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>
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>
This commit fixes a problem exposed by t13.lean.
It has a theorem of the form:
Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 := (show A by auto),
lemma2 := (show B by auto)
in (show B /\ A by auto)
When to_goal creates a goal for the metavariable associated with (show B /\ A by auto) it receives a context and proposition of the form
[ A : Bool, B : Bool, assumption : A /\ B, lemma1 := Conjunct1 assumption, lemma2 := Conjunct2 assumption ] |- B /\ A
The context_entries "lemma1 := Conjunct1 assumption" and "lemma2 := Conjunct2 assumption" do not have a domain (aka type).
Before this commit, to_goal would simply replace and references to "lemma1" and "lemma2" in "B /\ A" with their definitions.
Note that, "B /\ A" does not contain references to "lemma1" and "lemma2". Then, the following goal is created
A : Bool, B : Bool, assumption : A /\ B |- B /\ A
That is, the lemmas are not available when solving B /\ A.
Thus, the tactic auto produced the following (weird) proof for T1, where the lemmas are computed but not used.
Theorem T1 (A B : Bool) (assumption : A ∧ B) : B ∧ A :=
let lemma1 := Conjunct1 assumption,
lemma2 := Conjunct2 assumption
in Conj (Conjunct2 assumption) (Conjunct1 assumption)
This commit fixed that. It computes the types of "Conjunct1 assumption" and "Conjunct2 assumption", and creates the goal
A : Bool, B : Bool, assumption : A /\ B, lemma1 : A, lemma2 : B |- B /\ A
After this commit, the proof for theorem T1 is
Theorem T1 (A B : Bool) (assumption : A ∧ B) : B ∧ A :=
let lemma1 := Conjunct1 assumption,
lemma2 := Conjunct2 assumption
in Conj lemma2 lemma1
as expected.
Finally, this example suggests that the encoding
Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := (by auto),
lemma2 : B := (by auto)
in (show B /\ A by auto)
is more efficient than
Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 := (show A by auto),
lemma2 := (show B by auto)
in (show B /\ A by auto)
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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>
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>
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>
