4dd6cead83
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>
12 lines
253 B
Text
12 lines
253 B
Text
Set: pp::colors
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Set: pp::unicode
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Defined: xor
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⊤ ⊕ ⊥
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⊥
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⊤
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Assumed: a
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a ⊕ a ⊕ a
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Subst::explicit : Π (A : Type U) (a b : A) (P : A → Bool), (P a) → (a == b) → (P b)
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Proved: EM2
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EM2 : Π a : Bool, a ∨ ¬ a
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EM2 a : a ∨ ¬ a
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