/* Part of SWI-Prolog 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. 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(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 ]). :- autoload(library(error),[must_be/2,domain_error/2]). /** Binary associations Assocs are Key-Value associations implemented as a balanced binary tree (AVL tree). __Warning: instantiation of keys__ AVL trees depend on the Prolog _standard order of terms_ to organize the keys as a (balanced) binary tree. This implies that any term may be used as a key. The tree may produce wrong results, such as not being able to find a key, if the ordering of keys changes after the key has been inserted into the tree. The user is responsible to ensure that variables used as keys or appearing in a term used as key that may affect ordering are not unified, with the exception of unification against new fresh variables. For this reason, _ground_ terms are safe keys. When using non-ground terms, either make sure the variables appear in places that do not affect the standard order relative to other keys in the tree or make sure to not unify against these variables as long as the tree is being used. @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. Does _not_ validate that keys are % sufficiently instantiated to ensure the tree remains valid if a key % is further instantiated. is_assoc(Assoc) :- nonvar(Assoc), is_assoc(Assoc, _Min, _Max, _Depth). is_assoc(t,X,X,0) :- !. is_assoc(t(K,_,-,t,t),K,K,1) :- !. is_assoc(t(K,_,>,t,t(RK,_,-,t,t)),K,RK,2) :- !, K @< RK. is_assoc(t(K,_,<,t(LK,_,-,t,t),t),LK,K,2) :- !, 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 LMax @< K, K @< RMin, Depth is max(LDepth, RDepth)+1. 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(Key0,Val0,_,L,R), Val) => gen_assoc_(Key, Key0,Val0,L,R, Val). gen_assoc_(_Key, t, _Val) => fail. gen_assoc_(Key, _,_,L,_, Val) :- gen_assoc_(Key, L, Val). gen_assoc_(Key, Key,Val0,_,_, Val) :- Val = Val0. gen_assoc_(Key, _,_,_,R, Val) :- gen_assoc_(Key, R, Val). %! get_assoc(+Key, +Assoc, -Value) is semidet. % % True if Key-Value is an association in Assoc. :- 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(_, t, _) => fail. 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, Assoc, NVal) => Assoc = t(K,NV,B,NL,NR), compare(Rel, Key, K), get_assoc(Rel, Key, V, L, R, Val, NV, NL, NR, NVal). get_assoc(_Key, t, _Val, _, _) => fail. 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, _) => true. 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, _, Assoc) => Assoc = t. map_assoc_(t(Key,Val,B,L0,R0), Pred, Assoc) => Assoc = 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, _, _) => fail. 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, _, _) => fail. 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, Assoc, Changed) => Assoc = t(Key,Val,-,t,t), Changed = 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(t, _, _, _, _) => fail. % 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), compound_name_arity(X, t, 5) ).