Commit graph

712 commits

Author SHA1 Message Date
Leonardo de Moura
3726688711 test(lua): add test to demonstrate the different between list(A) where A is a parameter, and where A is an index
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-20 12:17:16 -07:00
Leonardo de Moura
11fc917102 test(lua): add tests for improving kernel_bindings coverage
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-20 12:16:12 -07:00
Leonardo de Moura
c5e8c10c9d fix(library/normalize): bug in normalize
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-20 11:53:58 -07:00
Leonardo de Moura
fae07771ec test(lua): add more universe level expression tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-20 11:41:17 -07:00
Leonardo de Moura
8872d4a531 refactor(kernel): rename definition class to declaration
The name was misleading since not every declaration is a definition.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-20 10:41:38 -07:00
Leonardo de Moura
00b1a84051 feat(library/kernel_bindings): expose environment::for_each method in the Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-20 10:16:19 -07:00
Leonardo de Moura
9e55c8766f test(lua): add normalize and type_check tests for terms containing metavariables
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-20 09:56:27 -07:00
Leonardo de Moura
ddccca529a test(lua): add test for mutually recursive inductive type recursor/eliminator
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-20 09:41:50 -07:00
Leonardo de Moura
eb6807e1d3 test(lua): add another add_inductive example
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-19 17:48:35 -07:00
Leonardo de Moura
4f15240a71 test(lua): add tests for new Pi/Fun notation in Lua
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-19 17:17:15 -07:00
Leonardo de Moura
a72be5eea4 test(lua): add example suggested by Cody
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-19 17:06:19 -07:00
Leonardo de Moura
3e3d3c8380 feat(kernel/inductive): check in add_inductive whether the environment supports inductive datatypes or not
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-19 15:44:15 -07:00
Leonardo de Moura
a7aacaa782 feat(library/kernel_bindings): improve list_level support in the Lua interface
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-19 15:18:48 -07:00
Leonardo de Moura
48b436c1c8 test(lua): add Martin-lof identity type test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-19 13:42:49 -07:00
Leonardo de Moura
f3ed20a229 feat(kernel/inductive): add normalizer extension for inductive datatypes, add procedure for creating an standard (empty) Lean environment
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-19 12:52:25 -07:00
Leonardo de Moura
2aacb769dd feat(kernel/inductive): generate computational rules RHS for inductive datatypes
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-19 09:08:19 -07:00
Leonardo de Moura
28b70b4e04 feat(kernel/inductive): use nondependent elimination when the datatype is in Bool/Prop
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-18 15:39:48 -07:00
Leonardo de Moura
45252e2229 feat(kernel/inductive): add eliminator/recursor for inductive datatype declarations
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-18 14:17:57 -07:00
Leonardo de Moura
f53254b389 test(lua): fix n6.lua, and add more tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-18 13:52:16 -07:00
Leonardo de Moura
405b24861c feat(util/name): add methods append_after and append_before
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-18 13:49:24 -07:00
Leonardo de Moura
fcf94ad7c2 test(lua): add test for inductive datatype positivity check
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 20:12:55 -07:00
Leonardo de Moura
950d69b977 test(lua): add tests for exercising datatype validation code
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 20:10:45 -07:00
Leonardo de Moura
b5d07bec2e test(lua): add some comments to inductive datatype test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 19:30:43 -07:00
Leonardo de Moura
8fcb84c8f2 feat(kernel/inductive): finish inductive datatype declaration validation
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 19:19:32 -07:00
Leonardo de Moura
d03e35aaac feat(kernel/inductive): add datatype and introduction rules declarations to environment, and fix tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 13:59:06 -07:00
Leonardo de Moura
53e02a902c test(lua): add is_geq (for universe level) tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 13:42:12 -07:00
Leonardo de Moura
a85a6b685b feat(kernel/formatter): add binding_body_fresh, let_body_fresh, and simplify formatter
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 12:30:03 -07:00
Leonardo de Moura
5ce134e24e chore(kernel): binder => binding where appropriate
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 11:37:27 -07:00
Leonardo de Moura
3a0861bca7 test(lean): remove old test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 10:42:10 -07:00
Leonardo de Moura
9f06cd553e test(lean): remove tests using Lean old syntax and kernel
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 10:38:53 -07:00
Leonardo de Moura
989bcdc7ad test(lua): add inductive datatype simple tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 09:25:03 -07:00
Leonardo de Moura
4ec89e8561 feat(library/kernel_bindings): add sugar for level expressions in the Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-17 08:10:36 -07:00
Leonardo de Moura
755fac8114 test(lua): add test simulating HoTT compatible environment
Type.{0} is predicative
   Type.{0} is proof relevant
   Id       is proof irrelevant
   Path     is proof relevant

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-16 15:32:01 -07:00
Leonardo de Moura
69e72c278d feat(kernel): add proof irrelevance for classes
We can use this feature to implement proof irrelevance for Identity types.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-16 15:30:32 -07:00
Leonardo de Moura
193aa4a83f feat(library/kernel_bindings): improve Pi and Fun Lua APIs, and allow users to provide binder information
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-16 14:09:00 -07:00
Leonardo de Moura
40b3129e7b refactor(kernel): improve names
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-16 11:28:05 -07:00
Leonardo de Moura
924b2344af fix(lua/res1): make sure the test works with Lua 5.1
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-15 14:47:42 -07:00
Leonardo de Moura
da31e60b02 test(lua): add more tests for type checker
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-15 14:17:58 -07:00
Leonardo de Moura
90c4957071 test(lua): add tests for resolve macro
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-15 13:53:11 -07:00
Leonardo de Moura
7c0cc3111a fix(kernel/type_checker): we must use different caches for infer_type and check
The new test tc4.lua exposes the problem being fixed.
We need separate caches otherwise we may mistakenly assume that an expression was already checked by the type checker, while only its type was inferred.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-15 13:53:11 -07:00
Leonardo de Moura
6e78256b87 feat(library/kernel_bindings): expose is_bi_equal predicate in the Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-14 17:24:49 -07:00
Leonardo de Moura
606e6226c2 fix(kernel/type_checker): the type checker cache was not taking into account binder information
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-14 17:14:57 -07:00
Leonardo de Moura
2e1a0bd50c feat(kernel/expr): add is_contextual binder info
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-14 14:54:27 -07:00
Leonardo de Moura
52d682b832 test(lua): unit tests for let expressions
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-14 14:29:44 -07:00
Leonardo de Moura
e57b943adf test(lua): add constraint generation test when type checking with metavars
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-14 11:06:48 -07:00
Leonardo de Moura
eea561c74b test(lua): add more expr API unit tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-13 09:20:25 -07:00
Leonardo de Moura
cfa9520655 test(lua): add more level API unit tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-13 09:20:10 -07:00
Leonardo de Moura
9ed700a5a6 feat(kernel/environment): add forget method
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-13 08:40:46 -07:00
Leonardo de Moura
7b15e558a2 refactor(kernel/converter): implement eta in whnf instead of is_def_eq.
Without cumulativity, we do not have problems with Eta at whnf anymore.
When we had cumulativity, we could not not simply reduce
     (fun x : A, f x) ==> f
This step is correct only if domain(f) was definitionally equal to f.
Here is a problematic example for systems with cumulativity
Given, f : Type.{2} -> Bool
     (fun x : Type.{1}, f x)

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-12 17:49:53 -07:00
Leonardo de Moura
c883c638d6 feat(library/kernel_bindings): expose expression tags in the Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-12 16:50:43 -07:00
Leonardo de Moura
20947de2f1 test(lua): add replace method test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-12 15:51:22 -07:00
Leonardo de Moura
9f86aa73c8 test(lua): add basic universe level tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-12 14:51:18 -07:00
Leonardo de Moura
ff9004dae2 refactor(kernel): add level normalizer, is_equivalent predicate, switch to is_equivalent in the type checker, fix bugs in is_lt predicate
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-11 18:05:02 -07:00
Leonardo de Moura
9d96f24766 refactor(kernel): remove convertability constraints
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-09 20:25:27 -07:00
Leonardo de Moura
7b6d555433 refactor(kernel): remove level constraints from definitions
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-09 20:11:50 -07:00
Leonardo de Moura
a650a4f9b5 fix(library/kernel_bindings): bug in mk_app, add expr_lt tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-09 19:54:52 -07:00
Leonardo de Moura
21e3e22017 test(lua/threads): re-activate Lua thread examples
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-08 18:52:15 -07:00
Leonardo de Moura
129d108d0b test(lua): add example for testing is_descendant
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-08 18:50:24 -07:00
Leonardo de Moura
c843243f64 feat(library/kernel_bindings): add add_decl and type_check functions to Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-08 18:08:32 -07:00
Leonardo de Moura
5a7f181efc feat(util/name_set): improve name_set Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-08 17:17:00 -07:00
Leonardo de Moura
f3c7bc948a feat(library/kernel_bindings): type_checker Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-07 19:04:15 -07:00
Leonardo de Moura
1a8d75c4f0 feat(util): name_set Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-07 18:32:53 -07:00
Leonardo de Moura
7fe61bc69c feat(util): name_generator Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-07 17:28:11 -07:00
Leonardo de Moura
62db010ba3 feat(library/kernel_bindings): add optional arguments to empty_environment Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-07 17:06:27 -07:00
Leonardo de Moura
4c5f88e63b feat(library/kernel_bindings): global level constructor/accessor/recognizer
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-07 16:22:45 -07:00
Leonardo de Moura
8ae0e46e9d feat(library/kernel_bindings): add new global level methods to environment Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-07 16:17:04 -07:00
Leonardo de Moura
9bf83390dc test(lua): add definition API tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-02 17:01:22 -07:00
Leonardo de Moura
dc627c9965 test(lua): add constraint API tests, and fix minor bugs
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-02 13:37:46 -07:00
Leonardo de Moura
7b4b862faa test(lua): add justification API tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-02 12:16:24 -07:00
Leonardo de Moura
340c0e0945 feat(library/kernel_bindings): substitution Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-01 15:30:30 -07:00
Leonardo de Moura
305815cb56 feat(library/kernel_bindings): expose expr_binder_info in the Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-05-01 11:23:37 -07:00
Leonardo de Moura
97e7e4e762 test(lua): remove obsolete test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-04-29 17:08:50 -07:00
Leonardo de Moura
fd034521dc feat(library/kernel_bindings): cleanup level Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-04-29 17:05:25 -07:00
Leonardo de Moura
93a61748e9 fix(kernel/level): bug in optional<level>() constructor
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-04-29 17:00:57 -07:00
Leonardo de Moura
984048f40d feat(library/kernel_bindings): new level Lua API
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-04-29 15:08:58 -07:00
Leonardo de Moura
a6116e3156 test(lua): reactivate some of the Lua unit tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-04-29 10:36:57 -07:00
Leonardo de Moura
e9dada5e14 refactor(builtin/kernel): use standard definition for 'or' and 'and'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-17 12:05:34 -08:00
Leonardo de Moura
1739b5c153 fix(kernel/type_checker): caching bug
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-12 10:43:01 -08:00
Leonardo de Moura
368fcb5ff9 refactor(builtin/kernel): rename refute to by_contradiction
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-12 08:49:19 -08:00
Leonardo de Moura
b7b868de85 fix(library/elaborator): bug reported by Jeremy Avigad
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-10 14:01:22 -08:00
Leonardo de Moura
a2d2e36f04 refactor(frontends/lean): remove notation for creating tuples
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-10 09:03:42 -08:00
Leonardo de Moura
4317f67bd2 fix(builtin/tactic): more meaningful error message when skip tactic is used in a full proof
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-09 18:57:33 -08:00
Leonardo de Moura
c45c1748d8 refactor(builtin/kernel): reorder congr1 arguments
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-09 16:15:44 -08:00
Leonardo de Moura
8df7c7b02d feat(kernel/type_checker): remove fallback that expands opaque definitions in the type checker
We should not rely on this feature. It can be quite expensive.
We invoke is_convertible in several places, in particular, if we are using overloading. For example, the frontend uses is_convertible to check which overload should be used. Thus, it will make several calls such as

   is_convertible(num, Nat)

If is_convertible starts unfolding opaque definitions, we would keep expanding num.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-09 11:31:24 -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
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
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
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
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
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
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
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
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
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
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
cc96b50644 feat(frontends/lean): support for nary-tuples, improve notation for non-dependent tuples, add support in the elaborator for sigma types
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-03 20:53:11 -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
640ebcc040 test(tests/lean/exp): add example for Steve
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-03 11:35:40 -08:00
Leonardo de Moura
e4afa3dc43 fix(tests/lean/map): incorrect output
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-03 00:05:19 -08:00
Leonardo de Moura
87f9c9b27e fix(tests/lean/map): make sure the unit test produce the same result in different platforms
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-02 20:29:34 -08:00
Leonardo de Moura
e2add5c9f2 test(tests/lean): add heterogeneous equality simplification example
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-02 20:27:39 -08:00
Leonardo de Moura
6be50f0133 refactor(builtin/heq): merge cast and heq modules
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-02 15:01:48 -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
2b7bc7b673 test(tests/lean/exp): simulating HOL constructions
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-31 17:59:57 -08:00
Leonardo de Moura
e3dc552c39 fix(library/simplifier): nontermination
The example tests/lua/simp1.lua demonstrates the issue.
The higher-order matcher matches closed terms that are definitionally equal.
So, given a definition

    definition a := 1

it will match 'a' with '1' since they are definitionally equal.

Then, if we have a theorem

    theorem a_eq_1 : a = 1

as a rewrite rule, it was triggering the following infinite loop when simplifying the expression "a"

   a --> 1 --> 1 --> 1 ...

The first simplification is expected. The other ones are not.
The problem is that "1" is definitionally equal to "a", and they match.
The rewrite_rule_set manager accepts the rule a --> 1 since the left-hand-side does not occur in the right-hand-side.

To avoid this loop, we test if the new expression is not equal to the previous one.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-31 15:55:21 -08:00
Leonardo de Moura
1d85267d26 fix(library/simplifier): assumptions/context may contain equations where the left-hand-side is a metavariable or semantic attachment
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-31 15:38:22 -08:00
Leonardo de Moura
110ca84984 feat(library/simplifier): allow the user to associate a simplifier monitor with the lua_State object
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-31 13:49:24 -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
b45ab9dc30 feat(library/elaborator): use equality constraints instead of convertability constraints on definitions
Convertability constraints are harder to solve than equality constraints, and it seems they don't buy us anything definitions. They are just increasing the search space for the elaborator.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-30 14:13:21 -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
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
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
ea6bf224e5 feat(frontends/lean): make the parser accept (Type -> ...)
Before this commit, the parser would accept only a universe level or a ')' after '(' 'Type'

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 15:23:20 -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
0bb8fe75b3 test(tests/lean): new simplifier test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 14:21:18 -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
4dc3aa46c3 feat(frontends/lean): allow tactics to be used in axiom/variable declarations and in the type of definitions/theorems; add a new test showing the need for this feature
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 12:02:12 -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
62408a6adc test(tests/lean): move simp_loop test to slow subdirectory
This example produces a stackoverflow on Valgrind.
We don't execute Valgrind on tests in the slow subdirectory.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 10:32:48 -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
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
72c607846a test(tests/lean): add Jeremy's proof to test suite
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-28 16:05:46 -08:00
Leonardo de Moura
7f53cb9601 feat(frontends/lean/parser): add_rewrite take the 'using' command into account
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-28 01:15:28 -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
db45d02078 fix(tests/lean): test discrepancy on OSX
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-27 23:31:35 -08:00
Leonardo de Moura
7b88d68afb test(tests/lean): add test using simplifier monitor for tracking failures
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-27 15:11:16 -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
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
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
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
e8bba1ebf3 fix(frontends/lean/frontend): the definition of the explicit version @f must be definitionally equal to f
Before this commit, the explicit version @f of a constant f with implicit arguments as not definitionally equal to f.

For example, if we had

variable f {A : Type} : A -> Bool

Then, the definition of @f was

definition @f (A : Type) (a : A) : Bool := f A a

This definition is equivalent to
     fun A a, f A a
which is not definitionally equal to
     f
since definitionally equality in Lean ignores Eta conversion.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 20:34:28 -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
5b13ef1b90 test(tests/lean): new simplifier test
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-25 10:56:49 -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
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
35ad156a46 fix(tests/lean): make sure pretty print and parse test passes
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:23:55 -08:00
Leonardo de Moura
8f455f5965 fix(frontends/lean): bug in scope construct
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:23:29 -08:00
Leonardo de Moura
7f3e2b3ef4 fix(frontends/lean/parser): bug in 'using' construct
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-24 17:09:46 -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
1a3660180e test(tests/lean): add new simplifier test
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
cd87cb3de4 test(tests/lean): add test for congruence theorem that uses an argument before simplification
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 13:26:09 -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
5ba2525eab test(tests/lean): add test disabling contextual simplifications
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-23 12:57:05 -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
1638a7bb02 fix(frontends/lean/pp): compute local shared nodes, and avoid unnecessary let's
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-22 21:44:24 -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
331b5846c6 test(library/simplifier): add test for the single_pass option in the simplifier
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-21 13:47:54 -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
1ef75a9ba6 test(tests/lua): add test/example that demonstrates how to collect statistics of used theorems
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 18:04:22 -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
d1bd56b3d3 fix(tests/lean): adjust test to reflect recent changes
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 14:47:03 -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
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
5224df56a3 test(tests/lean): add example showing how to 'sort' argumentes of AC operators using the simplifier
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 08:36:48 -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
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
bcede6925f fix(tests/lean): add expected result file
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 16:31:35 -08:00
Leonardo de Moura
19f3c281c3 test(tests/lean): matrix multiplication example
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 16:29:32 -08:00
Leonardo de Moura
999984e701 fix(tests/lean): remove unnecessary theorems
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 12:55:33 -08:00
Leonardo de Moura
cc11b9e125 test(tests/lean): rewriting proof example
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 12:53:21 -08:00
Leonardo de Moura
d322f63113 feat(frontends/lea): add commands for creating and managing rewrite rule sets
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 12:03:59 -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
7492fd5a2c feat(library/simplifier): add support for simplification by evaluation
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 10:34:55 -08:00
Leonardo de Moura
11719713ec feat(library/hop_match): optionally unfold constants when performing higher order matching
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 10:32:06 -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
ed009f4c88 feat(kernel/simplifier): add support for Beta-reduction in the simplifier
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-19 00:40:20 -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
32c5bc25e3 refactor(library/simplifier): cleanup rewrite_rule_set, and use it in the simplifier
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-18 20:52:33 -08:00
Leonardo de Moura
feea96e84d feat(library/simplifier): add rewrite_rule_set extension for managing rewrite rules in an environment
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-18 15:43:24 -08:00
Leonardo de Moura
40b7ed13c2 fix(tests/lean): adjust tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-17 19:27:32 -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
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
5453a8f2f1 test(tests/lua): hop_match experiment
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-16 00:15:31 -08:00
Leonardo de Moura
3238c7e2a0 feat(library/simplifier): add is_permutation_ceq predicate
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 19:53:52 -08:00
Leonardo de Moura
2368c936d3 test(tests/lua): exercise fields method for semantic attachments
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 17:24:18 -08:00
Leonardo de Moura
57e58c598c fix(tests/lean): adjust tests to reflect recent changes
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 16:35:33 -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