## 4.14 Database

SWI-Prolog offers several ways to store data in globally accessible memory, i.e., outside the Prolog stacks. Data stored this way notably does not change on backtracking. Typically it is a bad idea to use any of the predicates in this section for realising global variables that can be assigned to. Typically, first consider representing data processed by your program as terms passed around as predicate arguments. If you need to reason over multiple solutions to a goal, consider findall/3, aggregate/3 and related predicates.

Nevertheless, there are scenarios where storing data outside the Prolog stacks is a good option. Below are the main options for storing data:

Using dynamic predicates
  Dynamic predicates are predicates for which the list of clauses is modified at runtime using asserta/1, assertz/1, retract/1 or retractall/1. Following the ISO standard, predicates that are modified this way need to be declared using the dynamic/1 directive. These facilities are defined by the ISO standard and widely supported. The mechanism is often considered slow in the literature. Performance depends on the Prolog implementation. In SWI-Prolog, querying dynamic predicates has the same performance as static ones. The manipulation predicates are fast. Using retract/1 or retractall/1 on a predicate registers the predicate as‘dirty’. Dirty predicates are cleaned by garbage_collect_clauses/0, which is normally automatically invoked. Some workloads may result in significant performance reduction due to skipping retracted clauses and/or clause garbage collection.

  Dynamic predicates can be wrapped using library `library(persistency)` to maintain a backup of the data on disk. Dynamic predicates come in two flavours, shared between threads and local to each thread. The latter version is created using the directive thread_local/1.

The recorded database
  The‘recorded database’registers a list of terms with a key, an atom or compound term. The list is managed using recorda/3, recordz/3 and erase/1. It is queried using recorded/3. The recorded database is not part of the ISO standard but fairly widely supported, notably in implementations building on the‘Edinburgh tradition’. There are few reasons to use this database in SWI-Prolog due to the good performance of dynamic predicates. Advantages are (1) the handle provides a direct reference to a term, (2) cyclic terms can be stored and (3) attributes (section 8.1) are preserved. Disadvantages are (1) the terms in a list associated with a key are not indexed, (2) the poorly specified immediate update semantics (see section 4.14.1.1 applies to the recorded database and (3) reduced portability.
The flag/3 predicate
  The predicate flag/3 associates one simple value (number or atom) with a key (atom, integer or compound). It is an old SWI-Prolog specific predicate that should be considered deprecated, although there is no plan to remove it.
Using global variables
  The predicates b_setval/2 and nb_setval/2 associate a term living on the Prolog stack with a name, either backtrackable or non-backtrackable. Backtrackable and non-backtrackable assignment without using a global name can be realised with setarg/3 and nb_setarg/3. Notably the latter are used to realise aggregation as e.g., aggregate_all/3 performs.
Tries
  As of version 7.3.21, SWI-Prolog provides tries (prefix trees) to associate a term variant with a value. Tries have been introduced to support tabling and are described in section 4.14.4.

### 4.14.1 Managing (dynamic) predicates

[ISO]abolish(:PredicateIndicator)
  Removes all clauses of a predicate with functor Functor and arity Arity from the database. All predicate attributes (dynamic, multifile, index, etc.) are reset to their defaults. Abolishing an imported predicate only removes the import link; the predicate will keep its old definition in its definition module.

  According to the ISO standard, abolish/1 can only be applied to dynamic procedures. This is odd, as for dealing with dynamic procedures there is already retract/1 and retractall/1. The abolish/1 predicate was introduced in DEC-10 Prolog precisely for dealing with static procedures. In SWI-Prolog, abolish/1 works on static procedures, unless the Prolog flag iso is set to `true`.

  It is advised to use retractall/1 for erasing all clauses of a dynamic predicate.

abolish(+Name, +Arity)
  Same as `abolish(Name/Arity)`. The predicate abolish/2 conforms to the Edinburgh standard, while abolish/1 is ISO compliant.
copy_predicate_clauses(:From, :To)
  Copy all clauses of predicate From to To. The predicate To must be dynamic or undefined. If To is undefined, it is created as a dynamic predicate holding a copy of the clauses of From. If To is a dynamic predicate, the clauses of From are added (as in assertz/1) to the clauses of To. To and From must have the same arity. Acts as if defined by the program below, but at a much better performance by avoiding decompilation and compilation.

      copy_predicate_clauses(From, To) :-
              head(From, MF:FromHead),
              head(To, MT:ToHead),
              FromHead =.. [_|Args],
              ToHead =.. [_|Args],
              forall(clause(MF:FromHead, Body),
                     assertz(MT:ToHead, Body)).

      head(From, M:Head) :-
              strip_module(From, M, Name/Arity),
              functor(Head, Name, Arity).

redefine_system_predicate(+Head)
  This directive may be used both in module `user` and in normal modules to redefine any system predicate. If the system definition is redefined in module `user`, the new definition is the default definition for all sub-modules. Otherwise the redefinition is local to the module. The system definition remains in the module `system`.

  Redefining system predicate facilitates the definition of compatibility packages. Use in other contexts is discouraged.

[ISO,nondet]retract(+Term)
  When Term is an atom or a term it is unified with the first unifying fact or clause in the database. The fact or clause is removed from the database. The retract/1 predicate respects the logical update view. This implies that retract/1 succeeds for all clauses that match Term when the predicate was called. The example below illustrates that the first call to retract/1 succeeds on `bee` on backtracking despite the fact that `bee` is already retracted.88Example by Jan Burse

      :- dynamic insect/1.
      insect(ant).
      insect(bee).

      ?- (   retract(insect(I)),
             writeln(I),
             retract(insect(bee)),
             fail
         ;   true
         ).
      ant ;
      bee.

  If multiple threads start a retract on the same predicate at the same time their notion of the entry generation is adjusted such that they do not retract the same first clause. This implies that, if multiple threads use `once(retract(Term))`, no two threads will retract the same clause. Note that on backtracking over retract/1, multiple threads may retract the same clause as both threads respect the logical update view.

[ISO,det]retractall(+Head)
  All facts or clauses in the database for which the head unifies with Head are removed. If all arguments of Head are non-sharing variables (see is_most_general_term/1), all clauses are removed without inspecting the clauses. Cleaning all clauses of a dynamic predicate must use retractall/1 rather than abolish/1 as the latter completely wipes the predicate, including its properties. If Head refers to a predicate that is not defined, it is implicitly created as a dynamic predicate. See also dynamic/1.89The ISO standard only allows using dynamic/1 as a directive.
[ISO]asserta(+Term)
[ISO]assertz(+Term)
[deprecated]assert(+Term)
  Assert a clause (fact or rule) into the database. The predicate asserta/1 asserts the clause as first clause of the predicate while assertz/1 assert the clause as last clause. The deprecated assert/1 is equivalent to assertz/1. If the program space for the target module is limited (see set_module/1), asserta/1 can raise a `resource_error(program_space)` exception. The example below adds two facts and a rule. Note the double parentheses around the rule.

      ?- assertz(parent('Bob', 'Jane')).
      ?- assertz(female('Jane')).
      ?- assertz((mother(Child, Mother) :-
                      parent(Child, Mother),
                      female(Mother))).

asserta(+Term, -Reference)
assertz(+Term, -Reference)
[deprecated]assert(+Term, -Reference)
  Equivalent to asserta/1, assertz/1, assert/1, but in addition unifies Reference with a handle to the asserted clauses. The handle can be used to access this clause with clause/3 and erase/1.

#### 4.14.1.1 Update view

SWI-Prolog adheres to the logical update view, where backtrackable predicates that enter the definition of a predicate will not see any changes (either caused by assert/1 or retract/1) to the predicate. This view is the ISO standard. Logical updates are realised by keeping generation information on clauses. Each change to the database causes an increment of the generation of the database. Each goal is tagged with the generation in which it was started. Each clause is flagged with the generation it was created in as well as the generation it was erased. Only clauses with a‘created’ ...‘erased’interval that encloses the generation of the current goal are considered visible. The generation mechanism is also used to implement transactions See section 4.14.1.3.

Erased clauses are (eventually) reclaimed by the clause garbage collector implemented by garbage_collect_clauses/0. By default, the clause garbage collector runs in a thread named `gc`, together with the atom garbage collector (garbage_collect_atoms/0). See also the Prolog flag gc_thread.

#### 4.14.1.2 Indexing databases

The indexing capabilities of SWI-Prolog are described in section 2.17. Summarizing, SWI-Prolog creates indexes for any applicable argument, pairs of arguments and indexes on the arguments of compound terms when applicable. Extended JIT indexing is not widely supported among Prolog implementations. Programs that aim at portability should consider using term_hash/2 and term_hash/4 to design their database such that indexing on constant or functor (name/arity reference) on the first argument is sufficient. In some cases, using the predicates below to add one or more additional columns (arguments) to a database predicate may improve performance. The overall design of code using these predicates is given below. Note that as term_hash/2 leaves the hash unbound if Term is not ground. This causes the lookup to be fast if Term is ground and correct (but slow) otherwise.

    :- dynamic
        x/2.

    assert_x(Term) :-
        term_hash(Term, Hash),
        assertz(x(Hash, Term)).

    x(Term) :-
        term_hash(Term, Hash),
        x(Hash, Term).

[det]term_hash(+Term, -HashKey)
  If Term is a ground term (see ground/1), HashKey is unified with a positive integer value that may be used as a hash key to the value. If Term is not ground, the predicate leaves HashKey an unbound variable. Hash keys are in the range 0 ... 72,057,594,037,927,935 (2^56), the maximal integer that can be stored efficiently (see max_tagged_integer.

  This predicate may be used to build hash tables as well as to exploit argument indexing to find complex terms more quickly.

  The hash key does not rely on temporary information like addresses of atoms and may be assumed constant over different invocations and versions of SWI-Prolog.90Last change: version 9.3.28 The term_hash/2 predicate is cycle-safe.bugAll arguments that (indirectly) lead to a cycle have the same hash key. bugHashes differ between big and little endian machines and hashes for big integers (currently > 2^56) differ depending on the big integer backend (GMP or LibBF). See gmp_version.

[det]term_hash(+Term, +Depth, +Range, -HashKey)
  As term_hash/2, but only considers Term to the specified Depth. The top-level term has depth 1, its arguments have depth 2, etc. That is, Depth = 0 hashes nothing; Depth = 1 hashes atomic values or the functor and arity of a compound term, not its arguments; Depth = 2 also indexes the immediate arguments, etc.

  HashKey is in the range [0 ...Range-1]. Range must be in the range [1 ... 2147483647].

[det]variant_sha1(+Term, -SHA1)
  Compute a SHA1-hash from Term. The hash is represented as a 40-byte hexadecimal atom. Unlike term_hash/2 and friends, this predicate produces a hash key for non-ground terms. The hash is invariant over variable-renaming (see =@=/2) and constants over different invocations of Prolog.bugThe hash depends on word order (big/little-endian) and the wordsize (32/64 bits).

  This predicate raises an exception when trying to compute the hash on a cyclic term or attributed term. Attributed terms are not handled because subsumes_chk/2 is not considered well defined for attributed terms. Cyclic terms are not supported because this would require establishing a canonical cycle. That is, given A=[a|A] and B=[a,a|B], A and B should produce the same hash. This is not (yet) implemented.

  This hash was developed for lookup of solutions to a goal stored in a table. By using a cryptographic hash, heuristic algorithms can often ignore the possibility of hash collisions and thus avoid storing the goal term itself as well as testing using =@=/2.

[det]variant_hash(+Term, -HashKey)
  Similar to variant_sha1/2, but using a non-cryptographic hash and produces an integer result like term_hash/2. This version does deal with attributed variables, processing them as normal variables. This hash is primarily intended to speedup finding variant terms in a set of terms. bugAs variant_sha1/2, cyclic terms result in an exception.

#### 4.14.1.3 Transactions

Traditionally, Prolog database updates add or remove individual clauses. The Logical Update View ensures that a goal that is started on a dynamic predicate does not see modifications due to assert/1 or retract/1 during its life time. See section 4.14.1.1. In a multi-threaded context this assumption still holds for individual predicates: concurrent modifications to a dynamic predicate are invisible.

Transactions allow running a goal in isolation. The goals running inside the transaction‘see’the database as it was when the transaction was started together with database changes done by the transaction goal. Other threads see no changes until the transaction is committed. The commit, also if it involved multiple clauses spread over multiple predicates, becomes atomically visible to other threads. Transactions have several benefits Wielemaker, 2013

- If a database update requires multiple assert/1 and/or retract/1 operations, a transaction ensure either all are executed or the database remains unchanged. Notably unexpected exceptions or failures cannot leave the database in an inconsistent state.

- Other threads do not see the intermediate inconsistent states when a database update that consists of multiple assert and/or retract is performed in a transaction. This notably avoids the need to use locks (see with_mutex/2) in threads that read the data. A reading thread may still need to use snapshot/1 if a goal depends on multiple calls to dynamic predicates. Unlike locks, transaction and snapshot based synchronization allows both readers and writers to make progress simultaneously.91Read-write locks also provide readers and writers to make progress simultaneously, but readers see all intermediate states rather than a consistent state.

  Transactions on their own do not guarantee consistency. For example, when running the code below to update the temperature concurrently from multiple threads it is possible for the global state to have multiple temperature/1 clauses.

      update_temperature(Temp) :-
          transaction(( retractall(temperature(_)),
                        asserta(temperature(Temp)))).

  Global consistency can be achieved by wrapping the above transaction using with_mutex/2 or by using transaction/3 with a constraint that demands a single clause for temperature/1

- Transactions allow for “what if” reasoning over the dynamic database. This is particularly useful when combined with the deductive database facilities provided by tabling (see section 7).

SWI-Prolog transactions only affect the dynamic database. Static predicates are globally visible and shared at all times. In particular, transactions do not affect loading source files and thus, source files loaded inside a transaction (e.g., due to autoloading) are immediately globally visible. This may pose problems if loading source files provide clauses for dynamic predicates.

transaction(:Goal)
transaction(:Goal, +Options)
  Run Goal as once/1 in a transaction. This implies that access to dynamic predicates‘sees’the dynamic predicates at the moment the transaction is started, together with the modifications issued by Goal. Thus, Goal does not see changes to dynamic predicates from other threads and other threads do not see modifications by Goal (isolation). If Goal succeeds, all modifications become atomically visible to the other threads. If Goal fails or raises an exception all local modifications are discarded and transaction/1 fails or passes the exception.

  Currently the number of database changes inside a transaction (or snapshot, see snapshot/1) is limited to 2 ** 32 -1. If this limit is exceeded a `representation_error(transaction_generations)` exception is raised.

  Transactions may be nested. The above mentioned limitation for the number of database changes applies to the combined number in nested transactions.

  If Goal succeeds, the transaction is committed. This implies that (1) any clause that is asserted in the transaction and not retracted in the same transaction is made globally visible and (2) and clause the existed before the transaction and is retracted in the transaction becomes globally invisible. Multiple transactions may retract the same clause and be committed, i.e., committing a retract that was already performed is a no-op. All modifications become atomically visible to other threads. The transaction/3 variation allows for verifying constraints just before the commit takes place.

  Clause ordering Inside a transaction clauses can be added using asserta/1 and assertz/1. If only a single transaction is active at any point in time transactions preserve the usual ordering of clauses. However, if multiple transactions manipulate the same predicate(s) concurrently (typically using transaction/3), the final order of the clauses is the order in which the transactions asserted the clauses and not the order in which the transactions are committed.

  The transaction/1 variant is equivalent to `transaction(Goal,[])`. The transaction/2 variant processed the following options:

  bulk(+Boolean)
    When `true`, accumulate events from changes to dynamic predicates (see prolog_listen/2) and trigger these events as part of the commit phase. This implies that if the transaction is not committed the events are never triggered. Failure to trigger the events causes the transaction to be discarded. Experimental.
transaction(:Goal, :Constraint, +Mutex)
  Similar to transaction/1, but allows verifying Constraint during the commit phase. This predicate follows the steps below. Any failure or exception during this process discards the transaction and releases Mutex when applicable. Constraint may modify the database. Such modifications follow the semantics that apply for Goal.

  - Call `once(Goal)`
  - Lock Mutex
  - Change the visibility to the current global state combined with the changes made by Goal
  - Call `once(Constraint)`
  - Commit the changes
  - Unlock Mutex.

  This predicate is intended to execute multiple transactions with a time consuming Goal in part concurrently. For example, it can be used for a Compare And Swap (CAS) like design. We illustrate this using a simple counter in the code below. Note that the transaction fails if some other thread concurrently updated the counter. This is why we need the repeat/0 and a final !/0. The CAS-style update is in general useful if Goal is expensive and conflicts are rare.

      :- dynamic counter/1.

      increment_counter(Delta) :-
          repeat,
            transaction(( counter(Value),
                          Value2 is Value+Delta,
                        ),
                        ( retract(counter(Value)),
                          asserta(counter(Value2))
                        ),
                        counter_lock),
          !.

snapshot(:Goal)
  Similar to transaction/1, but always discards the local modifications. In other words, snapshot/1 allows a thread to examine a frozen state of the dynamic predicates and/or make isolated modifications without affecting other threads and without making permanent changes to the database. Where transactions allow the global state to be updated atomically from one consistent state to the next, a snapshot allows reasoning about a consistent state.
[nondet]current_transaction(-Goal)
  True when called inside a transaction running Goal. This predicate generates candidates from the current (nested) transaction outward. Goal is a plain goal if the calling context module is the same as matching transaction/1 or snapshot/1 and a qualified callable term otherwise. Note that this only enumerates transactions in the current thread.
transaction_updates(-Updates)
  Unify Updates with a list of database updates that would be effectuated if the transaction is going to be committed at this stage. Updates is a list of terms defined below. The elements are sorted on the change generation, i.e., the order in which the operations were performed.
  asserta(+ClauseRef)
  assertz(+ClauseRef)
    The given clause will be asserted at the start or end. Note that due to competing transactions the clause may no longer be the first/last clause of the predicate.
  erased(+ClauseRef)
    The given clause will be removed. This may be due to erase/1, retract/1 or retractall/1.

#### 4.14.1.4 Impact of transactions

Transactions interact with other facilities that depend on changing dynamic predicates. This section discusses these interactions.

Last modified generation
  Using the predicate_property/2 property `last_modified_generation(Generation)` we can determine whether a predicate was modified. When a predicate is changed inside a transaction this generation is not updated. The generation for dynamic predicates that are modified in the transaction is updated to the commit generation when the transaction is committed. Asking for the last modified generation inside the transaction examines the log of modified clauses and reports the generation as one of

  - The global modified generation if the predicate was not modified in the transaction and not modified outside the transaction to beyond the start generation of the transaction. If the modified generation is higher than the transaction start generation, this generation is reported. bugNote that the above implies that inside a transaction we observe a changing last modified generation for predicates that have only been modified outside the transaction while these changes are not visible.

  - The transaction start generation plus the local generation of the last change if the predicate is modified inside the transaction.
Wait for database changes
  The predicate thread_wait/2 does not wakeup threads for changes inside a transaction. The wakeup is delayed until the transaction is committed. Note that thread_wait/2 cannot be meaningfully called from inside a transaction because no external entities can cause changes to the dynamic database inside the transaction.
Incremental tabling
  Consistency of tables must be restored if the transaction is rolled back. For local tables this is realised as follows:

  - Tables are either marked to be invalidated on rollback or, for monotonic tabling individual answers are marked to be removed on rollback.
  - A table is marked to be invalidated if, while it is created or reevaluated, at least one dependent dynamic predicate has been modified inside the transaction.
  - Answers are marked to be retracted when they result from monotonic reevaluation based on changes inside the transaction.

  In other words: tables being reevaluated inside a transaction that do not depend on predicates modified inside the transaction remain valid. Monotonic tables that get new answers due to asserts inside the transaction have these answers removed during the rollback while the table remains valid. Monotonic tables that are for some reason invalidated inside the transaction are invalidated during the rollback.

  Correct interaction between tabling and transaction currently only deals with local tables. Shared tables should not be combined with transactions. Future versions may improve on that. A possible route is to make a local copy from a shared table when (re)evaluation is performed inside a transaction.

Status SWI-Prolog transaction basics and API are stable. Interaction with other parts of the system that depend on dynamic predicates is still unsettled. Future versions may support non-determinism through transactions and snapshots.

### 4.14.2 The recorded database

recorda(+Key, +Term, -Reference)
  Assert Term in the recorded database under key Key. Key is a small integer (range min_tagged_integer ...max_tagged_integer, atom or compound term. If the key is a compound term, only the name and arity define the key. Reference is unified with an opaque handle to the record (see erase/1).
recorda(+Key, +Term)
  Equivalent to `recorda(Key, Term, _)`.
recordz(+Key, +Term, -Reference)
  Equivalent to recorda/3, but puts the Term at the tail of the terms recorded under Key.
recordz(+Key, +Term)
  Equivalent to `recordz(Key, Term, _)`.
recorded(?Key, ?Value, ?Reference)
  True if Value is recorded under Key and has the given database Reference. If Reference is given, this predicate is semi-deterministic. Otherwise, it must be considered non-deterministic. If neither Reference nor Key is given, the triples are generated as in the code snippet below.92Note that, without a given Key, some implementations return triples in the order defined by recorda/2 and recordz/2. See also current_key/1.

              current_key(Key),
              recorded(Key, Value, Reference)

recorded(+Key, -Value)
  Equivalent to `recorded(Key, Value, _)`.
erase(+Reference)
  Erase a record or clause from the database. Reference is a db-reference returned by recorda/3, recordz/3 or recorded/3, clause/3, assert/2, asserta/2 or assertz/2. Fail silently if the referenced object no longer exists. Notably, if multiple threads attempt to erase the same clause one will succeed and the others will fail.
instance(+Reference, -Term)
  Unify Term with the referenced clause or database record. Unit clauses are represented as Head :- `true`.

### 4.14.3 Flags

The predicate flag/3 is the oldest way to store global non-backtrackable data in SWI-Prolog. Flags are global and shared by all threads. Their value is limited to atoms, small (64-bit) integers and floating point numbers. Flags are thread-safe. The flags described in this section must not be confused with Prolog flags described in section 2.12.

get_flag(+Key, -Value)
  True when Value is the value currently associated with Key. If Key does not exist, a new flag with value‘0’(zero) is created.
set_flag(+Key, Value)
  Set flag Key to Value. Value must be an atom, small (64-bit) integer or float.
flag(+Key, -Old, +New)
  True when Old is the current value of the flag Key and the flag has been set to New. New can be an arithmetic expression. The update is atomic. This predicate can be used to create a shared global counter as illustrated in the example below.

      next_id(Id) :-
          flag(my_id, Id, Id+1).

### 4.14.4 Tries

Tries (also called digital tree, radix tree or prefix tree maintain a mapping between a variant of a term (see =@=/2) and a value. They have been introduced in SWI-Prolog 7.3.21 as part of the implementation of tabling. The current implementation is rather immature. In particular, the following limitations currently apply:

- Tries only offer partial thread-safety. Multiple threads may concurrently insert values in a trie. Concurrent deletion and concurrent non-deterministic access is not supported.
- Tries should not be modified while non-deterministic predicates such as trie_gen/3 are running on the trie.
- Terms cannot be cyclic. Possibly this will not change because cyclic terms can only be supported after creating a canonical form of the term.
- Starting with SWI-Prolog 9.3.23, tries support attributed variables both in for keys and values. Tries holding attributed variables can also be compiled using trie_gen_compiled/2 or trie_gen_compiled/3.

We give the definition of these predicates for reference and debugging tabled predicates. Future versions are likely to get a more stable and safer implementation. The API to tries should not be considered stable.

trie_new(-Trie)
  Create a new trie and unify Trie with a handle to the trie. The trie handle is a blob. Tries are subject to atom garbage collection.
trie_destroy(+Trie)
  Destroy Trie. This removes all nodes from the trie and causes further access to Trie to raise an existence_error exception. The handle itself is reclaimed by atom garbage collection.
[semidet]is_trie(@Trie)
  True when Trie is a trie object. See also current_trie/1.
[nondet]current_trie(-Trie)
  True if Trie is a currently existing trie. As this enumerates and then filters all known atoms this predicate is slow and should only be used for debugging purposes. See also is_trie/1.
trie_insert(+Trie, +Key)
  Insert the term Key into Trie. If Key is already part of Trie the predicates fails silently. This is the same as trie_insert/3, but using a fixed reserved Value.
trie_insert(+Trie, +Key, +Value)
  Insert the term Key into Trie and associate it with Value. Value can be any term. If Key-Value is already part of Trie, the predicates fails silently. If Key is in Trie associated with a different value, a `permission_error` is raised.
trie_update(+Trie, +Key, +Value)
  As trie_insert/3, but if Key is in Trie, its associated value is updated.
trie_insert(+Trie, +Term, +Value, -Handle)
  As trie_insert/3, returning a handle to the trie node. This predicate is currently unsafe as Handle is an integer used to encode a pointer. It was used to implement a pure Prolog version of the `library(tabling)` library.
trie_delete(+Trie, +Key, ?Value)
  Delete Key from Trie if the value associated with Key unifies with Value.
trie_lookup(+Trie, +Key, -Value)
  True if the term Key is in Trie and associated with Value.
trie_term(+Handle, -Term)
  True when Term is a copy of the term associated with Handle. The result is undefined (including crashes) if Handle is not a handle returned by trie_insert_new/3 or the node has been removed afterwards.
[nondet]trie_gen(+Trie, ?Key)
  True when Key is a member of Trie. See also trie_gen_compiled/2.
[nondet]trie_gen(+Trie, ?Key, -Value)
  True when Key is associated with Value in Trie. Backtracking retrieves all pairs. Currently scans the entire trie, even if Key is partly known. Currently unsafe if Trie is modified while the values are being enumerated. See also trie_gen_compiled/3.
[nondet]trie_gen_compiled(+Trie, ?Key)
[nondet]trie_gen_compiled(+Trie, ?Key, -Value)
  Similar to trie_gen/3, but uses a compiled representation of Trie. The compiled representation is created lazily and manipulations of the trie (insert, delete) invalidate the current compiled representation. The compiled representation generates answers faster and, as it runs on a snapshot of the trie, is immune to concurrent modifications of the trie. This predicate is used to generate answers from answer tries as used for tabled execution. See section 7.
[nondet]trie_property(?Trie, ?Property)
  True if Trie exists with Property. Intended for debugging and statistical purposes. Retrieving some of these properties visit all nodes of the trie. Defined properties are
  value_count(-Count)
    Number of key-value pairs in the trie.
  node_count(-Count)
    Number of nodes in the trie.
  size(-Bytes)
    Required storage space of the trie.
  compiled_size(-Bytes)
    Required storage space for the compiled representation as used by trie_gen_compiled/2,3.
  hashed(-Count)
    Number of nodes that use a hashed index to its children.
  lookup_count(-Count)
    Number of trie_lookup/3 calls (only when compiled with `O_TRIE_STATS`).
  gen_call_count(-Count)
    Number of trie_gen/3 calls (only when compiled with `O_TRIE_STATS`).
  wait(-Count)
    Number of times a thread waited on this trie for another thread to complete it (shared tabling, only when compiled with `O_TRIE_STATS`).
  deadlock(-Count)
    Number of times this trie was part of a deadlock and its completion was abandoned (shared tabling, only when compiled with `O_TRIE_STATS`).

  In addition, a number of additional properties are defined on answer tries.

  invalidated(-Count)
    Number of times the trie was invalidated (incremental tabling).
  reevaluated(-Count)
    Number of times the trie was re-evaluated (incremental tabling).
  idg_affected_count(-Count)
    Number of answer tries affected by this one (incremental tabling).
  idg_dependent_count(-Count)
    Number of answer tries this one depends on (incremental tabling).
  idg_size(-Bytes)
    Number of bytes in the IDG node representation.