/* Part of SWI-Prolog
Author: Jan Wielemaker
E-mail: J.Wielemaker@vu.nl
WWW: http://www.swi-prolog.org
Copyright (c) 2011-2015, VU University 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
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POSSIBILITY OF SUCH DAMAGE.
*/
:- module(arithmetic,
[ arithmetic_function/1, % +Name/Arity
arithmetic_expression_value/2 % :Expression, -Value
]).
:- autoload(library(error),[type_error/2]).
:- autoload(library(lists),[append/3]).
:- set_prolog_flag(generate_debug_info, false).
/** <module> Extensible arithmetic
This module provides a portable partial replacement of SWI-Prolog's
user-defined arithmetic (evaluable) functions. It defines the
compatibility directive arithmetic_function/1 and support for both
runtime and compile-time evaluation of expressions that are a mixture
between Prolog predicates used as functions and built-in evaluable
terms.
*/
:- meta_predicate
arithmetic_function(:),
arithmetic_expression_value(:, -).
:- multifile
evaluable/2. % Term, Module
%! arithmetic_function(:NameArity) is det.
%
% Declare a predicate as an arithmetic function.
%
% @deprecated This function provides a partial work around for
% pure Prolog user-defined arithmetic functions that has been
% dropped in SWI-Prolog 5.11.23. Notably, it only deals with
% expression know at compile time.
arithmetic_function(Term) :-
throw(error(context_error(nodirective, arithmetic_function(Term)), _)).
arith_decl_clauses(NameArity,
[(:- public(PI)),
arithmetic:evaluable(Term, Q)
]) :-
prolog_load_context(module, M),
strip_module(M:NameArity, Q, Spec),
( Q == M
-> PI = Name/ImplArity
; PI = Q:Name/ImplArity
),
( Spec = Name/Arity
-> functor(Term, Name, Arity),
ImplArity is Arity+1
; type_error(predicate_indicator, Term)
).
%! eval_clause(+Term, -Clause) is det.
%
% Clause is a clause for evaluating the arithmetic expression
% Term.
eval_clause(roundtoward(_,Round), (eval(Gen,M,Result) :- Body)) :-
!,
Gen = roundtoward(Arg,Round),
eval_args([Arg], [PlainArg], M, Goals,
[Result is roundtoward(PlainArg,Round)]),
list_conj(Goals, Body).
eval_clause(Term, (eval(Gen, M, Result) :- Body)) :-
functor(Term, Name, Arity),
functor(Gen, Name, Arity),
Gen =.. [_|Args],
eval_args(Args, PlainArgs, M, Goals, [Result is NewTerm]),
NewTerm =.. [Name|PlainArgs],
list_conj(Goals, Body).
eval_args([], [], _, Goals, Goals).
eval_args([E0|T0], [A0|T], M, [eval(E0, M, A0)|GT], RT) :-
eval_args(T0, T, M, GT, RT).
list_conj([One], One) :- !.
list_conj([H|T0], (H,T)) :-
list_conj(T0, T).
eval_clause(Clause) :-
current_arithmetic_function(Term),
eval_clause(Term, Clause).
term_expansion(eval('$builtin', _, _), Clauses) :-
findall(Clause, eval_clause(Clause), Clauses).
%! arithmetic_expression_value(:Expression, -Result) is det.
%
% True when Result unifies with the arithmetic result of
% evaluating Expression.
arithmetic_expression_value(M:Expression, Result) :-
eval(Expression, M, Result).
eval(Number, _, Result) :-
number(Number),
!,
Result = Number.
eval(Term, M, Result) :-
evaluable(Term, M2),
visible(M, M2),
!,
call(M2:Term, Result).
eval('$builtin', _, _).
visible(M, M) :- !.
visible(M, Super) :-
import_module(M, Parent),
visible(Parent, Super).
/*******************************
* COMPILE-TIME *
*******************************/
math_goal_expansion(A is Expr, Goal) :-
expand_function(Expr, Native, Pre),
tidy((Pre, A is Native), 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).
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(Expression, NativeExpression, Goal) :-
do_expand_function(Expression, NativeExpression, Goal0),
tidy(Goal0, Goal).
do_expand_function(X, X, true) :-
evaluable(X),
!.
do_expand_function(roundtoward(Expr0, Round),
roundtoward(Expr, Round),
ArgCode) :-
!,
do_expand_function(Expr0, Expr, ArgCode).
do_expand_function(Function, Result, ArgCode) :-
current_arithmetic_function(Function),
!,
Function =.. [Name|Args],
expand_function_arguments(Args, ArgResults, ArgCode),
Result =.. [Name|ArgResults].
do_expand_function(Function, Result, (ArgCode, Pred)) :-
prolog_load_context(module, M),
evaluable(Function, M2),
visible(M, M2),
!,
Function =.. [Name|Args],
expand_predicate_arguments(Args, ArgResults, ArgCode),
append(ArgResults, [Result], PredArgs),
Pred =.. [Name|PredArgs].
do_expand_function(Function, _, _) :-
type_error(evaluable, Function).
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),
( callable(H1),
current_arithmetic_function(H1)
-> A = (A0, H is H1)
; A = A0,
H = H1
),
expand_predicate_arguments(T0, T, B).
%! evaluable(F) is semidet.
%
% True if F and all its subterms are evaluable terms or variables.
evaluable(F) :-
var(F),
!.
evaluable(F) :-
number(F),
!.
evaluable([_Code]) :- !.
evaluable(Func) :- % Funtional notation.
functor(Func, ., 2),
!.
evaluable(F) :-
string(F),
!,
string_length(F, 1).
evaluable(roundtoward(F,_Round)) :-
!,
evaluable(F).
evaluable(F) :-
current_arithmetic_function(F),
( compound(F)
-> forall(arg(_,F,A), evaluable(A))
; true
).
%! tidy(+GoalIn, -GoalOut)
%
% Cleanup the output from expand_function/3.
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).
/*******************************
* EXPANSION HOOK *
*******************************/
:- multifile
system:term_expansion/2,
system:goal_expansion/2.
system:term_expansion((:- arithmetic_function(Term)), Clauses) :-
arith_decl_clauses(Term, Clauses).
system:goal_expansion(Math, MathGoal) :-
math_goal_expansion(Math, MathGoal).