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lean2/tests/lean/elab1.lean.expected.out
Leonardo de Moura 20a36e98ec feat(library/elaborator): modify how elaborator handles constraints of the form ?M << P and P << ?M, where P is a proposition. 
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>
2013-11-29 09:15:01 -08:00

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Set: pp::colors
Set: pp::unicode
Assumed: f
Failed to solve
⊢ (?M::1 ≈ λ x : ℕ, x) ⊕ (?M::1 ≈ nat_to_int) ⊕ (?M::1 ≈ nat_to_real)
(line: 4: pos: 8) Coercion for
10
Failed to solve
⊢ Bool ≺ ℕ
Substitution
⊢ Bool ≺ ?M::0
(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
?M::1 10
⊤
Assignment
⊢ ℕ ≺ ?M::0
Substitution
⊢ (?M::5[inst:0 (10)]) 10 ≺ ?M::0
(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
?M::1 10
⊤
Assignment
x : ℕ ⊢ λ x : ℕ, ℕ ≈ ?M::5
Destruct/Decompose
x : ℕ ⊢ ℕ ≈ ?M::5 x
Destruct/Decompose
⊢ ℕ → ℕ ≈ Π x : ?M::4, ?M::5 x
Substitution
⊢ ?M::3 ≈ Π x : ?M::4, ?M::5 x
Function expected at
?M::1 10
Assignment
⊢ ℕ → ℕ ≺ ?M::3
Propagate type, ?M::1 : ?M::3
Assignment
⊢ ?M::1 ≈ λ x : ℕ, x
Assumption 0
Failed to solve
⊢ Bool ≺ ℤ
Substitution
⊢ Bool ≺ ?M::0
(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
?M::1 10
⊤
Assignment
⊢ ℤ ≺ ?M::0
Substitution
⊢ (?M::5[inst:0 (10)]) 10 ≺ ?M::0
(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
?M::1 10
⊤
Assignment
_ : ℕ ⊢ λ x : ℕ, ℤ ≈ ?M::5
Destruct/Decompose
_ : ℕ ⊢ ℤ ≈ ?M::5 _
Destruct/Decompose
⊢ ℕ → ℤ ≈ Π x : ?M::4, ?M::5 x
Substitution
⊢ ?M::3 ≈ Π x : ?M::4, ?M::5 x
Function expected at
?M::1 10
Assignment
⊢ ℕ → ℤ ≺ ?M::3
Propagate type, ?M::1 : ?M::3
Assignment
⊢ ?M::1 ≈ nat_to_int
Assumption 1
Failed to solve
⊢ Bool ≺ ℝ
Substitution
⊢ Bool ≺ ?M::0
(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
?M::1 10
⊤
Assignment
⊢ ℝ ≺ ?M::0
Substitution
⊢ (?M::5[inst:0 (10)]) 10 ≺ ?M::0
(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
?M::1 10
⊤
Assignment
_ : ℕ ⊢ λ x : ℕ, ℝ ≈ ?M::5
Destruct/Decompose
_ : ℕ ⊢ ℝ ≈ ?M::5 _
Destruct/Decompose
⊢ ℕ → ℝ ≈ Π x : ?M::4, ?M::5 x
Substitution
⊢ ?M::3 ≈ Π x : ?M::4, ?M::5 x
Function expected at
?M::1 10
Assignment
⊢ ℕ → ℝ ≺ ?M::3
Propagate type, ?M::1 : ?M::3
Assignment
⊢ ?M::1 ≈ nat_to_real
Assumption 2
Assumed: g
Error (line: 7, pos: 8) unexpected metavariable occurrence
Assumed: h
Failed to solve
x : ?M::0, A : Type ⊢ ?M::0[lift:0:2] ≺ A
(line: 11: pos: 27) Type of argument 2 must be convertible to the expected type in the application of
h
with arguments:
A
x
Assumed: my_eq
Failed to solve
A : Type, B : Type, a : ?M::0, b : ?M::1, C : Type ⊢ ?M::0[lift:0:3] ≺ C
(line: 15: pos: 51) Type of argument 2 must be convertible to the expected type in the application of
my_eq
with arguments:
C
a
b
Assumed: a
Assumed: b
Assumed: H
Error (line: 22, pos: 0) failed to synthesize metavar, its type is not a proposition
Failed to solve
⊢ b ≈ a
Substitution
⊢ b ≈ ?M::3
Destruct/Decompose
⊢ b == b ≺ ?M::3 == ?M::4
(line: 22: pos: 22) Type of argument 6 must be convertible to the expected type in the application of
Trans::explicit
with arguments:
?M::1
?M::2
?M::3
?M::4
Refl a
Refl b
Assignment
⊢ a ≈ ?M::3
Destruct/Decompose
⊢ a == a ≺ ?M::2 == ?M::3
(line: 22: pos: 22) Type of argument 5 must be convertible to the expected type in the application of
Trans::explicit
with arguments:
?M::1
?M::2
?M::3
?M::4
Refl a
Refl b
Failed to solve
⊢ (?M::0 ≈ Type) ⊕ (?M::0 ≈ Type 1) ⊕ (?M::0 ≈ Type 2) ⊕ (?M::0 ≈ Type M) ⊕ (?M::0 ≈ Type U)
Destruct/Decompose
⊢ Type ≺ ?M::0
(line: 24: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Failed to solve
⊢ (?M::1 ≈ Type 1) ⊕ (?M::1 ≈ Type 2) ⊕ (?M::1 ≈ Type 3) ⊕ (?M::1 ≈ Type M) ⊕ (?M::1 ≈ Type U)
Destruct/Decompose
⊢ Type 1 ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ Type
Assumption 0
Failed to solve
⊢ Type 1 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 1
Assumption 1
Failed to solve
⊢ Type 2 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 2
Assumption 2
Failed to solve
⊢ Type 3 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 3
Assumption 3
Failed to solve
⊢ Type M ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type M
Assumption 4
Failed to solve
⊢ Type U ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type U
Assumption 5
Failed to solve
⊢ (?M::1 ≈ Type 2) ⊕ (?M::1 ≈ Type 3) ⊕ (?M::1 ≈ Type 4) ⊕ (?M::1 ≈ Type M) ⊕ (?M::1 ≈ Type U)
Destruct/Decompose
⊢ Type 2 ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ Type 1
Assumption 6
Failed to solve
⊢ Type 2 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 2
Assumption 7
Failed to solve
⊢ Type 3 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 3
Assumption 8
Failed to solve
⊢ Type 4 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 4
Assumption 9
Failed to solve
⊢ Type M ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type M
Assumption 10
Failed to solve
⊢ Type U ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type U
Assumption 11
Failed to solve
⊢ (?M::1 ≈ Type 3) ⊕ (?M::1 ≈ Type 4) ⊕ (?M::1 ≈ Type 5) ⊕ (?M::1 ≈ Type M) ⊕ (?M::1 ≈ Type U)
Destruct/Decompose
⊢ Type 3 ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ Type 2
Assumption 12
Failed to solve
⊢ Type 3 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 3
Assumption 13
Failed to solve
⊢ Type 4 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 4
Assumption 14
Failed to solve
⊢ Type 5 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type 5
Assumption 15
Failed to solve
⊢ Type M ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type M
Assumption 16
Failed to solve
⊢ Type U ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type U
Assumption 17
Failed to solve
⊢
(?M::1 ≈ Type M+1) ⊕ (?M::1 ≈ Type M+2) ⊕ (?M::1 ≈ Type M+3) ⊕ (?M::1 ≈ Type M) ⊕ (?M::1 ≈ Type U)
Destruct/Decompose
⊢ Type M+1 ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ Type M
Assumption 18
Failed to solve
⊢ Type M+1 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type M+1
Assumption 19
Failed to solve
⊢ Type M+2 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type M+2
Assumption 20
Failed to solve
⊢ Type M+3 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type M+3
Assumption 21
Failed to solve
⊢ Type M ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type M
Assumption 22
Failed to solve
⊢ Type U ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type U
Assumption 23
Failed to solve
⊢
(?M::1 ≈ Type U+1) ⊕ (?M::1 ≈ Type U+2) ⊕ (?M::1 ≈ Type U+3) ⊕ (?M::1 ≈ Type M) ⊕ (?M::1 ≈ Type U)
Destruct/Decompose
⊢ Type U+1 ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ Type U
Assumption 24
Failed to solve
⊢ Type U+1 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type U+1
Assumption 25
Failed to solve
⊢ Type U+2 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type U+2
Assumption 26
Failed to solve
⊢ Type U+3 ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type U+3
Assumption 27
Failed to solve
⊢ Type M ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type M
Assumption 28
Failed to solve
⊢ Type U ≺ Type
Substitution
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
f::explicit
with arguments:
?M::0
Bool
Bool
Assignment
⊢ ?M::1 ≈ Type U
Assumption 29
Failed to solve
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ a ≺ if (if a b ⊤) a ⊤
Normalize
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ a ≺ (a ⇒ b) ⇒ a
Substitution
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ a ≺ ?M::5[lift:0:1]
Substitution
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ ?M::8 ≺ ?M::5[lift:0:1]
Destruct/Decompose
a : Bool, b : Bool, H : ?M::2 ⊢ Π H_na : ?M::7, ?M::8 ≺ Π _ : ?M::4, ?M::5[lift:0:1]
(line: 27: pos: 21) Type of argument 6 must be convertible to the expected type in the application of
DisjCases::explicit
with arguments:
?M::3
?M::4
?M::5
EM a
λ H_a : ?M::6, H
λ H_na : ?M::7, NotImp1 (MT H H_na)
Assignment
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ a ≈ ?M::8
Destruct/Decompose
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ if a b ⊤ ≈ if ?M::8 ?M::9 ⊤
Normalize
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ if a b ⊤ ≈ ?M::8 ⇒ ?M::9
Substitution
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ if a b ⊤ ≈ ?M::10
Destruct/Decompose
a : Bool,
b : Bool,
H : ?M::2,
H_na : ?M::7 ⊢
if (if a b ⊤) a ⊤ ≺ if ?M::10 ?M::11 ⊤
Normalize
a : Bool,
b : Bool,
H : ?M::2,
H_na : ?M::7 ⊢
(a ⇒ b) ⇒ a ≺ if ?M::10 ?M::11 ⊤
Substitution
a : Bool,
b : Bool,
H : ?M::2,
H_na : ?M::7 ⊢
?M::2[lift:0:2] ≺ if ?M::10 ?M::11 ⊤
Normalize
a : Bool,
b : Bool,
H : ?M::2,
H_na : ?M::7 ⊢
?M::2[lift:0:2] ≺ ?M::10 ⇒ ?M::11
(line: 29: pos: 48) Type of argument 3 must be convertible to the expected type in the application of
MT::explicit
with arguments:
?M::10
?M::11
H
H_na
Normalize assignment
?M::0
Assignment
a : Bool, b : Bool ⊢ ?M::2 ≈ ?M::0
Destruct/Decompose
a : Bool,
b : Bool ⊢
Π H : ?M::2, ?M::5 ≺ Π _ : ?M::0, ?M::1[lift:0:1]
(line: 27: pos: 4) Type of argument 3 must be convertible to the expected type in the application of
Discharge::explicit
with arguments:
?M::0
?M::1
λ H : ?M::2,
DisjCases
(EM a)
(λ H_a : ?M::6, H)
(λ H_na : ?M::7, NotImp1 (MT H H_na))
Assignment
a : Bool, b : Bool ⊢ ?M::0 ≈ (a ⇒ b) ⇒ a
Destruct/Decompose
a : Bool, b : Bool ⊢ ?M::0 ⇒ ?M::1 ≺ ((a ⇒ b) ⇒ a) ⇒ a
Destruct/Decompose
a : Bool ⊢
Π b : Bool, ?M::0 ⇒ ?M::1 ≺
Π b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
Destruct/Decompose
⊢
Π a b : Bool, ?M::0 ⇒ ?M::1 ≺
Π a b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
(line: 26: pos: 16) Type of definition 'pierce' must be convertible to expected type.
Assignment
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ ?M::10 ≈ ?M::8 ⇒ ?M::9
Destruct/Decompose
a : Bool, b : Bool, H : ?M::2, H_na : ?M::7 ⊢ ¬ ?M::10 ≺ ¬ (?M::8 ⇒ ?M::9)
(line: 29: pos: 40) Type of argument 3 must be convertible to the expected type in the application of
NotImp1::explicit
with arguments:
?M::8
?M::9
MT H H_na
Assignment
a : Bool, b : Bool, H : ?M::2 ⊢ (a ⇒ b) ⇒ a ≺ ?M::5
Normalize
a : Bool, b : Bool, H : ?M::2, H_a : ?M::6 ⊢ (a ⇒ b) ⇒ a ≺ ?M::5[lift:0:1]
Substitution
a : Bool, b : Bool, H : ?M::2, H_a : ?M::6 ⊢ ?M::2[lift:0:2] ≺ ?M::5[lift:0:1]
Destruct/Decompose
a : Bool,
b : Bool,
H : ?M::2 ⊢
Π H_a : ?M::6, ?M::2[lift:0:2] ≺ Π _ : ?M::3, ?M::5[lift:0:1]
(line: 27: pos: 21) Type of argument 5 must be convertible to the expected type in the application of
DisjCases::explicit
with arguments:
?M::3
?M::4
?M::5
EM a
λ H_a : ?M::6, H
λ H_na : ?M::7, NotImp1 (MT H H_na)
Normalize assignment
?M::0
Assignment
a : Bool, b : Bool ⊢ ?M::2 ≈ ?M::0
Destruct/Decompose
a : Bool, b : Bool ⊢ Π H : ?M::2, ?M::5 ≺ Π _ : ?M::0, ?M::1[lift:0:1]
(line: 27: pos: 4) Type of argument 3 must be convertible to the expected type in the application of
Discharge::explicit
with arguments:
?M::0
?M::1
λ H : ?M::2,
DisjCases (EM a) (λ H_a : ?M::6, H) (λ H_na : ?M::7, NotImp1 (MT H H_na))
Assignment
a : Bool, b : Bool ⊢ ?M::0 ≈ (a ⇒ b) ⇒ a
Destruct/Decompose
a : Bool, b : Bool ⊢ ?M::0 ⇒ ?M::1 ≺ ((a ⇒ b) ⇒ a) ⇒ a
Destruct/Decompose
a : Bool ⊢ Π b : Bool, ?M::0 ⇒ ?M::1 ≺ Π b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
Destruct/Decompose
⊢ Π a b : Bool, ?M::0 ⇒ ?M::1 ≺ Π a b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
(line: 26: pos: 16) Type of definition 'pierce' must be convertible to expected type.
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