1/*  Part of SWI-Prolog
    2
    3    Author:        Jan Wielemaker
    4    E-mail:        J.Wielemaker@vu.nl
    5    WWW:           http://www.swi-prolog.org
    6    Copyright (c) 2008-2025, University of Amsterdam,
    7                             VU University
    8                             SWI-Prolog Solutions b.v.
    9    Amsterdam All rights reserved.
   10
   11    Redistribution and use in source and binary forms, with or without
   12    modification, are permitted provided that the following conditions
   13    are met:
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   15    1. Redistributions of source code must retain the above copyright
   16       notice, this list of conditions and the following disclaimer.
   17
   18    2. Redistributions in binary form must reproduce the above copyright
   19       notice, this list of conditions and the following disclaimer in
   20       the documentation and/or other materials provided with the
   21       distribution.
   22
   23    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   24    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   25    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
   26    FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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   35*/
   36
   37:- module(terms,
   38          [ term_hash/2,                % @Term, -HashKey
   39            term_hash/4,                % @Term, +Depth, +Range, -HashKey
   40            term_size/2,                % @Term, -Size
   41            term_variables/2,           % @Term, -Variables
   42            term_variables/3,           % @Term, -Variables, +Tail
   43            variant/2,                  % @Term1, @Term2
   44            subsumes/2,                 % +Generic, @Specific
   45            subsumes_chk/2,             % +Generic, @Specific
   46            cyclic_term/1,              % @Term
   47            acyclic_term/1,             % @Term
   48            term_subsumer/3,            % +Special1, +Special2, -General
   49            term_factorized/3,          % +Term, -Skeleton, -Subsitution
   50            mapargs/3,                  % :Goal, ?Term1, ?Term2
   51            mapsubterms/3,              % :Goal, ?Term1, ?Term2
   52            mapsubterms_var/3,          % :Goal, ?Term1, ?Term2
   53            foldsubterms/4,             % :Goal, +Term, +State0, -State
   54            foldsubterms/5,             % :Goal, +Term1, ?Term2, +State0, -State
   55            same_functor/2,             % ?Term1, ?Term2
   56            same_functor/3,             % ?Term1, ?Term2, -Arity
   57            same_functor/4              % ?Term1, ?Term2, ?Name, ?Arity
   58          ]).   59
   60:- meta_predicate
   61    mapargs(2,?,?),
   62    mapsubterms(2,?,?),
   63    mapsubterms_var(2,?,?),
   64    foldsubterms(3,+,+,-),
   65    foldsubterms(4,+,?,+,-).   66
   67:- autoload(library(rbtrees),
   68	    [ rb_empty/1,
   69	      rb_lookup/3,
   70	      rb_insert/4,
   71	      rb_new/1,
   72	      rb_visit/2,
   73	      ord_list_to_rbtree/2,
   74	      rb_update/5
   75	    ]).   76:- autoload(library(error), [instantiation_error/1]).

 term_size(@Term, -Size) is det

True if Size is the size in cells occupied by Term on the global (term) stack. A cell is 8 bytes. The calculation does take sharing into account and handles cycles correctly. For example:

?- A = a(1,2,3), term_size(A,S).
S = 4.
?- A = a(1,2,3), term_size(a(A,A),S).
S = 7.
?- term_size(a(a(1,2,3), a(1,2,3)), S).
S = 11.

Note that small objects such as atoms and small integers have a size 0. Space is allocated for floats, large integers, strings and compound terms.

  108term_size(Term, Size) :-
  109    '$term_size'(Term, _, Size).

 variant(@Term1, @Term2) is semidet

Same as SWI-Prolog Term1 =@= Term2.

  115variant(X, Y) :-
  116    X =@= Y.

 subsumes_chk(@Generic, @Specific)

True if Generic can be made equivalent to Specific without changing Specific.

deprecated

- Replace by subsumes_term/2.

  125subsumes_chk(Generic, Specific) :-
  126    subsumes_term(Generic, Specific).

 subsumes(+Generic, @Specific)

True if Generic is unified to Specific without changing Specific.

deprecated

- It turns out that calls to this predicate almost always should have used subsumes_term/2. Also the name is misleading. In case this is really needed, one is adviced to follow subsumes_term/2 with an explicit unification.

  138subsumes(Generic, Specific) :-
  139    subsumes_term(Generic, Specific),
  140    Generic = Specific.

 term_subsumer(+Special1, +Special2, -General) is det

General is the most specific term that is a generalisation of Special1 and Special2. The implementation can handle cyclic terms.

author

- Inspired by LOGIC.PRO by Stephen Muggleton

Compatibility

- SICStus

  151%       It has been rewritten by  Jan   Wielemaker  to use the YAP-based
  152%       red-black-trees as mapping rather than flat  lists and use arg/3
  153%       to map compound terms rather than univ and lists.
  154
  155term_subsumer(S1, S2, G) :-
  156    cyclic_term(S1),
  157    cyclic_term(S2),
  158    !,
  159    rb_empty(Map),
  160    lgg_safe(S1, S2, G, Map, _).
  161term_subsumer(S1, S2, G) :-
  162    rb_empty(Map),
  163    lgg(S1, S2, G, Map, _).
  164
  165lgg(S1, S2, G, Map0, Map) :-
  166    (   S1 == S2
  167    ->  G = S1,
  168        Map = Map0
  169    ;   compound(S1),
  170        compound(S2),
  171        functor(S1, Name, Arity),
  172        functor(S2, Name, Arity)
  173    ->  functor(G, Name, Arity),
  174        lgg(0, Arity, S1, S2, G, Map0, Map)
  175    ;   rb_lookup(S1+S2, G0, Map0)
  176    ->  G = G0,
  177        Map = Map0
  178    ;   rb_insert(Map0, S1+S2, G, Map)
  179    ).
  180
  181lgg(Arity, Arity, _, _, _, Map, Map) :- !.
  182lgg(I0, Arity, S1, S2, G, Map0, Map) :-
  183    I is I0 + 1,
  184    arg(I, S1, Sa1),
  185    arg(I, S2, Sa2),
  186    arg(I, G, Ga),
  187    lgg(Sa1, Sa2, Ga, Map0, Map1),
  188    lgg(I, Arity, S1, S2, G, Map1, Map).

 lgg_safe(+S1, +S2, -G, +Map0, -Map) is det

Cycle-safe version of the above. The difference is that we insert compounds into the mapping table and check the mapping table before going into a compound.

  197lgg_safe(S1, S2, G, Map0, Map) :-
  198    (   S1 == S2
  199    ->  G = S1,
  200        Map = Map0
  201    ;   rb_lookup(S1+S2, G0, Map0)
  202    ->  G = G0,
  203        Map = Map0
  204    ;   compound(S1),
  205        compound(S2),
  206        functor(S1, Name, Arity),
  207        functor(S2, Name, Arity)
  208    ->  functor(G, Name, Arity),
  209        rb_insert(Map0, S1+S2, G, Map1),
  210        lgg_safe(0, Arity, S1, S2, G, Map1, Map)
  211    ;   rb_insert(Map0, S1+S2, G, Map)
  212    ).
  213
  214lgg_safe(Arity, Arity, _, _, _, Map, Map) :- !.
  215lgg_safe(I0, Arity, S1, S2, G, Map0, Map) :-
  216    I is I0 + 1,
  217    arg(I, S1, Sa1),
  218    arg(I, S2, Sa2),
  219    arg(I, G, Ga),
  220    lgg_safe(Sa1, Sa2, Ga, Map0, Map1),
  221    lgg_safe(I, Arity, S1, S2, G, Map1, Map).

 term_factorized(+Term, -Skeleton, -Substiution)

Is true when Skeleton is Term where all subterms that appear multiple times are replaced by a variable and Substitution is a list of Var=Value that provides the subterm at the location Var. I.e., After unifying all substitutions in Substiutions, Term == Skeleton. Term may be cyclic. For example:

?- X = a(X), term_factorized(b(X,X), Y, S).
Y = b(_G255, _G255),
S = [_G255=a(_G255)].

  238term_factorized(Term, Skeleton, Substitutions) :-
  239    rb_new(Map0),
  240    add_map(Term, Map0, Map),
  241    rb_visit(Map, Counts),
  242    common_terms(Counts, Common),
  243    (   Common == []
  244    ->  Skeleton = Term,
  245        Substitutions = []
  246    ;   ord_list_to_rbtree(Common, SubstAssoc),
  247        insert_vars(Term, Skeleton, SubstAssoc),
  248        mk_subst(Common, Substitutions, SubstAssoc)
  249    ).
  250
  251add_map(Term, Map0, Map) :-
  252    (   primitive(Term)
  253    ->  Map = Map0
  254    ;   rb_update(Map0, Term, Old, New, Map)
  255    ->  New is Old+1
  256    ;   rb_insert(Map0, Term, 1, Map1),
  257        assoc_arg_map(1, Term, Map1, Map)
  258    ).
  259
  260assoc_arg_map(I, Term, Map0, Map) :-
  261    arg(I, Term, Arg),
  262    !,
  263    add_map(Arg, Map0, Map1),
  264    I2 is I + 1,
  265    assoc_arg_map(I2, Term, Map1, Map).
  266assoc_arg_map(_, _, Map, Map).
  267
  268primitive(Term) :-
  269    var(Term),
  270    !.
  271primitive(Term) :-
  272    atomic(Term),
  273    !.
  274primitive('$VAR'(_)).
  275
  276common_terms([], []).
  277common_terms([H-Count|T], List) :-
  278    !,
  279    (   Count == 1
  280    ->  common_terms(T, List)
  281    ;   List = [H-_NewVar|Tail],
  282        common_terms(T, Tail)
  283    ).
  284
  285insert_vars(T0, T, _) :-
  286    primitive(T0),
  287    !,
  288    T = T0.
  289insert_vars(T0, T, Subst) :-
  290    rb_lookup(T0, S, Subst),
  291    !,
  292    T = S.
  293insert_vars(T0, T, Subst) :-
  294    functor(T0, Name, Arity),
  295    functor(T,  Name, Arity),
  296    insert_arg_vars(1, T0, T, Subst).
  297
  298insert_arg_vars(I, T0, T, Subst) :-
  299    arg(I, T0, A0),
  300    !,
  301    arg(I, T,  A),
  302    insert_vars(A0, A, Subst),
  303    I2 is I + 1,
  304    insert_arg_vars(I2, T0, T, Subst).
  305insert_arg_vars(_, _, _, _).
  306
  307mk_subst([], [], _).
  308mk_subst([Val0-Var|T0], [Var=Val|T], Subst) :-
  309    functor(Val0, Name, Arity),
  310    functor(Val,  Name, Arity),
  311    insert_arg_vars(1, Val0, Val, Subst),
  312    mk_subst(T0, T, Subst).

 mapargs(:Goal, ?Term1, ?Term2)

Term1 and Term2 have the same functor (name/arity) and for each matching pair of arguments call(Goal, A1, A2) is true.

  320mapargs(Goal, Term1, Term2) :-
  321    same_functor(Term1, Term2, Arity),
  322    mapargs_(1, Arity, Goal, Term1, Term2).
  323
  324mapargs_(I, Arity, Goal, Term1, Term2) :-
  325    I =< Arity,
  326    !,
  327    arg(I, Term1, A1),
  328    arg(I, Term2, A2),
  329    call(Goal, A1, A2),
  330    I2 is I+1,
  331    mapargs_(I2, Arity, Goal, Term1, Term2).
  332mapargs_(_, _, _, _, _).

 mapsubterms(:Goal, +Term1, -Term2) is det

 mapsubterms_var(:Goal, +Term1, -Term2) is det

Recursively map sub terms of Term1 into subterms of Term2 for every pair for which call(Goal, ST1, ST2) succeeds. Procedurably, the mapping for each (sub) term pair T1/T2 is defined as:

• If T1 is a variable
  • mapsubterms/3 unifies T2 with T1.
  • mapsubterms_var/3 treats variables as other terms.
• If call(Goal, T1, T2) succeeds we are done. Note that the mapping does not continue in T2. If this is desired, Goal must call mapsubterms/3 explicitly as part of its conversion.
• If T1 is a dict, map all values, i.e., the tag and keys are left untouched.
• If T1 is a list, map all elements, i.e., the list structure is left untouched.
• If T1 is a compound, use same_functor/3 to instantiate T2 and recurse over the term arguments left to right.
• Otherwise T2 is unified with T1.

Both predicates are implemented using foldsubterms/5.

  358mapsubterms(Goal, Term1, Term2) :-
  359    foldsubterms(map2(Goal), Term1, Term2, _, _).
  360mapsubterms_var(Goal, Term1, Term2) :-
  361    foldsubterms(map2_var(Goal), Term1, Term2, _, _).
  362
  363map2(Goal, Term1, Term2, _, _) :-
  364    nonvar(Term1),
  365    call(Goal, Term1, Term2).
  366
  367map2_var(Goal, Term1, Term2, _, _) :-
  368    call(Goal, Term1, Term2).

 foldsubterms(:Goal3, +Term1, +State0, -State) is semidet

 foldsubterms(:Goal4, +Term1, ?Term2, +State0, -State) is semidet

The predicate foldsubterms/5 calls call(Goal4, SubTerm1, SubTerm2, StateIn, StateOut) for each subterm, including variables, in Term1. If this call fails, StateIn and StateOut are the same. This predicate may be used to map subterms in a term while collecting state about the mapped subterms. The foldsubterms/4 variant does not map the term.

  380foldsubterms(Goal, Term1, State0, State) :-
  381    foldsubterms(fold1(Goal), Term1, _, State0, State).
  382
  383fold1(Goal, Term1, _Term2, State0, State) :-
  384    call(Goal, Term1, State0, State).
  385
  386foldsubterms(Goal, Term1, Term2, State0, State) :-
  387    call(Goal, Term1, Term2, State0, State),
  388    !.
  389foldsubterms(Goal, Term1, Term2, State0, State) :-
  390    is_dict(Term1),
  391    !,
  392    dict_pairs(Term1, Tag, Pairs1),
  393    fold_dict_pairs(Pairs1, Pairs2, Goal, State0, State),
  394    dict_pairs(Term2, Tag, Pairs2).
  395foldsubterms(Goal, Term1, Term2, State0, State) :-
  396    is_list(Term1),
  397    !,
  398    fold_some(Term1, Term2, Goal, State0, State).
  399foldsubterms(Goal, Term1, Term2, State0, State) :-
  400    compound(Term1),
  401    !,
  402    same_functor(Term1, Term2, Arity),
  403    foldsubterms_(1, Arity, Goal, Term1, Term2, State0, State).
  404foldsubterms(_, Term, Term, State, State).
  405
  406fold_dict_pairs([], [], _, State, State).
  407fold_dict_pairs([K-V0|T0], [K-V|T], Goal, State0, State) :-
  408    foldsubterms(Goal, V0, V, State0, State1),
  409    fold_dict_pairs(T0, T, Goal, State1, State).
  410
  411fold_some([], [], _, State, State).
  412fold_some([H0|T0], [H|T], Goal, State0, State) :-
  413    foldsubterms(Goal, H0, H, State0, State1),
  414    fold_some(T0, T, Goal, State1, State).
  415
  416foldsubterms_(I, Arity, Goal, Term1, Term2, State0, State) :-
  417    I =< Arity,
  418    !,
  419    arg(I, Term1, A1),
  420    arg(I, Term2, A2),
  421    foldsubterms(Goal, A1, A2, State0, State1),
  422    I2 is I+1,
  423    foldsubterms_(I2, Arity, Goal, Term1, Term2, State1, State).
  424foldsubterms_(_, _, _, _, _, State, State).

 same_functor(?Term1, ?Term2) is semidet

 same_functor(?Term1, ?Term2, -Arity) is semidet

 same_functor(?Term1, ?Term2, ?Name, ?Arity) is semidet

True when Term1 and Term2 are terms that have the same functor (Name/Arity). The arguments must be sufficiently instantiated, which means either Term1 or Term2 must be bound or both Name and Arity must be bound.

If Arity is 0, Term1 and Term2 are unified with Name for compatibility.

Compatibility

- SICStus

  441same_functor(Term1, Term2) :-
  442    same_functor(Term1, Term2, _Name, _Arity).
  443
  444same_functor(Term1, Term2, Arity) :-
  445    same_functor(Term1, Term2, _Name, Arity).
  446
  447same_functor(Term1, Term2, Name, Arity) :-
  448    (   nonvar(Term1)
  449    ->  functor(Term1, Name, Arity, Type),
  450        functor(Term2, Name, Arity, Type)
  451    ;   nonvar(Term2)
  452    ->  functor(Term2, Name, Arity, Type),
  453        functor(Term1, Name, Arity, Type)
  454    ;   functor(Term2, Name, Arity),
  455        functor(Term1, Name, Arity)
  456    )