lean2/tests/lean/tst5.lean

Variable N : Type
Variable a : N
Variable b : N
Show a = b
Check a = b
Set lean::pp::implicit true
Show a = b
Show (Type 1) = (Type 1)
Show true = false
Add homogeneous equality Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-08-30 21:26:12 +00:00			`Variable N : Type`
			`Variable a : N`
			`Variable b : N`
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			`Show a = b`
			`Check a = b`
Add homogeneous equality Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-08-30 21:26:12 +00:00			`Set lean::pp::implicit true`
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			`Show a = b`
			`Show (Type 1) = (Type 1)`
			`Show true = false`