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149 commits

Author SHA1 Message Date
Leonardo de Moura
9dc86e3cf5 fix(builtin/kernel): rename generalized proof_irrel axiom to hproof_irrel, and derive the restricted one 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-04 10:06:29 -08:00
Leonardo de Moura
9a677331da feat(builtin): simulate subtypes using sigma types 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-04 01:46:50 -08:00
Leonardo de Moura
8eec289ce1 feat(kernel): add dependent pairs 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-03 16:52:49 -08:00
Leonardo de Moura
6be50f0133 refactor(builtin/heq): merge cast and heq modules 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-02 15:01:48 -08:00
Leonardo de Moura
c56df132b8 refactor(kernel): remove semantic attachments from the kernel 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-02 14:48:27 -08:00
Leonardo de Moura
0ed35e2133 fix(build): kernel.lean depends on tactic.lua 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-30 23:15:44 -08:00
Leonardo de Moura
bc2d504ccc feat(builtin/kernel): add rewrite rules for if-then-else 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-30 22:38:35 -08:00
Leonardo de Moura
4d533c6a25 feat(builtin/kernel): add nonempty_range theorem 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-30 22:13:34 -08:00
Leonardo de Moura
ddaf948c72 feat(builtin/kernel): add nonempty_fun theorem 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-30 19:38:51 -08:00
Leonardo de Moura
759aa61f70 refactor(builtin/kernel): define if-then-else using Hilbert's operator 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-30 19:28:42 -08:00
Leonardo de Moura
01259b1e84 feat(kernel): make sure U is the maximal universe 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-29 16:31:00 -08:00
Leonardo de Moura
069e5edf6b fix(library/simplifier): include flag indicating if the proof generated by simplifier is a homogenous or heterogenous equality, use flag to fix bug in the simp_tactic 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-29 12:01:01 -08:00
Leonardo de Moura
b6985bd713 feat(builtin/kernel): add another rewrite rule 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-28 15:56:26 -08:00
Leonardo de Moura
e2540b68db fix(src/builtin/tactic): add default rule set if none is provided 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-28 15:56:01 -08:00
Leonardo de Moura
ceff335bb8 doc(doc/lean/tutorial): update tutorial 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-26 22:58:44 -08:00
Leonardo de Moura
4d25cb7f47 feat(library/tactic): add simplify_tactic based on the simplifier 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-26 18:53:18 -08:00
Leonardo de Moura
5e6c1d4904 refactor(builtin/heq): remove axiom hpiext since we don't use it anymore 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-26 13:11:17 -08:00
Leonardo de Moura
fafaa7e78e fix(library/simplifier): remove hack for handling some constants that expect an argument of type TypeU, the new approach is general 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-26 10:10:57 -08:00
Leonardo de Moura
844572c382 feat(library/simplifier): support for dependent simplification in Pi/forall expressions 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-26 00:32:05 -08:00
Leonardo de Moura
9fb3ccb4c0 feat(library/simplifier): support for dependent simplification in lambda expressions 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-25 16:54:42 -08:00
Leonardo de Moura
2bb33c55fe feat(builtin/kernel): add more theorems useful for simplification 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-24 18:52:50 -08:00
Leonardo de Moura
009217b499 feat(builtin/hep): replace hallext axiom with theorem 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-24 17:09:20 -08:00
Leonardo de Moura
dbc100cc2e feat(library/simplifier): cast elimination in the simplifier 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-23 17:28:14 -08:00
Leonardo de Moura
33193e1ab3 feat(library/simplifier): improve contextual simplifications 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-23 12:54:29 -08:00
Leonardo de Moura
8214c7add4 feat(library/elaborator): compensate the lack of eta-reduction (and eta-expanded normal forms) in the kernel normalizer 
Before this commit, the elaborator was solving constraints of the form

       ctx |- (?m x) == (f x)
as
       ?m <- (fun x : A, f x)    where A is the domain of f.

In our kernel, the terms f and (fun x, f x) are not definitionally equal.
So, the solution above is not the only one. Another possible solution is

       ?m  <- f

Depending of the circumstances we want  ?m <- (fun x : A, f x) OR ?m <- f.
For example, when Lean is elaborating the eta-theorem in kernel.lean, the first solution should be used:
       ?m <- (fun x : A, f x)

When we are elaborating the axiom_of_choice theorem, we need to use the second one:
       ?m <- f

Of course, we can always provide the parameters explicitly and bypass the elaborator.
However, this goes against the idea that the elaborator can do mechanical steps for us.

This commit addresses this issue by creating a case-split
       ?m <- (fun x : A, f x)
       OR
       ?m <- f

Another solution is to implement eta-expanded normal forms in the Kernel.

With this change, we were able to cleanup the following "hacks" in kernel.lean:
     @eps_ax A (nonempty_ex_intro H) P w Hw
     @axiom_of_choice A B P H
where we had to explicitly provided the implicit arguments

This commit also improves the imitation step for Pi-terms that are actually arrows.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-22 13:28:54 -08:00
Leonardo de Moura
6cb4d165c9 feat(builtin/kernel): dependent version of axiom of choice 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-22 11:04:27 -08:00
Leonardo de Moura
66553268d0 feat(builtin/kernel): add skolem_th, we need it to justify skolemization preprocessing step 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-22 09:41:07 -08:00
Leonardo de Moura
d9b5ebc738 refactor(builtin/kernel): cleanup Hilbert operator definition 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-22 09:18:40 -08:00
Leonardo de Moura
bcf60db23b fix(builtin/kernel): Hilbert operator only for non-empty types 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-22 08:52:31 -08:00
Leonardo de Moura
94a3136904 feat(builtin/kernel): add Hilbert's operator, and derive axiom of choice using it 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-22 08:21:11 -08:00
Leonardo de Moura
fbaf6e887f refactor(builtin/kernel): put the congruence theorems in a format that is easier for the simplifier to process 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-21 14:03:51 -08:00
Leonardo de Moura
97ead50a3e feat(builtin/Nat): flip orientation of associativity axioms for + and * 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-20 15:38:00 -08:00
Leonardo de Moura
ad219d43d9 refactor(*): semantic attachment parsing and simplification 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-20 14:44:45 -08:00
Leonardo de Moura
69d7ee316f feat(library/simplifier): improve simplification by evaluation 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-19 23:26:34 -08:00
Leonardo de Moura
6db10c577b feat(builtin/kernel): add proof irrelevance axiom 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-19 12:20:09 -08:00
Leonardo de Moura
bbf6e6a256 feat(builtin/kernel): create default rule set in the kernel, and adjust unit tests 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-19 11:24:20 -08:00
Leonardo de Moura
475df3d94e chore(builtin/kernel): add theorem for rewriter/simplifier 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-19 10:34:18 -08:00
Leonardo de Moura
7a3aab60c6 chore(builtin/kernel): remove \bowtie as notation for transitivity 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-18 21:11:12 -08:00
Leonardo de Moura
2753a0ffc0 fix(builtin/kernel): add ascii notation for transitivity 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-18 20:56:35 -08:00
Leonardo de Moura
27ab49ae9d feat(library/simplifier): bottom-up simplifier skeleton 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-18 12:49:41 -08:00
Leonardo de Moura
534838a36c chore(build): update automatically generated files 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 18:30:45 -08:00
Leonardo de Moura
d711ca4d1b feat(builtin/heq): add heq C++/Lean interface 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 18:30:21 -08:00
Leonardo de Moura
20c8b91d07 feat(builtin/if_then_else): add more theorems for rewriting 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 18:11:23 -08:00
Leonardo de Moura
ba88a3b05a chore(builtin/heq): remove unnecessary import 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 15:40:56 -08:00
Leonardo de Moura
70828af6db refactor(builtin/heq): cleanup universes 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 14:52:09 -08:00
Leonardo de Moura
fc4c6454a7 chore(tests/lean): adjust tests to reflect recent changes 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 14:36:55 -08:00
Leonardo de Moura
0660cdbdb7 feat(builtin/cast): use heq in the cast library 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 14:31:45 -08:00
Leonardo de Moura
52756c50fc fix(builtin/heq): extensionality axioms 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 12:56:36 -08:00
Leonardo de Moura
64795c6c42 feat(builtin): add heterogeneous equality theory 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 12:32:49 -08:00
Leonardo de Moura
baed98d5be chore(builtin/kernel): adjust emacs mode and fix typo 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-17 10:14:57 -08:00