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Author SHA1 Message Date
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
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
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
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
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
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
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
411f14415d feat(builtin): automatically generate Lean/C++ interface for builtin theories 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-09 18:09:53 -08:00
Leonardo de Moura
2179e57db3 refactor(builtin): move if_then_else to its own module 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-09 14:08:39 -08:00
Leonardo de Moura
87b238efcd chore(builtin/kernel): cleanup 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-09 09:00:05 -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
8e9d88c2cf refactor(builtin/kernel): prove iff::intro, and add a new name for it boolext (Boolean extensionality) 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-08 18:31:45 -08:00
Leonardo de Moura
a4b3d6d6c8 refactor(builtin/kernel): prove eta using function extensionality, and rename abst and abstpi to funext and allext 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-08 17:25:14 -08:00
Leonardo de Moura
bdec4c8799 refactor(builtin/Nat): mark constants as opaque 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-08 16:53:08 -08:00
Leonardo de Moura
2e3b92ef36 refactor(builtin/kernel): cleanup 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-08 16:52:43 -08:00
Leonardo de Moura
a6e0dcc96c fix(builtin/cast): remove dominj axiom, it is not consistent with the new semantics of Pi/forall 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-08 16:19:11 -08:00
Leonardo de Moura
2b2aa228e3 refactor(builtin/kernel): start with small universes 
The universe constraint manager is more flexible now.
We don't need to start with a huge universe  U >= 512.
We can start small, and increase it on demand.

If module mod1 needs it, it can always add

   universe U >= 3

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-08 12:35:00 -08:00
Leonardo de Moura
cfe576f551 fix(library/elaborator): bug in the elaborator 
The elaborator was not handling correctly constraints of the form

    ctx |- ?m << (Pi x : A, B)
    and
    ctx |- (Pi x : A, B) << ?m

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-08 12:10:50 -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
0bdecb6aa4 style(builtin/Nat): name convention 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-07 00:05:51 -08:00
Leonardo de Moura
62bb2ab2f9 fix(builtin/Nat): name convention 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-06 11:41:14 -08:00
Leonardo de Moura
7222a2d1a9 feat(builtin/kernel): use the same notation for mp, eq::mp and forall::elim 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-05 21:39:31 -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
66ec538c63 doc(doc/lean/calc.md): calculational proof documentation 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-03 11:52:21 -08:00
Leonardo de Moura
5b5cebe750 refactor(builtin/Nat): use obtain-from instead of ExistsElim, and use more user-friendly argument order for Induction 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-03 10:33:57 -08:00
Leonardo de Moura
d7efdff83d feat(builtin/Nat): add more leq theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-02 22:48:10 -08:00
Leonardo de Moura
cf35e7bed7 feat(frontends/lean): add support for disequalities in calculational proofs 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-02 22:47:45 -08:00
Leonardo de Moura
6329d1828d feat(frontends/lean): reuse name expression 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-02 20:08:21 -08:00
Leonardo de Moura
92c7145d7f feat(kernel/expr): maximize sharing before serializing 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-02 20:03:42 -08:00
Leonardo de Moura
2d5800ace4 feat(builtin/Nat): leq axiom, and some theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-02 18:24:32 -08:00
Leonardo de Moura
430b75f38f test(tests/lean): add version of the Nat library full of holes 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-02 12:31:13 -08:00
Leonardo de Moura
307099b1cb refactor(builtin/Nat): cleanup all proofs using calculational proof style 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-02 12:13:26 -08:00
Leonardo de Moura
111949b9be feat(frontends/lean): calculational proofs 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-02 10:53:14 -08:00
Leonardo de Moura
49425f1a5b feat(builtin/Nat): multiplication axioms and theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-01 21:32:07 -08:00
Leonardo de Moura
aa009b6b05 feat(builtin/Nat): add basic axioms and theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-01 15:53:53 -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
770145a361 feat(builtin): use namespaces when defining nat, int and real. 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-01 12:55:09 -08:00
Leonardo de Moura
c423198a69 feat(builtin/kernel): add Not.*Elim theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-01 11:35:21 -08:00
Leonardo de Moura
a8bc9fb4e0 refactor(builtin/kernel): mark exists as opaque after proving key theorems 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-01 11:00:32 -08:00
Leonardo de Moura
cc07c440e1 refactor(builtin): move pre-compiled object files to subdirectory 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2013-12-30 13:46:39 -08:00