assoc.pl

/*  Author:        R.A.O'Keefe, L.Damas, V.S.Costa, Glenn Burgess,
                   Jiri Spitz and Jan Wielemaker
    E-mail:        J.Wielemaker@vu.nl
    WWW:           http://www.swi-prolog.org
    Copyright (c)  2004-2018, various people and institutions
    All rights reserved.

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    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.

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       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
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:- module(assoc,
          [ empty_assoc/1,              % -Assoc
            is_assoc/1,                 % +Assoc
            assoc_to_list/2,            % +Assoc, -Pairs
            assoc_to_keys/2,            % +Assoc, -List
            assoc_to_values/2,          % +Assoc, -List
            gen_assoc/3,                % ?Key, +Assoc, ?Value
            get_assoc/3,                % +Key, +Assoc, ?Value
            get_assoc/5,                % +Key, +Assoc0, ?Val0, ?Assoc, ?Val
            list_to_assoc/2,            % +List, ?Assoc
            map_assoc/2,                % :Goal, +Assoc
            map_assoc/3,                % :Goal, +Assoc0, ?Assoc
            max_assoc/3,                % +Assoc, ?Key, ?Value
            min_assoc/3,                % +Assoc, ?Key, ?Value
            ord_list_to_assoc/2,        % +List, ?Assoc
            put_assoc/4,                % +Key, +Assoc0, +Value, ?Assoc
            del_assoc/4,                % +Key, +Assoc0, ?Value, ?Assoc
            del_min_assoc/4,            % +Assoc0, ?Key, ?Value, ?Assoc
            del_max_assoc/4             % +Assoc0, ?Key, ?Value, ?Assoc
          ]).

:- use_module(library(lists)).

/** <module> Binary associations

Assocs are Key-Value associations implemented as  a balanced binary tree
(AVL tree).

@see            library(pairs), library(rbtrees)
@author         R.A.O'Keefe, L.Damas, V.S.Costa and Jan Wielemaker
*/

/*
:- meta_predicate
    map_assoc(1, ?),
    map_assoc(2, ?, ?).
*/

%!  empty_assoc(?Assoc) is semidet.
%
%   Is true if Assoc is the empty association list.

empty_assoc(t).

%!  assoc_to_list(+Assoc, -Pairs) is det.
%
%   Translate Assoc to a list Pairs of Key-Value pairs.  The keys
%   in Pairs are sorted in ascending order.

assoc_to_list(Assoc, List) :-
    assoc_to_list(Assoc, List, []).

assoc_to_list(t(Key,Val,_,L,R), List, Rest) :-
    assoc_to_list(L, List, [Key-Val|More]),
    assoc_to_list(R, More, Rest).
assoc_to_list(t, List, List).


%!  assoc_to_keys(+Assoc, -Keys) is det.
%
%   True if Keys is the list of keys   in Assoc. The keys are sorted
%   in ascending order.

assoc_to_keys(Assoc, List) :-
    assoc_to_keys(Assoc, List, []).

assoc_to_keys(t(Key,_,_,L,R), List, Rest) :-
    assoc_to_keys(L, List, [Key|More]),
    assoc_to_keys(R, More, Rest).
assoc_to_keys(t, List, List).


%!  assoc_to_values(+Assoc, -Values) is det.
%
%   True if Values is the  list  of   values  in  Assoc.  Values are
%   ordered in ascending  order  of  the   key  to  which  they were
%   associated.  Values may contain duplicates.

assoc_to_values(Assoc, List) :-
    assoc_to_values(Assoc, List, []).

assoc_to_values(t(_,Value,_,L,R), List, Rest) :-
    assoc_to_values(L, List, [Value|More]),
    assoc_to_values(R, More, Rest).
assoc_to_values(t, List, List).

%!  is_assoc(+Assoc) is semidet.
%
%   True if Assoc is an association list. This predicate checks
%   that the structure is valid, elements are in order, and tree
%   is balanced to the extent guaranteed by AVL trees.  I.e.,
%   branches of each subtree differ in depth by at most 1.

is_assoc(Assoc) :-
    is_assoc(Assoc, _Min, _Max, _Depth).

is_assoc(t,X,X,0) :- !.
is_assoc(t(K,_,-,t,t),K,K,1) :- !, ground(K).
is_assoc(t(K,_,>,t,t(RK,_,-,t,t)),K,RK,2) :-
    % Ensure right side Key is 'greater' than K
    !, ground((K,RK)), K @< RK.

is_assoc(t(K,_,<,t(LK,_,-,t,t),t),LK,K,2) :-
    % Ensure left side Key is 'less' than K
    !, ground((LK,K)), LK @< K.

is_assoc(t(K,_,B,L,R),Min,Max,Depth) :-
    is_assoc(L,Min,LMax,LDepth),
    is_assoc(R,RMin,Max,RDepth),
    % Ensure Balance matches depth
    compare(Rel,RDepth,LDepth),
    balance(Rel,B),
    % Ensure ordering
    ground((LMax,K,RMin)),
    LMax @< K,
    K @< RMin,
    Depth is max(LDepth, RDepth)+1.

% Private lookup table matching comparison operators to Balance operators used in tree
balance(=,-).
balance(<,<).
balance(>,>).

%!  gen_assoc(?Key, +Assoc, ?Value) is nondet.
%
%   True if Key-Value is an association in Assoc. Enumerates keys in
%   ascending order on backtracking.
%
%   @see get_assoc/3.

gen_assoc(Key, Assoc, Value) :-
    (   ground(Key)
    ->  get_assoc(Key, Assoc, Value)
    ;   gen_assoc_(Key, Assoc, Value)
    ).

gen_assoc_(Key, t(_,_,_,L,_), Val) :-
    gen_assoc_(Key, L, Val).
gen_assoc_(Key, t(Key,Val,_,_,_), Val).
gen_assoc_(Key, t(_,_,_,_,R), Val) :-
    gen_assoc_(Key, R, Val).


%!  get_assoc(+Key, +Assoc, -Value) is semidet.
%
%   True if Key-Value is an association in Assoc.
%
%   @error type_error(assoc, Assoc) if Assoc is not an association list.

get_assoc(Key, Assoc, Val) :-
    must_be(assoc, Assoc),
    get_assoc_(Key, Assoc, Val).

/*
:- if(current_predicate('$btree_find_node'/5)).
get_assoc_(Key, Tree, Val) :-
    Tree \== t,
    '$btree_find_node'(Key, Tree, 0x010405, Node, =),
    arg(2, Node, Val).
:- else.
*/
get_assoc_(Key, t(K,V,_,L,R), Val) :-
    compare(Rel, Key, K),
    get_assoc(Rel, Key, V, L, R, Val).

get_assoc(=, _, Val, _, _, Val).
get_assoc(<, Key, _, Tree, _, Val) :-
    get_assoc(Key, Tree, Val).
get_assoc(>, Key, _, _, Tree, Val) :-
    get_assoc(Key, Tree, Val).
% :- endif.


%!  get_assoc(+Key, +Assoc0, ?Val0, ?Assoc, ?Val) is semidet.
%
%   True if Key-Val0 is in Assoc0 and Key-Val is in Assoc.

get_assoc(Key, t(K,V,B,L,R), Val, t(K,NV,B,NL,NR), NVal) :-
    compare(Rel, Key, K),
    get_assoc(Rel, Key, V, L, R, Val, NV, NL, NR, NVal).

get_assoc(=, _, Val, L, R, Val, NVal, L, R, NVal).
get_assoc(<, Key, V, L, R, Val, V, NL, R, NVal) :-
    get_assoc(Key, L, Val, NL, NVal).
get_assoc(>, Key, V, L, R, Val, V, L, NR, NVal) :-
    get_assoc(Key, R, Val, NR, NVal).


%!  list_to_assoc(+Pairs, -Assoc) is det.
%
%   Create an association from a list Pairs of Key-Value pairs. List
%   must not contain duplicate keys.
%
%   @error domain_error(unique_key_pairs, List) if List contains duplicate keys

list_to_assoc(List, Assoc) :-
    (  List = [] -> Assoc = t
    ;  keysort(List, Sorted),
           (  ord_pairs(Sorted)
           -> length(Sorted, N),
              list_to_assoc(N, Sorted, [], _, Assoc)
           ;  throw(error(domain_error(unique_key_pairs, List), list_to_assoc/2))
           )
    ).

list_to_assoc(1, [K-V|More], More, 1, t(K,V,-,t,t)) :- !.
list_to_assoc(2, [K1-V1,K2-V2|More], More, 2, t(K2,V2,<,t(K1,V1,-,t,t),t)) :- !.
list_to_assoc(N, List, More, Depth, t(K,V,Balance,L,R)) :-
    N0 is N - 1,
    RN is N0 div 2,
    Rem is N0 mod 2,
    LN is RN + Rem,
    list_to_assoc(LN, List, [K-V|Upper], LDepth, L),
    list_to_assoc(RN, Upper, More, RDepth, R),
    Depth is LDepth + 1,
    compare(B, RDepth, LDepth),
    balance(B, Balance).

%!  ord_list_to_assoc(+Pairs, -Assoc) is det.
%
%   Assoc is created from an ordered list Pairs of Key-Value
%   pairs. The pairs must occur in strictly ascending order of
%   their keys.
%
%   @error domain_error(key_ordered_pairs, List) if pairs are not ordered.

ord_list_to_assoc(Sorted, Assoc) :-
    (  Sorted = [] -> Assoc = t
    ;  (  ord_pairs(Sorted)
           -> length(Sorted, N),
              list_to_assoc(N, Sorted, [], _, Assoc)
           ;  domain_error(key_ordered_pairs, Sorted)
           )
    ).

%!  ord_pairs(+Pairs) is semidet
%
%   True if Pairs is a list of Key-Val pairs strictly ordered by key.

ord_pairs([K-_V|Rest]) :-
    ord_pairs(Rest, K).
ord_pairs([], _K).
ord_pairs([K-_V|Rest], K0) :-
    K0 @< K,
    ord_pairs(Rest, K).

%!  map_assoc(:Pred, +Assoc) is semidet.
%
%   True if Pred(Value) is true for all values in Assoc.

map_assoc(Pred, T) :-
    map_assoc_(T, Pred).

map_assoc_(t, _).
map_assoc_(t(_,Val,_,L,R), Pred) :-
    map_assoc_(L, Pred),
    call(Pred, Val),
    map_assoc_(R, Pred).

%!  map_assoc(:Pred, +Assoc0, ?Assoc) is semidet.
%
%   Map corresponding values. True if Assoc is Assoc0 with Pred
%   applied to all corresponding pairs of of values.

map_assoc(Pred, T0, T) :-
    map_assoc_(T0, Pred, T).

map_assoc_(t, _, t).
map_assoc_(t(Key,Val,B,L0,R0), Pred, t(Key,Ans,B,L1,R1)) :-
    map_assoc_(L0, Pred, L1),
    call(Pred, Val, Ans),
    map_assoc_(R0, Pred, R1).


%!  max_assoc(+Assoc, -Key, -Value) is semidet.
%
%   True if Key-Value is in Assoc and Key is the largest key.

max_assoc(t(K,V,_,_,R), Key, Val) :-
    max_assoc(R, K, V, Key, Val).

max_assoc(t, K, V, K, V).
max_assoc(t(K,V,_,_,R), _, _, Key, Val) :-
    max_assoc(R, K, V, Key, Val).


%!  min_assoc(+Assoc, -Key, -Value) is semidet.
%
%   True if Key-Value is in assoc and Key is the smallest key.

min_assoc(t(K,V,_,L,_), Key, Val) :-
    min_assoc(L, K, V, Key, Val).

min_assoc(t, K, V, K, V).
min_assoc(t(K,V,_,L,_), _, _, Key, Val) :-
    min_assoc(L, K, V, Key, Val).


%!  put_assoc(+Key, +Assoc0, +Value, -Assoc) is det.
%
%   Assoc is Assoc0, except that Key is associated with
%   Value. This can be used to insert and change associations.

put_assoc(Key, A0, Value, A) :-
    insert(A0, Key, Value, A, _).

insert(t, Key, Val, t(Key,Val,-,t,t), yes).
insert(t(Key,Val,B,L,R), K, V, NewTree, WhatHasChanged) :-
    compare(Rel, K, Key),
    insert(Rel, t(Key,Val,B,L,R), K, V, NewTree, WhatHasChanged).

insert(=, t(Key,_,B,L,R), _, V, t(Key,V,B,L,R), no).
insert(<, t(Key,Val,B,L,R), K, V, NewTree, WhatHasChanged) :-
    insert(L, K, V, NewL, LeftHasChanged),
    adjust(LeftHasChanged, t(Key,Val,B,NewL,R), left, NewTree, WhatHasChanged).
insert(>, t(Key,Val,B,L,R), K, V, NewTree, WhatHasChanged) :-
    insert(R, K, V, NewR, RightHasChanged),
    adjust(RightHasChanged, t(Key,Val,B,L,NewR), right, NewTree, WhatHasChanged).

adjust(no, Oldree, _, Oldree, no).
adjust(yes, t(Key,Val,B0,L,R), LoR, NewTree, WhatHasChanged) :-
    table(B0, LoR, B1, WhatHasChanged, ToBeRebalanced),
    rebalance(ToBeRebalanced, t(Key,Val,B0,L,R), B1, NewTree, _, _).

%     balance  where     balance  whole tree  to be
%     before   inserted  after    increased   rebalanced
table(-      , left    , <      , yes       , no    ) :- !.
table(-      , right   , >      , yes       , no    ) :- !.
table(<      , left    , -      , no        , yes   ) :- !.
table(<      , right   , -      , no        , no    ) :- !.
table(>      , left    , -      , no        , no    ) :- !.
table(>      , right   , -      , no        , yes   ) :- !.

%!  del_min_assoc(+Assoc0, ?Key, ?Val, -Assoc) is semidet.
%
%   True if Key-Value  is  in  Assoc0   and  Key  is  the smallest key.
%   Assoc is Assoc0 with Key-Value   removed. Warning: This will
%   succeed with _no_ bindings for Key or Val if Assoc0 is empty.

del_min_assoc(Tree, Key, Val, NewTree) :-
    del_min_assoc(Tree, Key, Val, NewTree, _DepthChanged).

del_min_assoc(t(Key,Val,_B,t,R), Key, Val, R, yes) :- !.
del_min_assoc(t(K,V,B,L,R), Key, Val, NewTree, Changed) :-
    del_min_assoc(L, Key, Val, NewL, LeftChanged),
    deladjust(LeftChanged, t(K,V,B,NewL,R), left, NewTree, Changed).

%!  del_max_assoc(+Assoc0, ?Key, ?Val, -Assoc) is semidet.
%
%   True if Key-Value  is  in  Assoc0   and  Key  is  the greatest key.
%   Assoc is Assoc0 with Key-Value   removed. Warning: This will
%   succeed with _no_ bindings for Key or Val if Assoc0 is empty.

del_max_assoc(Tree, Key, Val, NewTree) :-
    del_max_assoc(Tree, Key, Val, NewTree, _DepthChanged).

del_max_assoc(t(Key,Val,_B,L,t), Key, Val, L, yes) :- !.
del_max_assoc(t(K,V,B,L,R), Key, Val, NewTree, Changed) :-
    del_max_assoc(R, Key, Val, NewR, RightChanged),
    deladjust(RightChanged, t(K,V,B,L,NewR), right, NewTree, Changed).

%!  del_assoc(+Key, +Assoc0, ?Value, -Assoc) is semidet.
%
%   True if Key-Value is  in  Assoc0.   Assoc  is  Assoc0 with
%   Key-Value removed.

del_assoc(Key, A0, Value, A) :-
    delete(A0, Key, Value, A, _).

% delete(+Subtree, +SearchedKey, ?SearchedValue, ?SubtreeOut, ?WhatHasChanged)
delete(t(Key,Val,B,L,R), K, V, NewTree, WhatHasChanged) :-
    compare(Rel, K, Key),
    delete(Rel, t(Key,Val,B,L,R), K, V, NewTree, WhatHasChanged).

% delete(+KeySide, +Subtree, +SearchedKey, ?SearchedValue, ?SubtreeOut, ?WhatHasChanged)
% KeySide is an operator {<,=,>} indicating which branch should be searched for the key.
% WhatHasChanged {yes,no} indicates whether the NewTree has changed in depth.
delete(=, t(Key,Val,_B,t,R), Key, Val, R, yes) :- !.
delete(=, t(Key,Val,_B,L,t), Key, Val, L, yes) :- !.
delete(=, t(Key,Val,>,L,R), Key, Val, NewTree, WhatHasChanged) :-
    % Rh tree is deeper, so rotate from R to L
    del_min_assoc(R, K, V, NewR, RightHasChanged),
    deladjust(RightHasChanged, t(K,V,>,L,NewR), right, NewTree, WhatHasChanged),
    !.
delete(=, t(Key,Val,B,L,R), Key, Val, NewTree, WhatHasChanged) :-
    % Rh tree is not deeper, so rotate from L to R
    del_max_assoc(L, K, V, NewL, LeftHasChanged),
    deladjust(LeftHasChanged, t(K,V,B,NewL,R), left, NewTree, WhatHasChanged),
    !.

delete(<, t(Key,Val,B,L,R), K, V, NewTree, WhatHasChanged) :-
    delete(L, K, V, NewL, LeftHasChanged),
    deladjust(LeftHasChanged, t(Key,Val,B,NewL,R), left, NewTree, WhatHasChanged).
delete(>, t(Key,Val,B,L,R), K, V, NewTree, WhatHasChanged) :-
    delete(R, K, V, NewR, RightHasChanged),
    deladjust(RightHasChanged, t(Key,Val,B,L,NewR), right, NewTree, WhatHasChanged).

deladjust(no, OldTree, _, OldTree, no).
deladjust(yes, t(Key,Val,B0,L,R), LoR, NewTree, RealChange) :-
    deltable(B0, LoR, B1, WhatHasChanged, ToBeRebalanced),
    rebalance(ToBeRebalanced, t(Key,Val,B0,L,R), B1, NewTree, WhatHasChanged, RealChange).

%     balance  where     balance  whole tree  to be
%     before   deleted   after    changed   rebalanced
deltable(-      , right   , <      , no        , no    ) :- !.
deltable(-      , left    , >      , no        , no    ) :- !.
deltable(<      , right   , -      , yes       , yes   ) :- !.
deltable(<      , left    , -      , yes       , no    ) :- !.
deltable(>      , right   , -      , yes       , no    ) :- !.
deltable(>      , left    , -      , yes       , yes   ) :- !.
% It depends on the tree pattern in avl_geq whether it really decreases.

% Single and double tree rotations - these are common for insert and delete.
/* The patterns (>)-(>), (>)-( <), ( <)-( <) and ( <)-(>) on the LHS
   always change the tree height and these are the only patterns which can
   happen after an insertion. That's the reason why we can use a table only to
   decide the needed changes.

   The patterns (>)-( -) and ( <)-( -) do not change the tree height. After a
   deletion any pattern can occur and so we return yes or no as a flag of a
   height change.  */


rebalance(no, t(K,V,_,L,R), B, t(K,V,B,L,R), Changed, Changed).
rebalance(yes, OldTree, _, NewTree, _, RealChange) :-
    avl_geq(OldTree, NewTree, RealChange).

avl_geq(t(A,VA,>,Alpha,t(B,VB,>,Beta,Gamma)),
        t(B,VB,-,t(A,VA,-,Alpha,Beta),Gamma), yes) :- !.
avl_geq(t(A,VA,>,Alpha,t(B,VB,-,Beta,Gamma)),
        t(B,VB,<,t(A,VA,>,Alpha,Beta),Gamma), no) :- !.
avl_geq(t(B,VB,<,t(A,VA,<,Alpha,Beta),Gamma),
        t(A,VA,-,Alpha,t(B,VB,-,Beta,Gamma)), yes) :- !.
avl_geq(t(B,VB,<,t(A,VA,-,Alpha,Beta),Gamma),
        t(A,VA,>,Alpha,t(B,VB,<,Beta,Gamma)), no) :- !.
avl_geq(t(A,VA,>,Alpha,t(B,VB,<,t(X,VX,B1,Beta,Gamma),Delta)),
        t(X,VX,-,t(A,VA,B2,Alpha,Beta),t(B,VB,B3,Gamma,Delta)), yes) :-
    !,
    table2(B1, B2, B3).
avl_geq(t(B,VB,<,t(A,VA,>,Alpha,t(X,VX,B1,Beta,Gamma)),Delta),
        t(X,VX,-,t(A,VA,B2,Alpha,Beta),t(B,VB,B3,Gamma,Delta)), yes) :-
    !,
    table2(B1, B2, B3).

table2(< ,- ,> ).
table2(> ,< ,- ).
table2(- ,- ,- ).

must_be(assoc, X) :-
    (   X == t
    ->  true
    ;   compound(X),
        functor(X, t, 5)
    ), !.
must_be(assoc, X) :-
    throw(error(type_error(assoc, X), _)).