lean2/tests/lean/cast3.lean.expected.out

  Set: pp::colors
  Set: pp::unicode
  Assumed: A
  Assumed: A'
  Assumed: B
  Assumed: B'
  Assumed: x
x
x == x
  Assumed: b
  Defined: f
  Assumed: H
  Assumed: a'
b
  Assumed: H2
  Defined: g
0
g (cast H2 f a') : ℕ
Cast B B' (RanInj H2 (Cast A' A (Symm (DomInj H2)) a')) b
  Assumed: A1
  Assumed: A2
  Assumed: A3
  Assumed: Ha
  Assumed: Hb
  Assumed: a
Cast A1 A3 (Trans Hb Ha) a
cast Hb (cast Ha a) : A3
-												Add casting propagation and normalization

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-07 03:45:26 +00:00
+								  Set: pp::colors
 								  Set: pp::unicode
 								  Assumed: A
 								  Assumed: A'
 								  Assumed: B
 								  Assumed: B'
 								  Assumed: x
 								x
-												refactor(equality): make homogeneous equality the default equality

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>

											
										
										
											2013-10-29 23:20:02 +00:00
+								x == x
-												Add casting propagation and normalization

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-07 03:45:26 +00:00
+								  Assumed: b
 								  Defined: f
 								  Assumed: H
 								  Assumed: a'
 								b
 								  Assumed: H2
 								  Defined: g
 
-												Display the input term in the output of the Check command. It is useful to see the fully elaborated term.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-09 05:54:22 +00:00
+								g (cast H2 f a') : ℕ
-												Add casting propagation and normalization

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-07 03:45:26 +00:00
+								Cast B B' (RanInj H2 (Cast A' A (Symm (DomInj H2)) a')) b
 								  Assumed: A1
 								  Assumed: A2
 								  Assumed: A3
 								  Assumed: Ha
 								  Assumed: Hb
 								  Assumed: a
 								Cast A1 A3 (Trans Hb Ha) a
-												Display the input term in the output of the Check command. It is useful to see the fully elaborated term.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

											
										
										
											2013-09-09 05:54:22 +00:00
+								cast Hb (cast Ha a) : A3