/* Part of SWI-Prolog
*/
:- 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).
%2
assoc_to_list2(Assoc, List) :-
assoc_to_list2(Assoc, List, []).
assoc_to_list2(t(Key,Val,_,L,R), List, Rest) :-
assoc_to_list2(L, List, [fc_Pair(Key,Val)|More]),
assoc_to_list2(R, More, Rest).
assoc_to_list2(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)
; domain_error(unique_key_pairs, List)
)
).
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(- ,- ,- ).
/*******************************
* ERRORS *
*******************************/
:- multifile
error:has_type/2.
error:has_type(assoc, X) :-
( X == t
-> true
; compound(X),
functor(X, t, 5)
).