr) => new Node(new Node(l, x, rl), rx, rr))));
}
public static Tree<T> RotateRight(Tree<T> t)
{
return t.Match(
() => t,
(l, x, r) => l.Match(
() => t,
(ll, lx, lr) => new Node(ll, lx, new Node(lr, x, r))));
}
}
For seriously.
Pattern matching is awesome
You can implement something similar to pattern matching in C# using the visitor pattern, but its not nearly as flexible because you can't effectively decompose complex data structures. Moreover, if you are using pattern matching, the compiler will tell you if you left out a case. How awesome is that?
Think about how you'd implement similar functionality in C# or languages without pattern matching. Think about how you'd do it without test-tests and casts at runtime. Its certainly not hard, just cumbersome and bulky. And you don't have the compiler checking to make sure you've covered every case.
So pattern matching helps you decompose and navigate data structures in a very convenient, compact syntax, it enables the compiler to check the logic of your code, at least a little bit. It really is a killer feature.
Short answer: Pattern matching arises because functional languages treat the equals sign as an assertion of equivalence instead of assignment.
Long answer: Pattern matching is a form of dispatch based on the “shape” of the value that it's given. In a functional language, the datatypes that you define are usually what are known as discriminated unions or algebraic data types. For instance, what's a (linked) list? A linked list List of things of some type a is either the empty list Nil or some element of type a Consed onto a List a (a list of as). In Haskell (the functional language I'm most familiar with), we write this
data List a = Nil
| Cons a (List a)
All discriminated unions are defined this way: a single type has a fixed number of different ways to create it; the creators, like Nil and Cons here, are called constructors. This means that a value of the type List a could have been created with two different constructors—it could have two different shapes. So suppose we want to write a head function to get the first element of the list. In Haskell, we would write this as
-- `head` is a function from a `List a` to an `a`.
head :: List a -> a
-- An empty list has no first item, so we raise an error.
head Nil = error "empty list"
-- If we are given a `Cons`, we only want the first part; that's the list's head.
head (Cons h _) = h
Since List a values can be of two different kinds, we need to handle each one separately; this is the pattern matching. In head x, if x matches the pattern Nil, then we run the first case; if it matches the pattern Cons h _, we run the second.
Short answer, explained: I think one of the best ways to think about this behavior is by changing how you think of the equals sign. In the curly-bracket languages, by and large, = denotes assignment: a = b means “make a into b.” In a lot of functional languages, however, = denotes an assertion of equality: let Cons a (Cons b Nil) = frob x asserts that the thing on the left, Cons a (Cons b Nil), is equivalent to the thing on the right, frob x; in addition, all variables used on the left become visible. This is also what's happening with function arguments: we assert that the first argument looks like Nil, and if it doesn't, we keep checking.
It means that instead of writing
double f(int x, int y) {
if (y == 0) {
if (x == 0)
return NaN;
else if (x > 0)
return Infinity;
else
return -Infinity;
} else
return (double)x / y;
}
You can write
f(0, 0) = NaN;
f(x, 0) | x > 0 = Infinity;
| else = -Infinity;
f(x, y) = (double)x / y;
Hey, C++ supports pattern matching too.
static const int PositiveInfinity = -1;
static const int NegativeInfinity = -2;
static const int NaN = -3;
template <int x, int y> struct Divide {
enum { value = x / y };
};
template <bool x_gt_0> struct aux { enum { value = PositiveInfinity }; };
template <> struct aux<false> { enum { value = NegativeInfinity }; };
template <int x> struct Divide<x, 0> {
enum { value = aux<(x>0)>::value };
};
template <> struct Divide<0, 0> {
enum { value = NaN };
};
#include <cstdio>
int main () {
printf("%d %d %d %d\n", Divide<7,2>::value, Divide<1,0>::value, Divide<0,0>::value, Divide<-1,0>::value);
return 0;
};
Pattern matching is sort of like overloaded methods on steroids. The simplest case would be the same roughly the same as what you seen in java, arguments are a list of types with names. The correct method to call is based on the arguments passed in, and it doubles as an assignment of those arguments to the parameter name.
Patterns just go a step further, and can destructure the arguments passed in even further. It can also potentially use guards to actually match based on the value of the argument. To demonstrate, I'll pretend like JavaScript had pattern matching.
function foo(a,b,c){} //no pattern matching, just a list of arguments
function foo2([a],{prop1:d,prop2:e}, 35){} //invented pattern matching in JavaScript
In foo2, it expects a to be an array, it breaks apart the second argument, expecting an object with two props (prop1,prop2) and assigns the values of those properties to variables d and e, and then expects the third argument to be 35.
Unlike in JavaScript, languages with pattern matching usually allow multiple functions with the same name, but different patterns. In this way it is like method overloading. I'll give an example in erlang:
fibo(0) -> 0 ;
fibo(1) -> 1 ;
fibo(N) when N > 0 -> fibo(N-1) + fibo(N-2) .
Blur your eyes a little and you can imagine this in javascript. Something like this maybe:
function fibo(0){return 0;}
function fibo(1){return 1;}
function fibo(N) when N > 0 {return fibo(N-1) + fibo(N-2);}
Point being that when you call fibo, the implementation it uses is based on the arguments, but where Java is limited to types as the only means of overloading, pattern matching can do more.
Beyond function overloading as shown here, the same principle can be applied other places, such as case statements or destructuring assingments. JavaScript even has this in 1.7.
Pattern matching allows you to match a value (or an object) against some patterns to select a branch of the code. From the C++ point of view, it may sound a bit similar to the switch statement. In functional languages, pattern matching can be used for matching on standard primitive values such as integers. However, it is more useful for composed types.
First, let's demonstrate pattern matching on primitive values (using extended pseudo-C++ switch):
switch(num) {
case 1:
// runs this when num == 1
case n when n > 10:
// runs this when num > 10
case _:
// runs this for all other cases (underscore means 'match all')
}
The second use deals with functional data types such as tuples (which allow you to store multiple objects in a single value) and discriminated unions which allow you to create a type that can contain one of several options. This sounds a bit like enum except that each label can also carry some values. In a pseudo-C++ syntax:
enum Shape {
Rectangle of { int left, int top, int width, int height }
Circle of { int x, int y, int radius }
}
A value of type Shape can now contain either Rectangle with all the coordinates or a Circle with the center and the radius. Pattern matching allows you to write a function for working with the Shape type:
switch(shape) {
case Rectangle(l, t, w, h):
// declares variables l, t, w, h and assigns properties
// of the rectangle value to the new variables
case Circle(x, y, r):
// this branch is run for circles (properties are assigned to variables)
}
Finally, you can also use nested patterns that combine both of the features. For example, you could use Circle(0, 0, radius) to match for all shapes that have the center in the point [0, 0] and have any radius (the value of the radius will be assigned to the new variable radius).
This may sound a bit unfamiliar from the C++ point of view, but I hope that my pseudo-C++ make the explanation clear. Functional programming is based on quite different concepts, so it makes better sense in a functional language!
Pattern matching is where the interpreter for your language will pick a particular function based on the structure and content of the arguments you give it.
It is not only a functional language feature but is available for many different languages.
The first time I came across the idea was when I learned prolog where it is really central to the language.
e.g.
last([LastItem], LastItem).
last([Head|Tail], LastItem) :-
last(Tail, LastItem).
The above code will give the last item of a list. The input arg is the first and the result is the second.
If there is only one item in the list the interpreter will pick the first version and the second argument will be set to equal the first i.e. a value will be assigned to the result.
If the list has both a head and a tail the interpreter will pick the second version and recurse until it there is only one item left in the list.
For many people, picking up a new concept is easier if some easy examples are provided, so here we go:
Let's say you have a list of three integers, and wanted to add the first and the third element. Without pattern matching, you could do it like this (examples in Haskell):
Prelude> let is = [1,2,3]
Prelude> head is + is !! 2
4
Now, although this is a toy example, imagine we would like to bind the first and third integer to variables and sum them:
addFirstAndThird is =
let first = head is
third = is !! 3
in first + third
This extraction of values from a data structure is what pattern matching does. You basically "mirror" the structure of something, giving variables to bind for the places of interest:
addFirstAndThird [first,_,third] = first + third
When you call this function with [1,2,3] as its argument, [1,2,3] will be unified with [first,_,third], binding first to 1, third to 3 and discarding 2 (_ is a placeholder for things you don't care about).
Now, if you only wanted to match lists with 2 as the second element, you can do it like this:
addFirstAndThird [first,2,third] = first + third
This will only work for lists with 2 as their second element and throw an exception otherwise, because no definition for addFirstAndThird is given for non-matching lists.
Until now, we used pattern matching only for destructuring binding. Above that, you can give multiple definitions of the same function, where the first matching definition is used, thus, pattern matching is a little like "a switch statement on stereoids":
addFirstAndThird [first,2,third] = first + third
addFirstAndThird _ = 0
addFirstAndThird will happily add the first and third element of lists with 2 as their second element, and otherwise "fall through" and "return" 0. This "switch-like" functionality can not only be used in function definitions, e.g.:
Prelude> case [1,3,3] of [a,2,c] -> a+c; _ -> 0
0
Prelude> case [1,2,3] of [a,2,c] -> a+c; _ -> 0
4
Further, it is not restricted to lists, but can be used with other types as well, for example matching the Just and Nothing value constructors of the Maybe type in order to "unwrap" the value:
Prelude> case (Just 1) of (Just x) -> succ x; Nothing -> 0
2
Prelude> case Nothing of (Just x) -> succ x; Nothing -> 0
0
Sure, those were mere toy examples, and I did not even try to give a formal or exhaustive explanation, but they should suffice to grasp the basic concept.
You should start with the Wikipedia page that gives a pretty good explanation. Then, read the relevant chapter of the Haskell wikibook.
This is a nice definition from the above wikibook:
So pattern matching is a way of
assigning names to things (or binding
those names to those things), and
possibly breaking down expressions
into subexpressions at the same time
(as we did with the list in the
definition of map).
Here is a really short example that shows pattern matching usefulness:
Let's say you want to sort up an element in a list:
["Venice","Paris","New York","Amsterdam"]
to (I've sorted up "New York")
["Venice","New York","Paris","Amsterdam"]
in an more imperative language you would write:
function up(city, cities){
for(var i = 0; i < cities.length; i++){
if(cities[i] === city && i > 0){
var prev = cities[i-1];
cities[i-1] = city;
cities[i] = prev;
}
}
return cities;
}
In a functional language you would instead write:
let up list value =
match list with
| [] -> []
| previous::current::tail when current = value -> current::previous::tail
| current::tail -> current::(up tail value)
As you can see the pattern matched solution has less noise, you can clearly see what are the different cases and how easy it's to travel and de-structure our list.
I've written a more detailed blog post about it here.

Resources