After this commit, in the type checker, when checking convertability, we first compute a normal form without expanding opaque terms.
If the terms are convertible, then we are done, and saved a lot of time by not expanding unnecessary definitions.
If they are not, instead of throwing an error, we try again expanding the opaque terms.
This seems to be the best of both worlds.
The opaque flag is a hint for the type checker, but it would never prevent us from type checking a valid term.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit also adds a new test that exposes the problem.
The scoped_map should not be used for caching values in the normalizer and type_checker. When we extend the context, the meaning of all variables is modified (we are essentially performing a lift). So, the values stored in the cache are not correct in the new context.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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>
This modification was motivated by a bug exposed by tst17 at tests/kernel/type_checker.
metavar_env is now a smart point to metavar_env_cell.
ro_metavar_env is a read-only smart pointer. It is useful to make sure we are using proof_state correctly.
example showing that the approach for caching metavar_env is broken in the type_checker
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>
This commit allows us to build Lean without the pthread dependency.
It is also useful if we want to implement multi-threading on top of Boost.
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>
The type checker (and type inferer) were not handling correctly Pi expressions where the type universe cannot be established due to the occurrence of metavariables. In this case, a max-constraint is created. The problem is that the domain and body of the Pi are in different contexts. The constrain generated before this commit was incorrect, it could contain a free variable. This commit fix the issue by using the context of the body, and lifting the free variables in the domain by 1.
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>
Recursive functions that may go very deep should invoke the function check_stack. It throws an exception if the amount of stack space is limited.
The function check_system() is syntax sugar for
check_interrupted();
check_stack();
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The following call sequence is possible:
C++ -> Lua -> C++ -> Lua -> C++
The first block of C++ is the Lean main function.
The main function invokes the Lua interpreter.
The Lua interpreter invokes a C++ Lean API.
Then the Lean API invokes a callback implemented in Lua.
The Lua callback invokes another Lean API.
Now, suppose the Lean API throws an exception.
We want the C++ exception to propagate over the mixed C++/Lua call stack.
We use the clone/rethrow exception idiom to achieve this goal.
Before this commit, the C++ exceptions were converted into strings
using the method what(), and then they were propagated over the Lua
stack using lua_error. A lua_error was then converted into a lua_exception when going back to C++.
This solution was very unsatisfactory, since all C++ exceptions were being converted into a lua_exception, and consequently the structure of the exception was being lost.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The directory bindings/lua was getting too big and had too many dependencies.
Moreover, it was getting too painful to edit/maintain two different places.
Now, the bindings for module X are in the directory that defines X.
For example, the bindings for util/name.cpp are located at util/name.cpp.
The only exception is the kernel. We do not want to inflate the kernel
with Lua bindings. The bindings for the kernel classes are located
at bindings/kernel_bindings.
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>
We need weak references to environment objects because the environment has a reference to the type_checker and the type_checker has a reference back to the environment. Before, we were breaking the cycle using an "environment const &". This was a dangerous hack because the environment smart pointer passed to the type_checker could be on the stack. The weak_ref is much safer.
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>
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>
We may miss solutions, but the solutions found are much more readable.
For example, without this option, for elaboration problem
Theorem Example4 (a b c d e : N) (H: (a = b ∧ b = e ∧ b = c) ∨ (a = d ∧ d = c)) : (h a c) = (h c a) :=
DisjCases H
(fun H1 : _,
let AeqC := Trans (Conjunct1 H1) (Conjunct2 (Conjunct2 H1))
in CongrH AeqC (Symm AeqC))
(fun H1 : _,
let AeqC := Trans (Conjunct1 H1) (Conjunct2 H1)
in CongrH AeqC (Symm AeqC))
the elaborator generates
Theorem Example4 (a b c d e : N) (H : a = b ∧ b = e ∧ b = c ∨ a = d ∧ d = c) : (h a c) = (h c a) :=
DisjCases
H
(λ H1 : if
Bool
(if Bool (a = b) (if Bool (if Bool (if Bool (b = e) (if Bool (b = c) ⊥ ⊤) ⊤) ⊥ ⊤) ⊥ ⊤) ⊤)
⊥
⊤,
let AeqC := Trans (Conjunct1 H1) (Conjunct2 (Conjunct2 H1)) in CongrH AeqC (Symm AeqC))
(λ H1 : if Bool (if Bool (a = d) (if Bool (d = c) ⊥ ⊤) ⊤) ⊥ ⊤,
let AeqC := Trans (Conjunct1 H1) (Conjunct2 H1) in CongrH AeqC (Symm AeqC))
The solution is correct, but it is not very readable. The problem is that the elaborator expands the definitions of \/ and /\.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
Motivations:
- We have been writing several comments of the form "... trace/justification..." and "this trace object justify ...".
- Avoid confusion with util/trace.h
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This normalization rule is not really a computational rule.
It is essentially encoding the reflexivity axiom as computation.
It can also be abaused. For example, with this rule,
the following definition is valid:
Theorem Th : a = a := Refl b
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The printer and formatter objects are not trusted code.
We moved them to the kernel to be able to provide them as an argument to the trace objects.
Another motivation is to eliminate the kernel_exception_formatter hack.
With the formatter in the kernel, we can implement the pretty printer for kernel exceptions as a virtual method.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
Trace objects will be used to justify steps performed by engines such as the elaborator. We use them to implement non-chronological backtracking in the elaborator. They are also use to justify to the user why something did not work.
The unification constraints are in the kernel because the type checker may create them when type checking a term containing metavariables.
Remark: a minimalistic kernel does not need to include metavariables, unification constraints, nor trace objects. We include these objects in our kernel to minimize code duplication.
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>
The actual implementation of these two operators is outside of the
kernel. They are implemented in the file 'library/printer.cpp'.
We declare them in the kernel to prevent the following problem.
Suppose there is a file 'foo.cpp' that does not include
'library/printer.h', but contains
expr a;
...
std::cout << a << "\n";
...
The compiler does not generate an error message. It silently uses the
operator bool() to coerce the expression into a Boolean. This produces
counter-intuitive behavior, and may confuse developers.
