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Author SHA1 Message Date
Leonardo de Moura
ad7b13104f feat(*): add support for heterogeneous equality in the parser, elaborator and simplifier, adjusts unit test to reflect changes 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-07 15:03:16 -08:00
Leonardo de Moura
6d7ec9d7b6 refactor(kernel): add heterogeneous equality back to expr 
The main motivation is that we will be able to move equalities between universes.

For example, suppose we have
    A : (Type i)
    B : (Type i)
    H : @eq (Type j) A B
where j > i

We didn't find any trick for deducing (@eq (Type i) A B) from H.
Before this commit, heterogeneous equality as a constant with type

   heq : {A B : (Type U)} : A -> B -> Bool

So, from H, we would only be able to deduce

   (@heq (Type j) (Type j) A B)

Not being able to move the equality back to a smaller universe is
problematic in several cases. I list some instances in the end of the commit message.

With this commit, Heterogeneous equality is a special kind of expression.
It is not a constant anymore. From H, we can deduce

   H1 : A == B

That is, we are essentially "erasing" the universes when we move to heterogeneous equality.
Now, since A and B have (Type i), we can deduce (@eq (Type i) A B) from H1. The proof term is

  (to_eq (Type i) A B (to_heq (Type j) A B H))  :  (@eq (Type i) A B)

So, it remains to explain why we need this feature.

For example, suppose we want to state the Pi extensionality axiom.

axiom hpiext {A A' : (Type U)} {B : A → (Type U)} {B' : A' → (Type U)} :
      A = A' → (∀ x x', x == x' → B x == B' x') → (∀ x, B x) == (∀ x, B' x)

This axiom produces an "inflated" equality at (Type U) when we treat heterogeneous
equality as a constant. The conclusion

     (∀ x, B x) == (∀ x, B' x)

is syntax sugar for

   (@heq (Type U) (Type U) (∀ x : A, B x) (∀ x : A', B' x))

Even if A, A', B, B' live in a much smaller universe.

As I described above, it doesn't seem to be a way to move this equality back to a smaller universe.

So, if we wanted to keep the heterogeneous equality as a constant, it seems we would
have to support axiom schemas. That is, hpiext would be parametrized by the universes where
A, A', B and B'. Another possibility would be to have universe polymorphism like Agda.
None of the solutions seem attractive.

So, we decided to have heterogeneous equality as a special kind of expression.
And use the trick above to move equalities back to the right universe.

BTW, the parser is not creating the new heterogeneous equalities yet.
Moreover, kernel.lean still contains a constant name heq2 that is the heterogeneous
equality as a constant.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-07 10:28:10 -08:00
Leonardo de Moura
30570c843f feat(builtin): add optional type 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-05 17:33:06 -08:00
Leonardo de Moura
0283887ee9 refactor(builtin/kernel): move the heq axioms into kernel.lean 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-04 14:17:34 -08:00
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
4fcc292332 feat(frontends/lean): parse and pretty print pair/tuple projection operators proj1 and proj2, fix bug in the type checker 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-03 22:10:01 -08:00
Leonardo de Moura
5c991f8fbf feat(frontends/lean): parse and pretty print tuples/pairs 
This commit also fixes a bug in the type checker when processing dependent pairs.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-03 20:10:30 -08:00
Leonardo de Moura
5e5ab1429d feat(frontends/lean): parse and pretty print sigma types 
This commit also fixes some bugs in the implementation of Sigma types.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-02-03 18:16:00 -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
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
2aaded261e fix(kernel/environment): imported predicate 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-30 23:02:19 -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
8c1f6b9055 fix(kernel/typechecker): allow elaborator to infer (Type U+1) 
In the new test elab8.lean, the parameter B is in (Type U+1).
Before, this commit, the type checker was forcing all metavariables that must be types to be <= (Type U). This restriction was preventing the elaborator from succeeding in reasonable cases.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-30 14:00:01 -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
24452289dd feat(library/simplifier): make sure the simplifier can handle meta-variables 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-28 20:30:47 -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
55fde28954 feat(kernel/type_checker): optionally provide metavariable environment in the methods: is_definitionally_equal, is_convertible and ensure_pi 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-27 17:47:03 -08:00
Leonardo de Moura
160dc71cb5 refactor(kernel/type_checker): use read-only metavariable environment in methods that do not require write access to the metavariable environment 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-27 17:38:06 -08:00
Leonardo de Moura
05b4d8411b refactor(kernel/normalizer): normalizer only needs read access to metavariable environment 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-27 17:03:36 -08:00
Leonardo de Moura
3b152d1a9e refactor(kernel): use ro_metavar_env instead of metavar_env in places where we only need to read the metavariable environment 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-27 16:44:43 -08:00
Leonardo de Moura
b26035fcf6 feat(kernel/type_checker): improve application type mismatch error messages 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-27 09:45:17 -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
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
26bea77721 fix(library/simplifier): bug in heterogeneous equality support, and universe commutativity support in the simplifier 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-24 17:09:46 -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
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
029d74ec11 chore(kernel): remove comment, we decided to have Eta as a simplification rule 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-21 14:35:05 -08:00
Leonardo de Moura
95b6e61738 feat(kernel/max_sharing): check for imminent stack overflows and interruptions in the expression sharing maximizer 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-21 14:33:49 -08:00
Leonardo de Moura
2089b85532 refactor(kernel/instantiate): remove code duplication 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-21 14:30:38 -08:00
Leonardo de Moura
7299b2d5d6 chore(kernel): remove dead file 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-21 14:21:13 -08:00
Leonardo de Moura
6bcd8e3ee5 fix(library/expr_lt): use expression depth instead of size to obtain a monotonic total order on terms 
It is not incorrect to use size, but it can easily overflow due to sharing.
The following script demonstrates the problem:

local f = Const("f")
local a = Const("a")
function mk_shared(d)
   if d == 0 then
      return a
   else
      local c = mk_shared(d-1)
      return f(c, c)
   end
end
print(mk_shared(33):size())

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-20 17:40:49 -08:00
Leonardo de Moura
217e56ea03 feat(kernel/expr): make sure semantic attachments are smaller than other kinds of expression 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-20 14:10:44 -08:00
Leonardo de Moura
5060bdbf14 fix(kernel/expr): compilation warning 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-20 13:12:49 -08:00
Leonardo de Moura
ac9f8f340d feat(kernel/expr): add efficient get_size() function for expressions 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-20 12:28:37 -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
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
39c3b17eb7 feat(library/simplifier): add support for Eta-reduction in the simplifier 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-01-19 00:40:35 -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
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