package datalog

Datalog

An in-memory datalog implementation for OCaml.

It features two main algorithm:

• bottom-up focuses on big sets of rules with small relations, with frequent updates of the relations. Therefore, it tries to achieve good behavior in presence of incremental modifications of the relations.

• top-down resembles prolog (and allows nested subterms). It handles stratified negation and only explores the part of the search space that is relevant to a given query.

Bottom-Up

This version, backward, features a backward-chaining operation. It resembles top-down algorithms because goals (possibly non-ground literals) can be added to the db; it means that if G is a goal and A :- B1,B2,...,Bn is a clause, if A and B1 are unifiable with subst, then subst(B1) is also a goal. Handlers (semantic attachments) can be provided by the user, to be called on every goal. The point is that the handlers can add facts that solve the goal by adding facts that match it.

For instance, a handler may solve goals of the form lt_than(i,j) (where i and j are integers) by adding the fact lt(i,j) if i < j is really true. Another example: if symbols are strings, then the goal concat("foo", "bar", X) may be solved by adding the fact concat("foo", "bar", "foobar"). The tool datalog_cli has build-in definitions of lt, le (lower or equal) and equal; see the last example. Thus, goals are a way to call semantic attachments in a goal-oriented way.

A relational query mode is available (its signature is in Datalog.BottomUp.S.Query, see the module's documentation. It allows to make one-shot queries on a db (the result won't update if facts or clauses are added later), with a simple relational model with negation.

Top-Down

There is also a top-down, prolog-like algorithm that should be very efficient for querying only a subpart of the intensional database (the set of all facts that can be deduced from rules). The main module is Datalog_top_down, and it has its own parser and lexer. An executable (not installed but compiled) is topDownCli.exe. A very important distinction is that terms can be nested (hence the distinct AST and parsers).

The format of semantic attachments for symbols is simpler: a handler, when queried with a given goal, can return a set of clauses whose heads will then be unified with the goal.

CamlInterface

The module Datalog_caml_interface in the library datalog.caml_interface contains a universal embedding of OCaml's types, with helpers to build unary, binary, and ternary atoms that directly relate OCaml values.

Small example:

# #require "datalog";;
# #require "datalog.caml_interface";;
# module CI = Datalog_caml_interface;;
module CI = Datalog_caml_interface
# let edge = CI.Rel2.create ~k1:CI.Univ.int ~k2:CI.Univ.int "edge";;
val edge : (int, int) CI.Rel2.t = <abstr>
# let db = CI.Logic.DB.create();;
val db : CI.Logic.DB.t = <abstr>
# CI.Rel2.symmetry db edge;;
- : unit = ()
# CI.Rel2.add_list db edge [1,2; 2,3; 3,4];;
- : unit = ()
# CI.Rel2.find db edge;;
- : (int * int) list = [(4, 3); (3, 2); (2, 1); (3, 4); (2, 3); (1, 2)]

The relation edge is really intensional: if we add axioms to it, CI.Rel2.find will return an updated view.

# CI.Rel2.transitive db edge;;
- : unit = ()
# CI.Rel2.find db edge;;
- : (int * int) list =
[(1, 3); (2, 4); (1, 4); (4, 1); (3, 1); (4, 2); (4, 3); (3, 2); (2, 1);
 (1, 1); (3, 3); (4, 4); (2, 2); (3, 4); (2, 3); (1, 2)]

One can also directly load a Datalog file (atoms: ints and strings) and access it using (properly typed) relations:

# let db = CI.Logic.DB.create ();;
val db : CI.Logic.DB.t = <abstr>
# CI.Parse.load_file db "tests/clique10.pl";;
- : bool = true
# let edge = CI.Rel2.create ~k1:CI.Univ.int ~k2:CI.Univ.int "edge";;
val edge : (int, int) CI.Rel2.t = <abstr>
# let reachable = CI.Rel2.create ~k1:CI.Univ.int ~k2:CI.Univ.int "reachable";;
val reachable : (int, int) CI.Rel2.t = <abstr>
# CI.Rel2.find db reachable;;
- : (int * int) list =
[(5, 0); (5, 1); (4, 0); (5, 2); (4, 1); (3, 0); (10, 7); (5, 3); (10, 8);
 (9, 7); (4, 2); (3, 1); (2, 0); (5, 4); (10, 9); (9, 8); (8, 7); (4, 3);
 (3, 2); (2, 1); (1, 0); (5, 5); (10, 10); (9, 9); (8, 8); (7, 7); (4, 4);
 (3, 3); (2, 2); (1, 1); (0, 0); (0, 1); (1, 2); (2, 3); (3, 4); (4, 5);
 (5, 6); (6, 7); (7, 8); (8, 9); (9, 10); (8, 10); (7, 9); (6, 8); (5, 7);
 (4, 6); (3, 5); (2, 4); (1, 3); (0, 2); (7, 10); (6, 9); (5, 8); (4, 7);
 (3, 6); (2, 5); (1, 4); (0, 3); (6, 10); (5, 9); (4, 8); (3, 7); (2, 6);
 (1, 5); (0, 4); (5, 10); (4, 9); (3, 8); (2, 7); (1, 6); (0, 5); (4, 10);
 (3, 9); (2, 8); (1, 7); (0, 6); (3, 10); (2, 9); (1, 8); (0, 7); (2, 10);
 (1, 9); (0, 8); (1, 10); (0, 9); (0, 10)]

Documentation

You can consult the online documentation

License

The code is distributed under the bsd_license See the LICENSE file.

Build

It is recommended to use opam: opam install datalog.

Manual build:

You need OCaml >= 4.02 with dune. Just type in the root directory:

$ make
$ cp src/bottom_up_cli/datalog_cli.exe ./datalog_cli

How to use it

There are two ways to use datalog:

• With the command line tool, datalog_cli.exe, or datalog_cli if you installed it on your system; just type in

$ ./src/datalog_cli <problem_file>

• The libraries datalog, datalog.top_down, datalog.unix, datalog.caml_interface. See the .mli files for documentation, or the online documentation. For both Datalog_top_down and Datalog.BottomUp, functors are provided to use your own datatype for symbols (constants); however, a default implementation with strings as symbols is available as Datalog.Default (which is used by the parser Datalog.Parser) for bottom-up and in Datalog_top_down.Default for top-down.

A few example files, suffixed with .pl, can be found in tests/. For instance, you can try:

$ cat tests/clique10.pl
% generate problem of size 10
reachable(X,Y) :- edge(X,Y).
reachable(X,Y) :- edge(X,Z), reachable(Z,Y).
same_clique(X,Y) :- reachable(X,Y), reachable(Y,X).
edge(0, 1).
edge(1, 2).
edge(2, 3).
edge(3, 4).
edge(4, 5).
edge(5, 0).
edge(5, 6).
edge(6, 7).
edge(7, 8).
edge(8, 9).
edge(9, 10).
edge(10, 7).
$ ./datalog_cli tests/clique10.pl --pattern 'same_clique(1,X)'
% start datalog
% parse file tests/clique10.pl
% process 15 clauses
% computing fixpoint...
% done.
% facts matching pattern same_clique(1, X0):
  same_clique(1, 4).
  same_clique(1, 5).
  same_clique(1, 3).
  same_clique(1, 2).
  same_clique(1, 1).
  same_clique(1, 0).
...

Or

$ ./datalog_cli tests/graph200.pl --size --sum reachable
% start datalog
% parse file tests/graph200.pl
% process 205 clauses
% computing fixpoint...
% done.
% size of saturated set: 41209
% number of fact with head reachable: 40401
...

Or

$ ./datalog_cli tests/graph10.pl --goal 'increasing(3,7)' --pattern 'increasing(3,X)'
% start datalog
% parse file tests/graph10.pl
% process 15 clauses
% computing fixpoint...
% done.
% facts matching pattern increasing(3, X0):
  increasing(3, 10).
  increasing(3, 7).
  increasing(3, 6).
  increasing(3, 4).
  increasing(3, 5).
  increasing(3, 8).
  increasing(3, 9).
...

Or

$ ./datalog_cli tests/small.pl --query '(X,Y) :- ancestor(X,john), father(X,Y), not mother(Y,Z)'
% start datalog
% parse file tests/small.pl
% process 12 clauses
% computing fixpoint...
% done.
% query plan: (match[0] ancestor(X0, john) |><| match[1,0] father(X0, X1)) |> match[2,1] mother(X1, X2)
% query answer:
    'jean-jacques', alphonse
    brad, john
...

Aggregates in top-down:

$ cat test.pl
foo(a, 1).
foo(a, 2).
foo(b, 10).
foo(b, 11).
foo(c, 0).

bar(A, S) :- S := sum B : foo(A, B).

$ topDownCli -load foo.pl -builtin '(X,Y) :- bar(X,Y)'
  (a, 3).
  (b, 21).
  (c, 0).

TODOs/ideas

• Goal subsumption

• Clause subsumption (when selected lit is ground)

• Clause retraction

• Library of standard interpreted predicates