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Author SHA1 Message Date
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
Leonardo de Moura
5bee259a00 refactor(kernel): remove unnecessary universe 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-16 18:06:25 -08:00
Leonardo de Moura
a43020b31b refactor(kernel): remove heterogeneous equality 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-16 17:39:12 -08:00
Leonardo de Moura
1da4294793 refactor(builtin): more theorems, fix iff notation 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-16 09:26:50 -08:00
Leonardo de Moura
398d83b6d5 chore(builtin/Nat): use iff 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-16 02:06:53 -08:00
Leonardo de Moura
4dc98bc73b refactor(builtin/kernel): use iff instead of = for Booleans 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-16 02:05:09 -08:00
Leonardo de Moura
8c2f78a756 feat(builtin): minimize use of heterogenous equality in the kernel, add simpler version of congruence theorems for non-dependent types 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-15 16:34:23 -08:00
Leonardo de Moura
c73398a0b8 refactor(library/simplifier): relax rule for conditional equalities 
The idea is to support conditional equations where the left-hand-side does not contain all theorem arguments, but the missing arguments can be inferred using type inference.
For example, we will be able to have the eta theorem as rewrite rule:

theorem eta {A : TypeU} {B : A → TypeU} (f : ∀ x : A, B x) : (λ x : A, f x) = f
:= funext (λ x : A, refl (f x))

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-15 16:06:00 -08:00
Leonardo de Moura
3daac17ea8 feat(library/simplifier): convert disequalities (a ≠ b) into equations '(a = b) = false' 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-15 15:30:16 -08:00
Leonardo de Moura
1176093afa refactor(library/simplifier): simplifier should only use homogeneous equalities 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-15 14:58:32 -08:00
Leonardo de Moura
07059b0531 feat(library): add if_then_else Lean/C++ interface 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-14 16:10:49 -08:00
Leonardo de Moura
f8eaae7218 feat(builtin/kernel): add new useful theorems for the simplifier 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-13 18:21:22 -08:00
Leonardo de Moura
29fec3fecc fix(builtin/util): bug incorrect encoding of \t and \n in regular expression, and missing local 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-12 17:40:41 -08:00
Leonardo de Moura
6508e63a17 feat(builtin/macros): add assume/take macros for making proof scripts more readable 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-11 18:36:37 -08:00
Leonardo de Moura
781720a26a feat(builtin/kernel): add left_comm theorem 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-11 18:08:08 -08:00
Leonardo de Moura
a1a467a65f refactor(builtin): move congruence theorems to kernel/if_then_else modules 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-11 13:48:28 -08:00
Leonardo de Moura
a0a92f11b7 feat(builtin/congr): add congruence theorems for contextual simplification 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-11 13:37:36 -08:00
Leonardo de Moura
53537d0684 feat(builtin/kernel): 'implication' simplification theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-11 13:35:20 -08:00
Leonardo de Moura
50f281b430 feat(builtin/kernel): add eqf_intro and eqf_elim theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-11 11:13:54 -08:00
Leonardo de Moura
745c702ffb fix(build): dependency problem on some platforms 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-10 19:06:15 -08:00
Leonardo de Moura
d4a7d796a5 feat(builtin): prove strong induction theorem, add < theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-10 18:46:33 -08:00
Leonardo de Moura
5fb718c03a fix(build): broken dependencies between lean executable and .olean, *_decls.cpp and *_decls.h files 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-10 10:58:35 -08:00