lean2/tests/lean/eq1.lean

Import int.
Variable i : Int
Check i = 0
SetOption pp::coercion true
Check i = 0
refactor(builtin): only load the kernel and natural numbers by default Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-30 21:35:37 +00:00			`Import int.`
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			`Variable i : Int`
			`Check i = 0`
feat(frontends/lean): rename command Set to SetOption It is not nice to have Set as a reserved keyword. See example examples/lean/set.lean Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-19 05:18:45 +00:00			`SetOption pp::coercion 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			`Check i = 0`