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Revision 1640, 0.7 KB
(checked in by tranquil, 16 months ago)
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* finished fork of semantics.ma
* unification of Errors under the monad notations brings problems in type checking when res and IO are used together. Needs a lot of annotations, and may break the pre-fork material
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| 1 | include "basics/relations.ma". |
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| 2 | |
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| 3 | definition proper ≝ λA,B.λrelA : relation A.λrelB : relation B. |
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| 4 | λf,g : A → B. |
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| 5 | ∀a,a' : A.relA a a' → relB (f a) (g a'). |
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| 6 | |
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| 7 | definition proper_contra ≝ λA,B.λrelA : relation A.λrelB : relation B. |
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| 8 | λf,g : A → B. |
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| 9 | ∀a,a' : A.relA a' a → relB (f a) (g a'). |
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| 10 | |
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| 11 | |
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| 12 | interpretation "proper" 'proper r s = (proper ? ? r s). |
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| 13 | interpretation "proper contravariant" 'proper_contra r s = (proper_contra ? ? r s). |
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| 14 | |
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| 15 | notation "r ++> s" right associative with precedence 51 for |
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| 16 | @{'proper $r $s}. |
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| 17 | |
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| 18 | notation "r -+> s" right associative with precedence 51 for |
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| 19 | @{'proper_contra $r $s}. |
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| 20 | |
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| 21 | (* avoid notation from kikcing in in outputm to avoid things like X ⊨ Prod *) |
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| 22 | notation > "f ⊨ p " with precedence 50 for @{$p $f $f}. |
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