Pure (programming language): Difference between revisions

Revision as of 20:02, 6 January 2025

Revision as of 21:26, 6 January 2025

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Pure has efficient support for vectors and matrices (similar to that of [[MATLAB]] and [[GNU Octave]]), including vector and matrix comprehensions. E.g., a [[Gaussian elimination]] algorithm with [[partial pivoting]] can be implemented in Pure thus:

Namespaces, types and interfaces belong to the standard repertoire:

<syntaxhighlight lang="q">

nonfix nil;

gauss_elimination x::matrix = p,x

type bintree nil | bintree (bin x left right);

when n,m = dim x; p,_,x = foldl step (0..n-1,0,x) (0..m-1) end;

outfix « »;

namespace foo (« »);

infixr (::^) ^;

x^y = 2*x+y;

namespace;

interface stack with

step (p,i,x) j

push s::stack x;

= if max_x==0 then p,i,x else

pop s::stack;

// updated row permutation and index:

top s::stack;

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;

type stack [];

/* Swap rows i and j of the matrix x. */

push xs@[] x | push xs@(_:_) x = x:xs;

swap x i j = x!!(transp i j (0..n-1),0..m-1) when n,m = dim x end;

pop (x:xs) = xs;

top (x:xs) = x;

/* 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;

</syntaxhighlight>

As a language based on [[term rewriting]], Pure fully supports [[symbolic computation]] with expressions. Here is an example showing the use of local rewriting rules to [[polynomial expansion|expand]] and [[factorization|factor]] simple arithmetic expressions:

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hello;

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Instead of manually compiling source files to LLVM bitcode modules, one can also place the source code into a Pure script, enclosing it in %< ... %> (inline code, e.g. C, Fortran 77/90 and so on).

==See also==