lean2/tests/lean/elab1.lean.expected.out

  Set: pp::colors
  Set: pp::unicode
  Assumed: f
Failed to solve
 ⊢ Bool ≺ ℕ
    (line: 2: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
        @f
    with arguments:
        ℕ
        10
        ⊤
  Assumed: g
Error (line: 5, pos: 8) invalid expression, it still contains metavariables after elaboration, metavariable: ?M::1, type:
Type
  Assumed: h
Failed to solve
x : ?M::0, A : Type ⊢ ?M::0 ≺ A
    (line: 9: pos: 27) Type of argument 2 must be convertible to the expected type in the application of
        h
    with arguments:
        A
        x
  Assumed: my_eq
Failed to solve
A : Type, B : Type, a : ?M::0, b : ?M::1, C : Type ⊢ ?M::0[lift:0:3] ≺ C
    (line: 13: pos: 51) Type of argument 2 must be convertible to the expected type in the application of
        my_eq
    with arguments:
        C
        a
        b
  Assumed: a
  Assumed: b
  Assumed: H
Failed to solve
 ⊢ ?M::0 ⇒ ?M::3 ∧ a ≺ b
    (line: 18: pos: 18) Type of definition 't1' must be convertible to expected type.
Failed to solve
 ⊢ b == b ≺ a == b
    (line: 20: pos: 22) Type of argument 6 must be convertible to the expected type in the application of
        @trans
    with arguments:
        ?M::1
        a
        a
        b
        refl a
        refl b
Failed to solve
 ⊢ ?M::1 ≺ Type
    (line: 22: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
        @f
    with arguments:
        ?M::0
        Bool
        Bool
Error (line: 25, pos: 31) unknown identifier 'EM'
-												Improve elaborator error messages

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-04 20:21:57 +00:00
+								  Set: pp::colors
 								  Set: pp::unicode
 								  Assumed: f
-												fix(tests/lean): adjust error messages in the expected output

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-25 02:08:35 +00:00
+								Failed to solve
-												refactor(builtin): only load the kernel and natural numbers by default

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-12-30 21:35:37 +00:00
+								 ⊢ Bool ≺ ℕ
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								    (line: 2: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
-												feat(kernel, library/elaborator, frontends/lean): improve how elaborator_exceptions are displayed in the Lean frontend

This commit affects different modules.
I used the following approach:
1- I store the metavariable environment at unification_failure_justifications. The idea is to capture the set of instantiated metavariables at the time of failure.
2- I added a remove_detail function. It removes propagation steps from the justification tree object. I also remove the backtracking search space associated with higher-order unificiation. I keep only the search related to case-splits due to coercions and overloads.

3- I use the metavariable environment captured at step 1 when pretty printing the justification of an elaborator_exception.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-04 01:13:10 +00:00
+								        @f
 								    with arguments:
 								        ℕ
 
 								        ⊤
-												Improve elaborator error messages

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-04 20:21:57 +00:00
+								  Assumed: g
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								Error (line: 5, pos: 8) invalid expression, it still contains metavariables after elaboration, metavariable: ?M::1, type:
-												feat(frontends/lean): improve error messages when elaborator cannot instantiate all metavariables

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-12-21 06:00:50 +00:00
+								Type
-												Improve elaborator error messages

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-04 20:21:57 +00:00
+								  Assumed: h
-												fix(tests/lean): adjust error messages in the expected output

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-25 02:08:35 +00:00
+								Failed to solve
-												feat(kernel/metavar): make sure that a metavariable 'm' can only be assigned to a term that contains free variables available in the context associated with 'm'

This commit also simplifies the method check_pi in the type_checker and type_inferer.
It also fixes process_meta_app in the elaborator.
The problem was in the method process_meta_app and process_meta_inst.
They were processing convertability constrains as equality constraints.
For example, process_meta_app would handle

    ctx |- Type << ?f b

as

    ctx |- Type =:= ?f b

This is not correct because a ?f that returns (Type U) for b satisfies the first but not the second.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-12-14 20:25:00 +00:00
+								x : ?M::0, A : Type ⊢ ?M::0 ≺ A
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								    (line: 9: pos: 27) Type of argument 2 must be convertible to the expected type in the application of
-												fix(tests/lean): adjust error messages in the expected output

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-25 02:08:35 +00:00
+								        h
 								    with arguments:
 								        A
 								        x
-												refactor(equality): make homogeneous equality the default equality

It was not a good idea to use heterogeneous equality as the default equality in Lean.
It creates the following problems.

- Heterogeneous equality does not propagate constraints in the elaborator.
For example, suppose that l has type (List Int), then the expression
     l = nil
will not propagate the type (List Int) to nil.

- It is easy to write false. For example, suppose x has type Real, and the user
writes x = 0. This is equivalent to false, since 0 has type Nat. The elaborator cannot introduce
the coercion since x = 0 is a type correct expression.

Homogeneous equality does not suffer from the problems above.
We keep heterogeneous equality because it is useful for generating proof terms.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-29 23:20:02 +00:00
+								  Assumed: my_eq
-												fix(tests/lean): adjust error messages in the expected output

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-25 02:08:35 +00:00
+								Failed to solve
-												refactor(kernel/metavar): avoid using unique names for default metavariable prefix

The problem is that unique names depend on the order compilation units are initialized. The order of initialization is not specified by the C++ standard. Then, different compilers (or even the same compiler) may produce different initialization orders, and consequently the metavariable prefix is going to be different for different builds. This is not a bug, but it makes unit tests to fail since the output produced by different builds is different for the same input file.
Avoiding unique name feature in the default metavariable prefix avoids this problem.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-11-07 18:16:22 +00:00
+								A : Type, B : Type, a : ?M::0, b : ?M::1, C : Type ⊢ ?M::0[lift:0:3] ≺ C
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								    (line: 13: pos: 51) Type of argument 2 must be convertible to the expected type in the application of
-												refactor(equality): make homogeneous equality the default equality

It was not a good idea to use heterogeneous equality as the default equality in Lean.
It creates the following problems.

- Heterogeneous equality does not propagate constraints in the elaborator.
For example, suppose that l has type (List Int), then the expression
     l = nil
will not propagate the type (List Int) to nil.

- It is easy to write false. For example, suppose x has type Real, and the user
writes x = 0. This is equivalent to false, since 0 has type Nat. The elaborator cannot introduce
the coercion since x = 0 is a type correct expression.

Homogeneous equality does not suffer from the problems above.
We keep heterogeneous equality because it is useful for generating proof terms.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-29 23:20:02 +00:00
+								        my_eq
-												fix(tests/lean): adjust error messages in the expected output

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-25 02:08:35 +00:00
+								    with arguments:
 								        C
 								        a
 								        b
-												Improve elaborator error messages

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-04 20:21:57 +00:00
+								  Assumed: a
 								  Assumed: b
 								  Assumed: H
-												fix(library/elaborator): strength elaborator procedure for handling equality and convertability constraints

This commit improves the condition for showing that an equality(and convertability) constraint cannot be solved. A nice consequence is that Lean produces nicer error messages. For example, the error message for unit test elab1.lean is more informative.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-12-06 21:04:26 +00:00
+								Failed to solve
-												feat(library/elaborator): only expand definitions that are not marked as hidden

The elaborator produces better proof terms. This is particularly important when we have to prove the remaining holes using tactics.
For example, in one of the tests, the elaborator was producing the sub-expression

 (λ x : N, if ((λ x::1 : N, if (P a x x::1) ⊥ ⊤) == (λ x : N, ⊤)) ⊥ ⊤)

After, this commit it produces

 (λ x : N, ¬ ∀ x::1 : N, ¬ P a x x::1)

The expressions above are definitionally equal, but the second is easier to work with.

Question: do we really need hidden definitions?
Perhaps, we can use only the opaque flag.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-12-20 10:16:41 +00:00
+								 ⊢ ?M::0 ⇒ ?M::3 ∧ a ≺ b
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								    (line: 18: pos: 18) Type of definition 't1' must be convertible to expected type.
-												feat(kernel): add unexpected_metavar_occurrence exception

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-25 02:56:44 +00:00
+								Failed to solve
-												feat(kernel, library/elaborator, frontends/lean): improve how elaborator_exceptions are displayed in the Lean frontend

This commit affects different modules.
I used the following approach:
1- I store the metavariable environment at unification_failure_justifications. The idea is to capture the set of instantiated metavariables at the time of failure.
2- I added a remove_detail function. It removes propagation steps from the justification tree object. I also remove the backtracking search space associated with higher-order unificiation. I keep only the search related to case-splits due to coercions and overloads.

3- I use the metavariable environment captured at step 1 when pretty printing the justification of an elaborator_exception.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-04 01:13:10 +00:00
+								 ⊢ b == b ≺ a == b
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								    (line: 20: pos: 22) Type of argument 6 must be convertible to the expected type in the application of
 								        @trans
-												feat(kernel, library/elaborator, frontends/lean): improve how elaborator_exceptions are displayed in the Lean frontend

This commit affects different modules.
I used the following approach:
1- I store the metavariable environment at unification_failure_justifications. The idea is to capture the set of instantiated metavariables at the time of failure.
2- I added a remove_detail function. It removes propagation steps from the justification tree object. I also remove the backtracking search space associated with higher-order unificiation. I keep only the search related to case-splits due to coercions and overloads.

3- I use the metavariable environment captured at step 1 when pretty printing the justification of an elaborator_exception.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-04 01:13:10 +00:00
+								    with arguments:
 								        ?M::1
 								        a
 								        a
 								        b
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								        refl a
 								        refl b
-												feat(kernel): add unexpected_metavar_occurrence exception

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-10-25 02:56:44 +00:00
+								Failed to solve
-												feat(kernel, library/elaborator, frontends/lean): improve how elaborator_exceptions are displayed in the Lean frontend

This commit affects different modules.
I used the following approach:
1- I store the metavariable environment at unification_failure_justifications. The idea is to capture the set of instantiated metavariables at the time of failure.
2- I added a remove_detail function. It removes propagation steps from the justification tree object. I also remove the backtracking search space associated with higher-order unificiation. I keep only the search related to case-splits due to coercions and overloads.

3- I use the metavariable environment captured at step 1 when pretty printing the justification of an elaborator_exception.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-04 01:13:10 +00:00
+								 ⊢ ?M::1 ≺ Type
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								    (line: 22: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
-												feat(kernel, library/elaborator, frontends/lean): improve how elaborator_exceptions are displayed in the Lean frontend

This commit affects different modules.
I used the following approach:
1- I store the metavariable environment at unification_failure_justifications. The idea is to capture the set of instantiated metavariables at the time of failure.
2- I added a remove_detail function. It removes propagation steps from the justification tree object. I also remove the backtracking search space associated with higher-order unificiation. I keep only the search related to case-splits due to coercions and overloads.

3- I use the metavariable environment captured at step 1 when pretty printing the justification of an elaborator_exception.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-04 01:13:10 +00:00
+								        @f
 								    with arguments:
 								        ?M::0
 								        Bool
 								        Bool
-												feat(*): change name conventions for Lean builtin libraries

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2014-01-06 03:10:21 +00:00
+								Error (line: 25, pos: 31) unknown identifier 'EM'