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>
27 lines
413 B
Text
27 lines
413 B
Text
Set: pp::colors
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Set: pp::unicode
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Assumed: A
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Assumed: A'
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Assumed: B
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Assumed: B'
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Assumed: x
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x
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x == x
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Assumed: b
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Defined: f
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Assumed: H
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Assumed: a'
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b
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Assumed: H2
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Defined: g
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0
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g (cast H2 f a') : ℕ
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Cast B B' (RanInj H2 (Cast A' A (Symm (DomInj H2)) a')) b
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Assumed: A1
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Assumed: A2
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Assumed: A3
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Assumed: Ha
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Assumed: Hb
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Assumed: a
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Cast A1 A3 (Trans Hb Ha) a
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cast Hb (cast Ha a) : A3
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