Pure is a dynamically typed, functional programming language based on term rewriting. It has facilities for user-defined syntax, macros, multiple-precision numbers, and compilation to native code through the LLVM.
Pure comes with an interpreter and debugger, provides automatic memory management, and has powerful functional and symbolic programming capabilities as well as interface to C libraries (e.g. for numerics, low-level protocols, and other such tasks). At the same time, Pure is a "small" language designed from scratch; its interpreter is not large, and the library modules are written in Pure itself. The syntax of Pure resembles that of Miranda and Haskell, but it is a free-format language and thus uses explicit delimiters (rather than indentation) to indicate program structure.
The Pure language is a successor of the Q language created previously by the same author, Albert Gräf at the University of Mainz in Germany. Compared to Q, it offers some important new features (in particular, local functions, efficient vector and matrix support and the built-in C interface) and programs run much faster as they are JIT-compiled to native code on the fly. Pure is mostly aimed at mathematical applications and scientific computing right now, but its interactive interpreter environment, the C interface and the growing collection of addon modules make it suitable as a kind of functional scripting language for a variety of other applications, such as artificial intelligence, symbolic computation, and real-time multimedia processing.
Pure plugins are available for the Gnumeric spreadsheet and Miller Puckette's Pure Data graphical multimedia software, which make it possible to extend these programs with functions written in the Pure language.
Pure is free software distributed (mostly) under the GNU Lesser General Public License version 3 (or later).
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 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 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;
Symbolic computation example with local rule sets:
expand = reduce with (a+b)*c = a*c+b*c; a*(b+c) = a*b+a*c; end; factor = reduce with a*c+b*c = (a+b)*c; a*b+a*c = a*(b+c); end; /* Example: */ expand ((a+b)*2); // yields a*2+b*2 factor (a*2+b*2); // yields (a+b)*2
Calling C from Pure is very easy. E.g., the following imports the puts
function from the C library and uses it to print the string "Hello, world!"
on the terminal:
extern int puts(char*); hello = puts "Hello, world!"; hello;