% File : ASSOC.PL % Author : R.A.O'Keefe % Updated: 9 November 1983 % Purpose: Binary tree implementation of "association lists". % Note : the keys should be ground, the associated values need not be. /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Adapted for SWI-Prolog by Jan Wielemaker, January 2004. To the best of my knowledge, this file is in the public domain and can therefore safely be distributed with SWI-Prolog and used in applications without restrictions. Various versions of this file exists. This one is copied from the YAP library. The SICStus library contains one using AVL trees to ensure proper balancing. Although based on this library they changed the argument order of some of the predicates. Richard O'Keefe has told me he is working on a new version of this library. This new version, as it becomes available, is likely to replace this one. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Balancing code merged from L.Damas, V.S.Costa, AVL trees in YAP. Tree is either: *) empty (t/0) or *) t(Key,Value,Balance,Left,Right) Left,Right: trees Balance: <, -, or > denoting |L|-|R| = 1, 0, or -1, respectively TODO: get_next_assoc/4, get_prev_assoc/4 for SICStus compatibility */ /* Added del_assoc/4, del_min_assoc/4 and del_max_assoc/4 Ported by Glenn Burgess from a language called Pure. Jiri Spitz ported the Pure AVL library from this SWI-Prolog library, but the deletion code was added by Jiri. Full circle. Also added is_assoc/1, which makes testing much easier. */ :- 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, +Assoc, ?Old, ?NewAssoc, +New list_to_assoc/2, % +List, ?Assoc map_assoc/2, % :Goal, +Assoc map_assoc/3, % :Goal, +AssocIn, ?AssocOut max_assoc/3, % +Assoc, ?Key, ?Value min_assoc/3, % +Assoc, ?Key, ?Value ord_list_to_assoc/2, % +List, ?Assoc put_assoc/4, % +Key, +Assoc, +Value, ?NewAssoc del_assoc/4, % +Key, +Assoc, +Value, ?NewAssoc del_min_assoc/4, % +Assoc, ?Key, ?Value, ?NewAssoc del_max_assoc/4 % +Assoc, ?Key, ?Value, ?NewAssoc ]). :- use_module(library(error)). /** 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 @license Public domain */ :- meta_predicate map_assoc(1, ?), map_assoc(2, ?, ?). %% empty_assoc(-Assoc) is det. %% empty_assoc(+Assoc) is semidet. % % Is true if Assoc is the empty assoc. empty_assoc(t). %% assoc_to_list(+Assoc, -Pairs:list(Key-Value)) is semidet. % % Translate Assoc to a list of 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:ord_set) 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:list) 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) % % True if Assoc is an AVL-tree association list 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. % % @see get_assoc/3. 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 assoc. get_assoc(Key, Assoc, Val) :- must_be(assoc, Assoc), Assoc = t(K,V,_,L,R), 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). %% get_assoc(+Key, +AssocIn, +Val, -AssocOut, +NewVal) is semidet. % % True if Key-Val is in AssocIn and Key-NewVal is in AssocOut. 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(+List:list(Key-Value), -Assoc) is det. % % Create an assoc from a pair-list. % % @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(+List:list(Key-Value), -Assoc) is det. % % Create an assoc from an ordered pair-list without duplicate 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(+List:list(Key-Value)) 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, ?AssocIn, ?AssocOut) is semidet. % % True if for every Key, Pred(ValIn, ValOut) is true. 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. 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. 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, +AssocIn, +Value, -AssocOut) is det. % % Add Key-Value to AssocIn. If Key is already in AssocIn, the % associated value is replaced. 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(+AssocIn, ?Key, ?Val, -AssocOut) % % True if Key-Value is in AssocIn and Key is the smallest. % AssocOut is AssocIn with Key-Value removed. Warning: this will % succeed with no bindings for Key or Val if input Tree is t. del_min_assoc(Tree, Key, Val, NewTree) :- del_min_assoc(Tree, Key, Val, NewTree, _DepthChanged). del_min_assoc(t, _, _, t,no). 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(+AssocIn, ?Key, ?Val, -AssocOut) % % True if Key-Value is in AssocIn and Key is the greatest. % AssocOut is AssocIn with Key-Value removed. Warning: this will % succeed with no bindings for Key or Val if input Tree is t. del_max_assoc(Tree, Key, Val, NewTree) :- del_max_assoc(Tree, Key, Val, NewTree, _DepthChanged). del_max_assoc(t, _, _, t,no). 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, +AssocIn, ?Value, -AssocOut) % % True if Key-Value is in AssocIn. AssocOut is AssocOut with % Key-Value removed. del_assoc(Key, A0, Value, A) :- delete(A0, Key, Value, A, _). % delete(+Subtree, +SearchedKey, ?SearchedValue, ?SubtreeOut, ?WhatHasChanged) delete(t, _, _, t, no). % deletion from empty tree succeeds with no bindings 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) ).