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'''Pure''' is [[free software]] distributed under the [[GNU General Public License]] version 3.
==Examples==
The [[Fibonacci numbers]] (naive and inefficient algorithm):
fib 0 = 0;
fib 1 = 1;
fib n = fib (n-2) + fib (n-1) if n>1;
Better ([[tail-recursive]] and [[linear-time]]) version:
fib n = fibs (0,1) n with
fibs (a,b) n = if n<=0 then a else fibs (b,a+b) (n-1);
end;
Compute the first 20 Fibonacci numbers:
map fib (1..20);
A version of the [[sieve of Eratosthenes]] which computes the stream ([[Lazy evaluation|lazy]] [[List (computing)|list]]) of all [[prime numbers]]:
primes = sieve (2..inf) with
sieve (p:qs) = p : sieve [q | q = qs; q mod p] &;
end;
Algorithm for the [[Eight queens puzzle|n queens problem]] which employs a [[list comprehension]] to organize the backtracking search:
queens n = search n 1 [] with
search n i p = [reverse p] if i>n;
= cat [search n (i+1) ((i,j):p) | j = 1..n; safe (i,j) p];
safe (i,j) p = ~any (check (i,j)) p;
check (i1,j1) (i2,j2)
= i1==i2 || j1==j2 || i1+j1==i2+j2 || i1-j1==i2-j2;
end;
[[Gaussian elimination]] algorithm in Pure:
gauss_elimination x::matrix = p,x
when n,m = dim x; p,_,x = foldl step (0..n-1,0,x) (0..m-1) end;
step (p,i,x) j
= if max_x==0 then p,i,x else
// updated row permutation and index:
transp i max_i p, i+1,
{// the top rows of the matrix remain unchanged:
x!!(0..i-1,0..m-1);
// the pivot row, divided by the pivot element:
{x!(i,l)/x!(i,j) | l=0..m-1};
// subtract suitable multiples of the pivot row:
{x!(k,l)-x!(k,j)*x!(i,l)/x!(i,j) | k=i+1..n-1; l=0..m-1}}
when
n,m = dim x; max_i, max_x = pivot i (col x j);
x = if max_x>0 then swap x i max_i else x;
end with
pivot i x = foldl max (0,0) [j,abs (x!j)|j=i..#x-1];
max (i,x) (j,y) = if x<y then j,y else i,x;
end;
/* Swap rows i and j of the matrix x. */
swap x i j = x!!(transp i j (0..n-1),0..m-1) when n,m = dim x end;
/* Apply a transposition to a permutation. */
transp i j p = [p!tr k | k=0..#p-1]
with tr k = if k==i then j else if k==j then i else k end;
/* Example: */
let x = dmatrix {2,1,-1,8; -3,-1,2,-11; -2,1,2,-3};
x; gauss_elimination x;
Calling [[C (programming language)|C]] from Pure is very easy. E.g., the following imports the <code>puts</code> function from the C library and uses it to print the string <code>"Hello, world!"</code> on the terminal:
extern int puts(char*);
hello = puts "Hello, world!";
hello;
==External links==
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