/* Part of SWI-Prolog Author: Jan Wielemaker E-mail: J.Wielemaker@vu.nl WWW: http://www.swi-prolog.org Copyright (c) 2011-2016, 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 ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ :- module(varnumbers, [ numbervars/1, % +Term varnumbers/2, % +Term, -Copy max_var_number/3, % +Term, +Start, -Max varnumbers/3, % +Term, +No, -Copy varnumbers_names/3 % +Term, -Copy, -VariableNames ]). :- use_module(library(error)). :- use_module(library(assoc)). :- use_module(library(apply)). /** Utilities for numbered terms This library provides the inverse functionality of the built-in numbervars/3. Note that this library suffers from the known issues that '$VAR'(X) is a normal Prolog term and, -unlike the built-in numbervars-, the inverse predicates do _not_ process cyclic terms. The following predicate is true for any acyclic term that contains no '$VAR'(X), integer(X) terms and no constraint variables: == always_true(X) :- copy_term(X, X2), numbervars(X), varnumbers(X, Copy), Copy =@= X2. == @see numbervars/4, =@=/2 (variant/2). @compat This library was introduced by Quintus and available in many related implementations, although not with exactly the same set of predicates. */ %! numbervars(+Term) is det. % % Number variables in Term using $VAR(N). Equivalent to % numbervars(Term, 0, _). % % @see numbervars/3, numbervars/4 numbervars(Term) :- numbervars(Term, 0, _). %! varnumbers(+Term, -Copy) is det. % % Inverse of numbervars/1. Equivalent to varnumbers(Term, 0, % Copy). varnumbers(Term, Copy) :- varnumbers(Term, 0, Copy). %! varnumbers(+Term, +Start, -Copy) is det. % % Inverse of numbervars/3. True when Copy is a copy of Term with % all variables numbered >= Start consistently replaced by fresh % variables. Variables in Term are _shared_ with Copy rather than % replaced by fresh variables. % % @error domain_error(acyclic_term, Term) if Term is cyclic. % @compat Quintus, SICStus. Not in YAP version of this library varnumbers(Term, Min, Copy) :- must_be(acyclic, Term), MaxStart is Min-1, max_var_number(Term, MaxStart, Max), NVars is Max-MaxStart, ( NVars == 0 -> Copy = Term ; roundup_next_power_two(NVars, Len), functor(Vars, v, Len), varnumbers(Term, MaxStart, Vars, Copy) ). varnumbers(Var, _, _, Copy) :- var(Var), !, Copy = Var. varnumbers(Var, _, _, Copy) :- atomic(Var), !, Copy = Var. varnumbers('$VAR'(I), Min, Vars, Copy) :- integer(I), I > Min, !, Index is I-Min, arg(Index, Vars, Copy). varnumbers(Term, Min, Vars, Copy) :- functor(Term, Name, Arity), functor(Copy, Name, Arity), varnumbers_args(1, Arity, Term, Min, Vars, Copy). varnumbers_args(I, Arity, Term, Min, Vars, Copy) :- I =< Arity, !, arg(I, Term, AT), arg(I, Copy, CT), varnumbers(AT, Min, Vars, CT), I2 is I + 1, varnumbers_args(I2, Arity, Term, Min, Vars, Copy). varnumbers_args(_, _, _, _, _, _). %! roundup_next_power_two(+Int, -NextPower) is det. % % NextPower is I**2, such that NextPower >= Int. roundup_next_power_two(1, 1) :- !. roundup_next_power_two(N, L) :- L is 1<<(msb(N-1)+1). %! max_var_number(+Term, +Start, -Max) is det. % % True when Max is the max of Start and the highest numbered % $VAR(N) term. % % @author Vitor Santos Costa % @compat YAP max_var_number(V, Max, Max) :- var(V), !. max_var_number('$VAR'(I), Max0, Max) :- integer(I), !, Max is max(I,Max0). max_var_number(S, Max0, Max) :- functor(S, _, Ar), max_var_numberl(Ar, S, Max0, Max). max_var_numberl(0, _, Max, Max) :- !. max_var_numberl(I, T, Max0, Max) :- arg(I, T, Arg), I2 is I-1, max_var_number(Arg, Max0, Max1), max_var_numberl(I2, T, Max1, Max). %! varnumbers_names(+Term, -Copy, -VariableNames) is det. % % If Term is a term with numbered and named variables using the % reserved term '$VAR'(X), Copy is a copy of Term where each % '$VAR'(X) is consistently replaced by a fresh variable and % Bindings is a list `X = Var`, relating the `X` terms with the % variable it is mapped to. % % @see numbervars/3, varnumbers/3, read_term/3 using the % `variable_names` option. varnumbers_names(Term, Copy, Bindings) :- must_be(acyclic, Term), empty_assoc(Named), varnumbers_names(Term, Named, BindingAssoc, Copy), assoc_to_list(BindingAssoc, BindingPairs), maplist(pair_equals, BindingPairs, Bindings). pair_equals(N-V, N=V). varnumbers_names(Var, Bindings, Bindings, Copy) :- var(Var), !, Copy = Var. varnumbers_names(Var, Bindings, Bindings, Copy) :- atomic(Var), !, Copy = Var. varnumbers_names('$VAR'(Name), Bindings0, Bindings, Copy) :- !, ( get_assoc(Name, Bindings0, Copy) -> Bindings = Bindings0 ; put_assoc(Name, Bindings0, Copy, Bindings) ). varnumbers_names(Term, Bindings0, Bindings, Copy) :- functor(Term, Name, Arity), functor(Copy, Name, Arity), varnumbers_names_args(1, Arity, Term, Bindings0, Bindings, Copy). varnumbers_names_args(I, Arity, Term, Bindings0, Bindings, Copy) :- I =< Arity, !, arg(I, Term, AT), arg(I, Copy, CT), varnumbers_names(AT, Bindings0, Bindings1, CT), I2 is I + 1, varnumbers_names_args(I2, Arity, Term, Bindings1, Bindings, Copy). varnumbers_names_args(_, _, _, Bindings, Bindings, _).