Commit graph

2080 commits

Author SHA1 Message Date
Leonardo de Moura
f28c56b188 feat(builtin/num): add auxiliary definitions and theorems for proving the primitive recursion theorem
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-08 19:36:17 -08:00
Leonardo de Moura
fa4b60963b feat(builtin/num): define lt predicate, and prove basic theorems
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-08 10:57:17 -08:00
Leonardo de Moura
0760b5b53d doc(todo): update todo list 2014-02-08 09:23:56 -08:00
Leonardo de Moura
ded72f94b2 doc(todo): update todo list 2014-02-08 09:23:13 -08:00
Leonardo de Moura
1f3e0f7a38 chore(builtin/num): update object file
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-08 09:16:52 -08:00
Leonardo de Moura
aeaa803f9a feat(builtin): add num type (the base type that will be used to build nat, int, real)
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-08 09:12:53 -08:00
Leonardo de Moura
1c43020fc9 fix(library/tactic/goal): bug creating main proof builder
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-08 09:11:07 -08:00
Leonardo de Moura
24528ff685 fix(library/elaborator): fix glitches in the elaborator that were forcing us to provide parameters explicitly
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-07 18:02:08 -08:00
Leonardo de Moura
1ec01f5757 refactor(builtin): merge pair.lean with kernel.lean, and add basic theorems
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-07 16:04:44 -08:00
Leonardo de Moura
5454e2af32 doc(todo): remove item from todo list
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-07 15:04:10 -08:00
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
354d5607af chore(builtin/sum): cleanup
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 21:25:57 -08:00
Leonardo de Moura
d4b08fcf96 feat(library/elaborator): be 'lazy' when normalizing terms in the elaborator
Unification constraints of the form

         ctx |- ?m[inst:i v] == T

         and

         ctx |- (?m a1 ... an) == T

are delayed by elaborator because the produce case-splits.
On the other hand, the step that puts terms is head-normal form is eagerly applied.
This is a bad idea for constraints like the two above. The elaborator will put T in head normal form
before executing process_meta_app and process_meta_inst. This is just wasted work, and creates
fully unfolded terms for solvers and provers.

The new test demonstrates the problem. In this test, we mark several terms as non-opaque.
Without this commit, the produced goal is a huge term.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 21:08:00 -08:00
Leonardo de Moura
ff955f9830 chore(frontends/lean/parser): update comments
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 20:56:31 -08:00
Leonardo de Moura
593f1f2ebd fix(frontends/lean): allow user set constants defined in other namespaces as opaque
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 20:56:31 -08:00
Leonardo de Moura
363c4dc5c2 feat(library/elaborator): improve support for dependent pairs in the elaborator
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 20:56:31 -08:00
Leonardo de Moura
5efc60d1f1 doc(todo): add another item to todo list 2014-02-06 18:07:06 -08:00
Leonardo de Moura
4b4b5e3345 fix(frontends/lean): import explicit versions when using the command 'using'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 17:33:58 -08:00
Leonardo de Moura
ea06bb2885 feat(frontends/lean/pp): change how lift local entries are pretty printed
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 17:26:38 -08:00
Leonardo de Moura
a51139e63b feat(frontends/lean): position information in error messages
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 17:26:38 -08:00
Leonardo de Moura
e85b1f1ac0 feat(library/elaborator): expose elaborator configuration options
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 17:26:38 -08:00
Leonardo de Moura
45ef10e2c1 doc(todo): update todo list 2014-02-06 17:01:30 -08:00
Leonardo de Moura
e4579b93e4 fix(library/elaborator): try first projection before imitation in the higher-order unifier
Projections build more general solutions. This commit also adds a test that demonstrates the issue. Before this commit, the elaborator would produce the "constant" predicate (fun x, a + b = b + a).

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 13:35:05 -08:00
Leonardo de Moura
ef321e730f feat(builtin/tactic): add the 'skip' (bogus) tactic for ignoring a proof hole in a big proof
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 12:47:23 -08:00
Leonardo de Moura
eab0456b27 test(tests/lean): test super opaque style
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 11:33:27 -08:00
Leonardo de Moura
581ae0c83b chore(build): fix build dependencies
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 09:30:33 -08:00
Leonardo de Moura
db3bcdba55 refactor(builtin): move pair definition and theorems to pair.lean
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 09:20:52 -08:00
Leonardo de Moura
daf7075ce4 refactor(builtin/sum): use new 'have' expression to formalize optional-types
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 09:15:12 -08:00
Leonardo de Moura
5d698a60a7 refactor(builtin/sum): use new 'have' expression to formalize sum-types
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 08:59:05 -08:00
Leonardo de Moura
fdc4c9b53c test(tests/lean): add nested 'have' expression test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 08:13:04 -08:00
Leonardo de Moura
1d23d93e60 feat(frontends/lean): new 'have' expression
Add 'have' notation suggested by Jeremy Avigad.
Add his example to the test suite.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 08:03:59 -08:00
Leonardo de Moura
ba9a8f9d98 feat(frontends/lean): add 'show' expression syntax sugar
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 07:50:22 -08:00
Leonardo de Moura
90f5a4f813 feat(builtin/sum): cleanup, and avoid unicode character that is not available in some platforms
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 00:20:49 -08:00
Leonardo de Moura
c01f82aeb7 feat(builtin): add sum types
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-05 23:04:44 -08:00
Leonardo de Moura
419fb7464e fix(tests/lean): adjust tests to reflect recent changes
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-05 21:04:06 -08:00
Leonardo de Moura
87da23649b feat(builtin/optional): prove dichotomy and induction theorems for optional types
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-05 19:49:50 -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
aec9c84d0d fix(util/lua): deadlock
Errors in the Lua library produce longjmps.
The longjmp will not unwind the C++ stack.
In the new test, the lock was not being released, and the system was deadlocking in the next call that tried to lock the environment

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-04 15:16:29 -08:00
Leonardo de Moura
f4ec874c6e refactor(builtin): remove dead module heq
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-04 14:42:28 -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
493007b7bc fix(frontends/lean/pp): bug in tuple/pair pretty printing
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-04 13:58:01 -08:00
Leonardo de Moura
f03c09c10b feat(library/elaborator): add support for proj/pair/sigma in the the higher-order unification procedure
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-04 13:53:30 -08:00
Leonardo de Moura
413391b2b4 chore(tests/lean/sig2): remove unnecessary parenthesis from test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-04 11:37:08 -08:00
Leonardo de Moura
c9b72df34b fix(frontends/lean/parser): bug when applying tactics to synthesize remaining meta-variables
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-04 11:36:26 -08:00
Leonardo de Moura
96c9c7505a test(tests/lean): add another sigma-type test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-04 10:12:39 -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
61d0c792ff fix(frontends/lean/parser): bug in tuple/proj1/proj2
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-03 22:46:29 -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