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 extension does not have to be provided.
- It can also import Lua files.
- Hierachical names can be used instead of strings.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The idea is to allow users to define their own commands using Lua.
The builtin command Find is now written in Lua.
This commit also fixes a bug in the get_formatter() Lua API.
It also adds String arguments to macros.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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>
The parser had a nasty ambiguity. For example,
f Type 1
had two possible interpretations
(f (Type) (1))
or
(f (Type 1))
To fix this issue, whenever we want to specify a particular universe, we have to precede 'Type' with a parenthesis.
Examples:
(Type 1)
(Type U)
(Type M + 1)
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>
The modifications started at commit 1852c86948 made a big difference. For example, before these changes test tests/lean/implicit7.lean generated complicated constraints such as:
[x : Type; a : ?M::29[inst:1 ?M::0[lift:0:1]] x] ⊢ Pi B : Type, (Pi _ : x, (Pi _ : (?M::35[inst:0 #0, inst:1 #2, inst:2 #4, inst:3 #6, inst:5 #5, inst:6 #7, inst:7 #9, inst:9 #9, inst:10 #11, inst:13 ?M::0[lift:0:13]] x a B _), (?M::36[inst:1 #1, inst:2 #3, inst:3 #5, inst:4 #7, inst:6 #6, inst:7 #8, inst:8 #10, inst:10 #10, inst:11 #12, inst:14 ?M::0[lift:0:14]] x a B _ _))) ≈
?M::22 x a
After the changes, only very simple constraints are generated. The most complicated one is:
[] ⊢ Pi a : ?M::0, (Pi B : Type, (Pi _ : ?M::0, (Pi _ : B, ?M::0))) ≈ Pi x : ?M::17, ?M::18
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>
Remark: on Windows, Ctrl-D does not seem to work.
So, this commit also changes the Lean startup message.
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>
When using tactics for proving theorems, a common pattern is
Theorem T : <proposition> := _.
apply <tactic>.
...
done.
This commit allows the user to write the simplified form:
Theorem T : <proposition>.
apply <tactic>.
...
done.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
In expression code blocks, we do not have to write a "return".
After this commit, the argument of an apply command is a Lua expression instead of a Lua block of code. That is, we can now write
apply (** REPEAT(ORELSE(imp_tactic, conj_tactic, conj_hyp_tactic, assumption_tactic)) **)
instead of
apply (** return REPEAT(ORELSE(imp_tactic, conj_tactic, conj_hyp_tactic, assumption_tactic)) **)
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
For example, after this commit, we can write
simple_tac = REPEAT(ORELSE(imp_tactic, conj_tactic)) .. assumption_tactic
instead of
simple_tac = REPEAT(ORELSE(imp_tactic(), conj_tactic())) .. assumption_tactic()
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The unlock_guard and exec_unprotected will be useful also for implementing the Lua tactic API.
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>
copy_values is not a big if-then-else anymore.
Before this change, whenever we added a new kind of userdata, we would have to update copy_values.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
Lua API is an integral part of Lean. It does *not* have the same status
of external APIs (e.g., Python) we will add in the future.
We will reserve the directory bindings for external APIs for using Lean
as a library.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The idea is to make it clear that io_state is distinguish it from proof_state, and from leanlua_state.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
The main motivation is to break the remove the dependency frontends/lean <-- bindings/lua.
This dependency is undesirable because we want to expose the frontends/lean parser and pretty printer objects at bindings/lua.
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 token }} is a bad delimiter for blocks of Lua script code nested in Lean files.
The problem is that the sequence }} occurs very often in Lua code because Lua uses { and } to build tables/lists/arrays.
Here is an example of Lua code that contains the sequence }}
t = {{1, 2}, {2, 3}, {3, 4}}
In Lean, (* ... *) is used to create comments. Thus, (** ... **) code blocks will not affect
valid Lean files. It also looks reasonably good.
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>
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>
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>
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>
