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>
This commit also adds several new theorems that are useful for implementing the simplifier.
TODO: perhaps we should remove the declarations at basic_thms.h?
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The environment object is a "smart-pointer".
Before this commit, the use of "const &" for environment objects was broken.
For example, suppose we have a function f that should not modify the input environment.
Before this commit, its signature would be
void f(environment const & env)
This is broken, f's implementation can easilty convert it to a read-write pointer by using
the copy constructor.
environment rw_env(env);
Now, f can use rw_env to update env.
To fix this issue, we now have ro_environment. It is a shared *const* pointer.
We can convert an environment into a ro_environment, but not the other way around.
ro_environment can also be seen as a form of documentation.
For example, now it is clear that type_inferer is not updating the environment, since its constructor takes a ro_environment.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
After this commit, a value of type 'expr' cannot be a reference to nullptr.
This commit also fixes several bugs due to the use of 'null' expressions.
TODO: do the same for kernel objects, sexprs, etc.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
I also reduced the stack size to 8 Mb in the tests at tests/lean and tests/lean/slow. The idea is to simulate stackoverflow conditions.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
operator bool() may produce unwanted conversions.
For example, we had the following bug in the code base.
...
object const & obj = find_object(const_name(n));
if (obj && obj.is_builtin() && obj.get_name() == n)
...
obj.get_name() has type lean::name
n has type lean::expr
Both have 'operator bool()', then the compiler uses the operator to
convert them to Boolean, and then compare the result.
Of course, this is not our intention.
After this commit, the compiler correctly signs the error.
The correct code is
...
object const & obj = find_object(const_name(n));
if (obj && obj.is_builtin() && obj.get_name() == const_name(n))
...
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The new hash code has the property that given expr_cell * c1 and expr_cell * c2,
if c1 != c2 then there is a high propbability that c1->hash_alloc() != c2->hash_alloc().
The structural hash code hash() does not have this property because we may have
c1 != c2, but c1 and c2 are structurally equal.
The new hash code is only compatible with pointer equality.
By compatible we mean, if c1 == c2, then c1->hash_alloc() == c2->hash_alloc().
This property is obvious because hash_alloc() does not have side-effects.
The test tests/lua/big.lua exposes the problem fixed by this commit.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
Instead of having m_interrupted flags in several components. We use a thread_local global variable.
The new approach is much simpler to get right since there is no risk of "forgetting" to propagate
the set_interrupt method to sub-components.
The plan is to support set_interrupt methods and m_interrupted flags only in tactic objects.
We need to support them in tactics and tacticals because we want to implement combinators/tacticals such as (try_for T M) that fails if tactic T does not finish in M ms.
For example, consider the tactic:
try-for (T1 ORELSE T2) 5
It tries the tactic (T1 ORELSE T2) for 5ms.
Thus, if T1 does not finish after 5ms an interrupt request is sent, and T1 is interrupted.
Now, if you do not have a m_interrupted flag marking each tactic, the ORELSE combinator will try T2.
The set_interrupt method for ORELSE tactical should turn on the m_interrupted flag.
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>
For example, this feature is useful when displaying the integer value 10 with coercions enabled. In this case, we want to display "nat_to_int 10" instead of "10".
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>
- Use hierarchical names instead of unsigned integers to identify metavariables.
- Associate type with metavariable.
- Replace metavar_env with substitution.
- Rename meta_ctx --> local_ctx
- Rename meta_entry --> local_entry
- Disable old elaborator
- Rename unification_problems to unification_constraints
- Add metavar_generator
- Fix metavar unit tests
- Modify type checker to use metavar_generator
- Fix placeholder module
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
Fix (relevant) warnings produced by http://cppcheck.sourceforge.net.
Most warnings produced were incorrect. The tool does not seem to support some of the C++11 new features.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
