|
Last change
on this file since 304 was
260,
checked in by sacerdot, 10 years ago
|
- Minimal changes to make it compile with the standard distribution of
Matita once this directory is substituted to nlibrary
- ambiguity reduced by lower-casing booleans
|
|
File size:
762 bytes
|
| Line | |
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| 1 | include "Bool.ma". |
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| 2 | |
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| 3 | include "Universes.ma". |
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| 4 | include "Plogic/equality.ma". |
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| 5 | |
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| 6 | ninductive Maybe (A: Type[0]): Type[0] ≝ |
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| 7 | Nothing: Maybe A |
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| 8 | | Just: A → Maybe A. |
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| 9 | |
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| 10 | ndefinition is_just ≝ |
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| 11 | λA: Type[0]. |
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| 12 | λm: Maybe A. |
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| 13 | match m with |
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| 14 | [ Nothing ⇒ false |
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| 15 | | Just j ⇒ true |
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| 16 | ]. |
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| 17 | |
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| 18 | ndefinition is_nothing ≝ |
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| 19 | λA: Type[0]. |
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| 20 | λm: Maybe A. |
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| 21 | match m with |
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| 22 | [ Nothing ⇒ true |
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| 23 | | Just j ⇒ false |
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| 24 | ]. |
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| 25 | |
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| 26 | ndefinition to_maybe ≝ |
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| 27 | λA: Type[0]. |
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| 28 | λb: Bool. |
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| 29 | λa: A. |
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| 30 | match b with |
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| 31 | [ true ⇒ Just A a |
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| 32 | | false ⇒ Nothing A |
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| 33 | ]. |
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| 34 | |
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| 35 | nlemma to_maybe_is_just: |
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| 36 | ∀A: Type[0]. |
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| 37 | ∀a: A. |
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| 38 | ∀b: Bool. |
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| 39 | is_just A (to_maybe A b a) = b. |
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| 40 | #A a b. |
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| 41 | ncases b. |
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| 42 | nnormalize. |
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| 43 | @. |
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| 44 | nnormalize. |
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| 45 | @. |
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| 46 | nqed. |
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