/* $Id: expandmath.pl,v 1.3 2002/02/01 15:04:53 jan Exp $ Part of XPCE --- The SWI-Prolog GUI toolkit Author: Jan Wielemaker and Anjo Anjewierden E-mail: jan@swi.psy.uva.nl WWW: http://www.swi.psy.uva.nl/projects/xpce/ Copyright (C): 1985-2002, University of Amsterdam This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA As a special exception, if you link this library with other files, compiled with a Free Software compiler, to produce an executable, this library does not by itself cause the resulting executable to be covered by the GNU General Public License. This exception does not however invalidate any other reasons why the executable file might be covered by the GNU General Public License. */ :- module(expand_math, [expand_function/3]). :- use_module(expandgoal). :- require([ append/3 , genarg/3 ]). /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - This module cooperates with library(expandgoal), expanding mathematical expressions on systems that have limited math functions and that cannot define new math funtions. For each function f/n, it expects a predicate f/n+1, where the first n arguments are in the same order as the function, and the last is used for the return value. In ensures all arguments to the predicate are evaluated if they contain expressions. There are two configuration predicates: built_in(?Function) Says Function is a built-in mathematical function. It will not be converted, but its arguments will if they contain non-builtin functions. Numbers and variables are not converted either. math_alias(+Function, -Alias) Alows for alias definition. Some of these aliases are needed to call the right function (** --> pow for example). Some are used to expand mathematical constants (pi, e). Bugs: Only experssions appearing in the source-code as an argument to one of the math predicates is/2, =:=/2, =\=/2, >/2, =/2, = ExprB, Goal) :- expand_function(ExprA, NativeA, PreA), expand_function(ExprB, NativeB, PreB), tidy((PreA, PreB, NativeA > NativeB), Goal). math_goal_expansion(ExprA < ExprB, Goal) :- expand_function(ExprA, NativeA, PreA), expand_function(ExprB, NativeB, PreB), tidy((PreA, PreB, NativeA < NativeB), Goal). math_goal_expansion(ExprA >= ExprB, Goal) :- expand_function(ExprA, NativeA, PreA), expand_function(ExprB, NativeB, PreB), tidy((PreA, PreB, NativeA >= NativeB), Goal). math_goal_expansion(ExprA =< ExprB, Goal) :- expand_function(ExprA, NativeA, PreA), expand_function(ExprB, NativeB, PreB), tidy((PreA, PreB, NativeA =< NativeB), Goal). expand_function(_, _, _) :- % testing under SWI-Prolog prolog_load_context(module, quintus), !, fail. expand_function(Expression, NativeExpression, Goal) :- do_expand_function(Expression, NativeExpression, Goal0), tidy(Goal0, Goal). do_expand_function(X, X, true) :- all_builtin(X), !. do_expand_function(A0, X, Code) :- math_alias(A0, A), !, do_expand_function(A, X, Code). do_expand_function(Function, Result, ArgCode) :- built_in(Function), !, Function =.. [Name|Args], expand_function_arguments(Args, ArgResults, ArgCode), Result =.. [Name|ArgResults]. do_expand_function(Function, Result, (ArgCode, Pred)) :- Function =.. [Name|Args], expand_predicate_arguments(Args, ArgResults, ArgCode), append(ArgResults, [Result], PredArgs), Pred =.. [Name|PredArgs]. expand_function_arguments([], [], true). expand_function_arguments([H0|T0], [H|T], (A,B)) :- do_expand_function(H0, H, A), expand_function_arguments(T0, T, B). expand_predicate_arguments([], [], true). expand_predicate_arguments([H0|T0], [H|T], (A,B)) :- do_expand_function(H0, H1, A0), ( nonvar(H1), built_in(H1) -> A = (A0, H is H1) ; A = A0, H = H1 ), expand_predicate_arguments(T0, T, B). built_in(_+_). built_in(_-_). built_in(_*_). built_in(-_). built_in(+_). built_in(abs(_)). built_in(_/_). built_in(_//_). built_in(div(_,_)). built_in(mod(_,_)). built_in(\(_)). built_in(\(_,_)). built_in([_]). % "a" ... built_in(_/\_). built_in(_\/_). built_in(_>>_). built_in(_<<_). built_in(integer(_)). built_in(float(_)). built_in(max(_,_)). built_in(min(_,_)). all_builtin(F) :- var(F), !. all_builtin(F) :- number(F), !. all_builtin(F) :- built_in(F), \+ (genarg(_,F,A), \+ all_builtin(A)). math_alias(pi, 3.14159265358979323846). math_alias(e, 2.7182818284590452354). math_alias(atan(Y,X), atan2(Y,X)). math_alias(**(X,Y), pow(X,Y)). math_alias(X^Y, pow(X,Y)). math_alias(ceil(X), ceiling(X)). math_alias(random(M), random(0, M)). /******************************* * TIDY * *******************************/ tidy(A, A) :- var(A), !. tidy(((A,B),C), R) :- !, tidy((A,B,C), R). tidy((true,A), R) :- !, tidy(A, R). tidy((A,true), R) :- !, tidy(A, R). tidy((A, X is Y), R) :- var(X), var(Y), !, tidy(A, R), X = Y. tidy((A,B), (TA, TB)) :- !, tidy(A, TA), tidy(B, TB). tidy(A, A). /******************************* * THE HOOK * *******************************/ user:goal_expansion(A,B) :- expand_math:math_goal_expansion(A,B).