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>
10 lines
322 B
Text
10 lines
322 B
Text
Set: pp::colors
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Set: pp::unicode
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Assumed: f
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Assumed: g
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∀ a b : Type, ∃ c : Type, (g a b) = (f c)
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∀ a b : Type, ∃ c : Type, (g a b) = (f c) : Bool
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(λ a : Type,
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(λ b : Type, if ((λ x : Type, if ((g a b) == (f x)) ⊥ ⊤) == (λ x : Type, ⊤)) ⊥ ⊤) ==
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(λ x : Type, ⊤)) ==
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(λ x : Type, ⊤)
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