Commit graph

147 commits

Author SHA1 Message Date
Leonardo de Moura
a7a06ab0f8 feat(library/definitional/rec_on): automatically generate rec_on function for inductive datatypes 2014-10-25 13:08:59 -07:00
Leonardo de Moura
db25f933b0 feat(frontends/lean): use nice names for meta-variables when executing check c and c is a constant 2014-10-24 08:23:26 -07:00
Leonardo de Moura
f027acb5cb fix(frontends/lean): missing type info in expressions nested in tactics 2014-10-23 18:31:05 -07:00
Leonardo de Moura
212ae0b61c feat(frontends/lean): automatically add 'info' tactic in begin-end blocks
Actually, the tactic is only added when Lean is in collect-info mode.
2014-10-23 13:30:04 -07:00
Leonardo de Moura
e750c9b67a feat(frontends/lean): add 'info' tactic for producing PROOF_STATE info for emacs mode 2014-10-23 13:18:30 -07:00
Leonardo de Moura
5a553603d1 fix(library/general_notation): mark \tr as left associative 2014-10-22 22:18:40 -07:00
Leonardo de Moura
f0cc17af87 fix(frontends/lean/elaborator): missing type information when ! operator (aka consume_args) is used 2014-10-20 08:31:36 -07:00
Leonardo de Moura
555d26aa61 feat(frontends/lean/pp): take notation declarations into account when pretty printing
TODO: support foldl/foldr and binders
2014-10-19 08:41:29 -07:00
Leonardo de Moura
28128e0330 fix(frontends/lean): EXTRA_TYPE info 2014-10-16 12:25:18 -07:00
Leonardo de Moura
158682219f feat(frontends/lean): allow parameters only in contexts 2014-10-11 17:13:56 -07:00
Leonardo de Moura
3d65b1c25c fix(frontends/lean/elaborator): incorrect type information being reports in lean-mode, fixes #241 2014-10-10 15:41:55 -07:00
Leonardo de Moura
8f1b6178a7 chore(*): minimize the use of parameters 2014-10-09 07:13:06 -07:00
Leonardo de Moura
8947bf4347 feat(frontends/lean): display type of binders, closes #238 2014-10-08 22:54:10 -07:00
Leonardo de Moura
73aa024c31 refactor(library/logic): remove 'core' subdirectory 2014-10-05 10:50:13 -07:00
Leonardo de Moura
317e910054 refactor(library/data/bool): use new style 2014-10-05 09:50:55 -07:00
Leonardo de Moura
64f6601fe3 fix(frontends/lean/proof_qed_elaborator): information about synthesized variables in a proof-qed block was being lost 2014-10-04 09:15:42 -07:00
Leonardo de Moura
4946f55290 refactor(frontends/lean): constant/axiom are top-level commands, parameter/variable/hypothesis/conjecture are section/context-level commands
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-10-02 17:55:34 -07:00
Leonardo de Moura
bc6ebf34be feat(library/data/bool): do not use ! as notation for bnot, rename band/bor -> and/or 2014-10-01 17:00:03 -07:00
Leonardo de Moura
c46ec6a548 fix(frontends/lean): missing type information for INFO, fixes #218 2014-10-01 14:29:07 -07:00
Leonardo de Moura
113879a7dd feat(frontends/lean/server): sort exact matches by size in FINDP 2014-09-29 16:44:55 -07:00
Leonardo de Moura
0d6d746d98 feat(frontends/lean): check modification time of imported files
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-29 15:17:27 -07:00
Leonardo de Moura
69f50adb2e fix(frontends/lean/server): must save the starting environment/options when reprocessing file, fixes #209 2014-09-26 15:36:47 -07:00
Leonardo de Moura
10a4148adb fix(tests): make sure tests can be executed on Windows msys2 shell 2014-09-20 15:51:24 -07:00
Leonardo de Moura
4e2377ddfc refactor(frontends/lean): replace '[protected]' modifier with 'protected definition' and 'protected theorem', '[protected]' is not a hint.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-19 15:54:32 -07:00
Leonardo de Moura
b3e05a2fe9 refactor(frontends/lean/scanner): remove dependency to seekg and unget
methods

It is not safe to use seekg for textual files. Here is a fragment from a
C++ manual:

seekg() and seekp()

This pair of functions serve respectively to change the position of stream pointers get and put. Both functions are overloaded with two different prototypes:

     seekg ( pos_type position );
     seekp ( pos_type position );

Using this prototype the stream pointer is changed to an absolute position from the beginning of the file. The type required is the same as that returned by functions tellg and tellp.

      seekg ( off_type offset, seekdir direction );
      seekp ( off_type offset, seekdir direction );

Using this prototype, an offset from a concrete point determined by
parameter direction can be specified. It can be:

          ios::beg	offset specified from the beginning of the stream
          ios::cur	offset specified from the current position of the stream pointer
          ios::end	offset specified from the end of the stream

The values of both stream pointers get and put are counted in different
ways for text files than for binary files, since in text mode files some
modifications to the appearance of some special characters can
occur. For that reason it is advisable to use only the first prototype
of seekg and seekp with files opened in text mode and always use
non-modified values returned by tellg or tellp. With binary files, you
can freely use all the implementations for these functions. They should
not have any unexpected behavior.
2014-09-18 15:24:48 -07:00
Leonardo de Moura
78ad24a697 feat(frontends/lean/server): add SYNC command, closes #199 2014-09-16 18:42:34 -07:00
Leonardo de Moura
50f788a427 fix(tests/lean/interactive): adjust test to library reorg 2014-09-16 13:16:46 -07:00
Leonardo de Moura
851444b77a test(tests/lean/interactive): test for issue #193 2014-09-15 16:07:23 -07:00
Leonardo de Moura
af2c3b1815 fix(frontends/lean/info_manager): bug in save_environment_options,
server was displaying old results
2014-09-15 16:05:17 -07:00
Leonardo de Moura
b82092a123 fix(frontends/lean/parser): segmentation fault after REPLACE, fixes #172 2014-09-10 08:39:39 -07:00
Leonardo de Moura
9b9adf8831 refactor(library): replace decidable_eq with abbreviation 2014-09-09 16:09:05 -07:00
Leonardo de Moura
ee196bbf1a fix(frontends/lean/pp): pretty printing coercions to functions, fixes #151 2014-09-09 12:49:32 -07:00
Leonardo de Moura
05c6e1461e fix(tests/lean/interactive): interactive tests expected output, they must include the new '-- BEGINWAIT' messages
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-09 09:47:19 -07:00
Leonardo de Moura
6632a50015 refactor(library): add namespaces 'or', 'and' and 'iff'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-04 21:25:21 -07:00
Leonardo de Moura
364bba2129 feat(frontends/lean/inductive_cmd): prefix introduction rules with the name of the inductive datatype
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-04 17:26:36 -07:00
Leonardo de Moura
8743394627 refactor(kernel/inductive): replace recursor name, use '.rec' instead of '_rec'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-04 15:04:57 -07:00
Leonardo de Moura
ffc871ea8c feat(frontends/lean/server): only display 'EXTRA_TYPE' info when the column number is provided to the 'INFO' command, closes #133
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-04 14:02:53 -07:00
Leonardo de Moura
9d0a4d21d4 chore(tests/lean/interactive): adjust test expected output
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-04 10:00:42 -07:00
Leonardo de Moura
e51c4ad2e9 feat(frontends/lean): rename 'using' command to 'open'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-03 16:00:38 -07:00
Leonardo de Moura
2ca0a22e2c fix(tests/lean/interactive/in4): adjust test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-03 01:35:46 -07:00
Leonardo de Moura
b7d7f12b8e fix(frontends/lean/info_manager): several bugs: invalid flag was not being reset for empty lines, merge with overwrite=false was adding 'poluting' state, --NAY generation
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-30 10:35:36 -07:00
Leonardo de Moura
59d3227eaa fix(tests/lean/interactive): test output
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-29 18:17:07 -07:00
Leonardo de Moura
9a4472cff5 fix(frontends/lean): wrong displayed type in proof with multiple sorry's, fixes #112
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-29 14:32:53 -07:00
Leonardo de Moura
8de9cab62d test(tests/lean/interactive): add --server test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-28 07:41:38 -07:00
Leonardo de Moura
c7e9e238ec fix(frontends/lean/server): ignore output produced by worker thread, fixes #98
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-27 10:46:49 -07:00
Leonardo de Moura
dd99e60a00 refactor(frontends/lean/info_manager): store environment+options in the info_manager, fixes #96
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-26 18:07:09 -07:00
Leonardo de Moura
cbc81ea6c5 chore(*): minimize dependencies on tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-24 19:58:48 -07:00
Leonardo de Moura
dbaf81e16d refactor(library): remove unnecessary 'standard' subdirectory
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-23 18:08:09 -07:00
Leonardo de Moura
c5a44aca44 fix(frontends/lean/elaborator): do not expose type information produced when synthesizing class instances
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-22 17:07:12 -07:00
Leonardo de Moura
4a96fefd96 fix(library/unifier): bug in unifier priority queue
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-18 18:58:50 -07:00
Leonardo de Moura
1d306c09ee fix(tests/lean/interactive): remove leftover from test output
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-17 17:29:52 -07:00
Leonardo de Moura
13af81d554 fix(tests/lean/interactive): adjust test output to reflect new features
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-17 15:23:53 -07:00
Leonardo de Moura
55b0a03e3d refactor(frontends/lean/info_manager): to allow cache to be used when producing info data, fixes #37, closes #45
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-17 12:16:32 -07:00
Leonardo de Moura
a173b7f6e6 test(tests/lean/interactive): add old 'interactive' tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-06 14:57:08 -07:00
Leonardo de Moura
fc8ddcb0ce feat(frontends/lean): improve 'check' command when used inside sections
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-07-10 14:07:41 +01:00
Leonardo de Moura
2ef7b9be2f feat(frontends/lean): add basic pretty printer
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-07-09 01:12:36 -07:00
Leonardo de Moura
f5f3816596 chore(tests): cleanup test scripts
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-06-29 09:03:39 -07:00
Leonardo de Moura
930960c54d fix(frontends/lean/builtin_cmds): abstract section parameters in the 'check' command
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-06-26 10:06:50 -07:00
Leonardo de Moura
891a3fb48b feat(frontends/lean): add command block reader with snapshot and resume
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-06-14 14:13:32 -07:00
Leonardo de Moura
9f06cd553e test(lean): remove tests using Lean old syntax and kernel
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 10:38:53 -07:00
Leonardo de Moura
a51139e63b feat(frontends/lean): position information in error messages
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 17:26:38 -08:00
Leonardo de Moura
ba9a8f9d98 feat(frontends/lean): add 'show' expression syntax sugar
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 07:50:22 -08:00
Leonardo de Moura
ccb9faf065 refactor(*): error messages
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-13 16:54:21 -08:00
Leonardo de Moura
84e211b81b fix(frontends/lean): missing ':' in error messages
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-09 11:19:58 -08:00
Leonardo de Moura
f7c7dd4ed4 feat(frontends/lean): include filename in error messages, use GNU error message style
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-09 11:01:27 -08:00
Leonardo de Moura
57c0006916 chore(*): cleanup lean builtin symbols, replace :: with _
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-09 08:33:52 -08:00
Leonardo de Moura
048151487e feat(kernel): use Pi as forall/implication
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-08 00:38:39 -08:00
Leonardo de Moura
8c956280d9 chore(frontends/lean): rename setoption and setopaque commands to set::option and set::opaque
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-06 11:41:03 -08:00
Leonardo de Moura
935c2a03a3 feat(*): change name conventions for Lean builtin libraries
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-05 19:21:44 -08:00
Leonardo de Moura
4ba097a141 feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-05 13:06:36 -08:00
Leonardo de Moura
6569b07b7c feat(frontends/lean/parser): rename 'show' expression to 'have'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-05 11:25:58 -08:00
Leonardo de Moura
9f08156a73 feat(frontends/lean/parser): combine Echo and Show commands into the 'print' command
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-05 11:03:35 -08:00
Leonardo de Moura
ce1213a020 feat(frontends/lean): use '(* ... *)' instead of '(** ... **)' for script code blocks
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-05 10:32:47 -08:00
Leonardo de Moura
028a9bd9bd feat(frontends/lean/scanner): use Lua style comments in Lean
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-05 08:53:27 -08:00
Leonardo de Moura
7726ccad28 chore(builtin): rename nat, int and real modules to Nat, Int and Real.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-01 13:52:25 -08:00
Leonardo de Moura
08718e33dc refactor(builtin): only load the kernel and natural numbers by default
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-30 13:35:37 -08:00
Leonardo de Moura
f1b97b18b4 refactor(frontends/lean/parser): tactic macros, and tactic Lua bindings
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-26 15:54:53 -08:00
Leonardo de Moura
bb81311e0a feat(frontends/lean/parser): include proof state in exception for tactic failure
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-20 17:15:12 -08:00
Leonardo de Moura
7772c16033 refactor(kernel): add unfold_opaque flag to normalizer, modify how type checker uses the opaque flag, remove hidden_defs, and mark most builtin definitions as opaque
After this commit, in the type checker, when checking convertability, we first compute a normal form without expanding opaque terms.
If the terms are convertible, then we are done, and saved a lot of time by not expanding unnecessary definitions.
If they are not, instead of throwing an error, we try again expanding the opaque terms.
This seems to be the best of both worlds.
The opaque flag is a hint for the type checker, but it would never prevent us from type checking  a valid term.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-20 12:47:47 -08:00
Leonardo de Moura
812c1a2960 feat(library/elaborator): only expand definitions that are not marked as hidden
The elaborator produces better proof terms. This is particularly important when we have to prove the remaining holes using tactics.
For example, in one of the tests, the elaborator was producing the sub-expression

 (λ x : N, if ((λ x::1 : N, if (P a x x::1) ⊥ ⊤) == (λ x : N, ⊤)) ⊥ ⊤)

After, this commit it produces

 (λ x : N, ¬ ∀ x::1 : N, ¬ P a x x::1)

The expressions above are definitionally equal, but the second is easier to work with.

Question: do we really need hidden definitions?
Perhaps, we can use only the opaque flag.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-20 02:16:49 -08:00
Leonardo de Moura
bff5a6bfb2 fix(frontends/lean/pp): make sure pp and parser are using the same precedences
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-19 12:46:14 -08:00
Leonardo de Moura
dd72269b13 feat(frontends/lean): rename command Set to SetOption
It is not nice to have Set as a reserved keyword. See example examples/lean/set.lean

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-18 21:18:48 -08:00
Leonardo de Moura
a75d05fdb4 fix(tests/lean/interactive): test driver (to avoid discrepancy between Win and Linux version)
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-06 17:03:12 -08:00
Leonardo de Moura
015bff8283 fix(library/tactic/goal): to_goal way of handling context_entries of the form (name, domain, body) where domain is null, and body is a proof term
This commit fixes a problem exposed by t13.lean.
It has a theorem of the form:

Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
     fun assumption : A /\ B,
          let lemma1 := (show A by auto),
              lemma2 := (show B by auto)
          in (show B /\ A by auto)

When to_goal creates a goal for the metavariable associated with (show B /\ A by auto) it receives a context and proposition of the form

 [ A : Bool, B : Bool, assumption : A /\ B, lemma1 := Conjunct1 assumption, lemma2 := Conjunct2 assumption ] |- B /\ A

The context_entries "lemma1 := Conjunct1 assumption" and "lemma2 := Conjunct2 assumption" do not have a domain (aka type).
Before this commit, to_goal would simply replace and references to "lemma1" and "lemma2" in "B /\ A" with their definitions.
Note that, "B /\ A" does not contain references to "lemma1" and "lemma2". Then, the following goal is created
     A : Bool, B : Bool, assumption : A /\ B |- B /\ A
That is, the lemmas are not available when solving B /\ A.
Thus, the tactic auto produced the following (weird) proof for T1, where the lemmas are computed but not used.

    Theorem T1 (A B : Bool) (assumption : A ∧ B) : B ∧ A :=
            let lemma1 := Conjunct1 assumption,
                lemma2 := Conjunct2 assumption
            in Conj (Conjunct2 assumption) (Conjunct1 assumption)

This commit fixed that. It computes the types of "Conjunct1 assumption" and "Conjunct2 assumption", and creates the goal
     A : Bool, B : Bool, assumption : A /\ B, lemma1 : A, lemma2 : B |- B /\ A

After this commit, the proof for theorem T1 is

Theorem T1 (A B : Bool) (assumption : A ∧ B) : B ∧ A :=
    let lemma1 := Conjunct1 assumption,
        lemma2 := Conjunct2 assumption
    in Conj lemma2 lemma1

as expected.

Finally, this example suggests that the encoding

Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
     fun assumption : A /\ B,
          let lemma1 : A := (by auto),
              lemma2 : B := (by auto)
          in (show B /\ A by auto)

is more efficient than

Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
     fun assumption : A /\ B,
          let lemma1 := (show A by auto),
              lemma2 := (show B by auto)
          in (show B /\ A by auto)

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-06 16:14:25 -08:00
Leonardo de Moura
0390f3c39b feat(library/tactic/boolean_tactics): avoid unnecessary Let expression in proof terms
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-06 15:01:54 -08:00
Leonardo de Moura
1df9d18891 feat(frontends/lean): allow 'tactic hints' to be associated with 'holes'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-06 14:49:39 -08:00
Leonardo de Moura
2ddcc32c1d fix(frontends/lean/notation): change the precedence of '->'
It should match the precedence of the implication '=>'.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-06 13:23:24 -08:00
Leonardo de Moura
d46cf5fdd5 fix(frontends/lean/parser): display failed state in noninteractive mode, stop processing tactic commands when a Lean command is found
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-06 05:13:29 -08:00
Leonardo de Moura
13f9454fe1 feat(library/tactic/proof_state): add option tactic::proof_state::goal_names
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 21:18:22 -08:00
Leonardo de Moura
e6fb6f7d1e feat(frontends/lean/parser): add assumption command, and allow Lean expressions (proof terms) to be used with apply tactic command
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 20:08:51 -08:00
Leonardo de Moura
0c059a9917 feat(library/tactic): use _tac suffix instead of _tactic like Isabelle
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 20:06:32 -08:00
Leonardo de Moura
1b176204b4 feat(frontends/lean/parser): allow the user to use a theorem/axiom name as an argument for the apply tactic command
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 19:03:12 -08:00
Leonardo de Moura
e1d44eec6b fix(frontends/lean/parser): bug in parse_tactic
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 17:40:55 -08:00
Leonardo de Moura
a564795fe6 fix(frontends/lean/parser): remove unnecessary '#' after error
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 17:27:08 -08:00
Leonardo de Moura
74a8b5f2f4 test(tests/lean/interactive): add back command test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 17:19:53 -08:00
Leonardo de Moura
e069ce640b feat(frontends/lean/parser): add tactic abort command
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 17:15:19 -08:00
Leonardo de Moura
34654ad06b feat(tests/lean/interactive): add interactive mode test script
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-05 16:56:20 -08:00