/* 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) 1999-2011, University of Amsterdam All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ :- 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).