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>
Before this commit, the elaborator would only assign ?M <- P, if P was normalized. This is bad since normalization may "destroy" the structure of P.
For example, consider the constraint
[a : Bool; b : Bool; c : Bool] ⊢ ?M::1 ≺ implies a (implies b (and a b))
Before this, ?M::1 will not be assigned to the "implies-term" because the "implies-term" is not normalized yet.
So, the elaborator would continue to process the constraint, and convert it into:
[a : Bool; b : Bool; c : Bool] ⊢ ?M::1 ≺ if Bool a (if Bool b (if Bool (if Bool a (if Bool b false true) true) false true) true) true
Now, ?M::1 is assigned to the term
if Bool a (if Bool b (if Bool (if Bool a (if Bool b false true) true) false true) true) true
This is bad, since the original structure was lost.
This commit also contains an example that only works after the commit is applied.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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>
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>
It is incorrect to apply substitutions during normalization.
The problem is that we do not have support for tracking justifications in the normalizer. So, substitutions were being silently applied during normalization. Thus, the correctness of the conflict resolution in the elaboration was being affected.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
We need that when we normalize the assignment in a metavariable environment.
That is, we replace metavariable in a substitution with other assignments.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
