Commit graph

456 commits

Author SHA1 Message Date
Leonardo de Moura
41f5e2a067 feat(library/simplifier): statically check (conditional) equations (aka rewrite rules) to verify whether we can skip type checking when using them in the simplifier
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 18:32:40 -08:00
Leonardo de Moura
4f3127d3d5 fix(library/simplifier): check if the given types are convertible to ceq expected types
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 15:15:55 -08:00
Leonardo de Moura
a19f9d4846 feat(library/simplifier): discard conditional equations that are clearly non-terminating
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 13:56:45 -08:00
Leonardo de Moura
dd6aae378f fix(library/simplifier): must use metavar_env in is_ceq, otherwise it may ceqs that contain metavariables
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 13:29:20 -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
92ba4e8b2d feat(library/simplifier): add support for metavariables in conditional rewrite rules
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 08:34:04 -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
ee4344076e feat(library/simplifier): improve error message when simplifier is looping
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-28 19:36:31 -08:00
Leonardo de Moura
b31ef34787 feat(library/simplifier): preserve binder names when applying higher-order rewrite rules
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-28 00:50:27 -08:00
Leonardo de Moura
6da1b447f0 fix(library/hop_match): do not match iff with =
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-28 00:21:05 -08:00
Leonardo de Moura
dbdbd211e3 fix(library/simplifier): compilation warning
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-27 23:29:53 -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
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
8bccfb947a feat(library/simplifier): expose simplier and simplifier_monitor objects in the Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-27 15:02:05 -08:00
Leonardo de Moura
c088825ef0 feat(library/simplifier): add simplifier_monitor interface
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-27 11:46:28 -08:00
Leonardo de Moura
579b751e01 fix(library/simplifier): compilation warning
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 23:16:24 -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
50df761d90 refactor(library/simplifier): remove the is_typem hack, it is not needed anymore now that we don't use hpiext anymore
Now, we are again using the following invariant for simplifier_fn::result
The type of in the equality of the result is definitionally equal to the
type of the resultant expression.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 12:21:23 -08:00
Leonardo de Moura
29e448f034 fix(library/simplifier): remove support in the simplifier for (forall x : A, B x) when it is not a proposition, the problem is that hpiext axiom produces an equality in a too big universe
For example, in the hpiext axiom, the resultant equality if for (Type M+1)

axiom hpiext {A A' : TypeM} {B : A -> TypeM} {B' : A' -> TypeM} :
      A = A' -> (∀ x x', x == x' -> B x = B' x') -> (∀ x, B x) = (∀ x, B' x)

even if the actual arguments A, A’, B, B’ "live" in a much smaller universe (e.g., Type).

So, it would be great if we could move the resultant equality back to the right universe.
I don't see how to do it right now.

The other solution would require a major rewrite of the code base.
We would have to support universe level arguments like Agda, and write the axiom hpiext as:

axiom hpiext {l : level} {A A' : (Type l)} {B : A -> (Type l)} {B' : A' -> (Type l)} :
      A = A' -> (∀ x x', x == x' -> B x = B' x') -> (∀ x, B x) = (∀ x, B' x)

This is the first instance I found where it is really handy to have this feature.
I think this would be a super clean solution, but it would require a big rewrite in the code base.
Another problem is that the actual semantics that Agda has for this kind of construction is not clear to me.
For instance, sometimes Agda reports that the type of an expression is (Set omega).

An easier to implement hack is to support "axiom templates".
We create instances of hipext "on-demand" for different universe levels.
This is essentially what Coq does, since the universe levels are implicit in Coq.
This is not as clean as the Agda approach, but it is much easier to implement.

A super dirty trick is to include some instances of hpiext for commonly used universes
(e.g., Type and (Type 1)).

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 12:10:34 -08:00
Leonardo de Moura
52ee9b35dd feat(library/simplifier): add support for simplifying even when heq module is not available
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 11:29:36 -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
89bb5fbf19 chore(library/simplifier): fix style
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-26 00:36:17 -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
7015089734 fix(library/simplifier): move to locally nameless approach in the simplifier. Contextual simplification may add rewriting rules with free variables, and it is a mess to manage them when using de Bruijn indices
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 10:49:44 -08:00
Leonardo de Moura
df3129e80d fix(library/hop_match): typo
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 10:08:53 -08:00
Leonardo de Moura
7a4eb4b8ed feat(library/simplifier): contextual simplification for A -> B
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 22:32:55 -08:00
Leonardo de Moura
c2381e43f1 fix(library/simplifier): bug in cast elimination
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 21:25:09 -08:00
Leonardo de Moura
8e0888828d fix(library/simplifier): missing check in mk_hcongr_th
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:09:46 -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
180be5c4a2 feat(library/simplifier): improve contextual simplifications
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 13:11:58 -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
d6692264e8 feat(library/simplifier): contextual simplifications
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 12:23:22 -08:00
Leonardo de Moura
17cce340f6 fix(library/elaborator): in optimization for metavariable free terms
The optimization was incorrect if the term indirectly contained a metavariable.
It could happen if the term contained a free variable that was assigned in the context to a term containing a metavariable.

This commit also adds a new test that exposes the problem.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 18:06:00 -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
425d31f513 chore(library/simplifier): fix style warning
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 21:45:55 -08:00
Leonardo de Moura
cca15f1390 feat(library/simplifier): congruence theorem compilation
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 21:16:23 -08:00
Leonardo de Moura
ead54bbf57 feat(library/simplifier): enforce max_steps option
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 12:12:17 -08:00
Leonardo de Moura
1ccfac5873 feat(library/simplifier): conditional rewriting
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 21:15:46 -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
cd19d4da01 feat(library/simplifier): memoize intermediate results
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 17:03:44 -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
56f5657ee7 fix(library/simplifier): ordered rewriting
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 13:13:16 -08:00
Leonardo de Moura
6a63ef3bc5 feat(library/expr_lt): make sure the total order on terms is monotonic
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 13:07:18 -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
913d893204 feat(library/simplifier): add support for 'permutation' rewrite rules
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 08:29:31 -08:00
Leonardo de Moura
8e90d17a0b fix(library/hop_match): style
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 23:28:12 -08:00