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Paolo G. Giarrusso
iris
Commits
9c192c8d
Commit
9c192c8d
authored
1 year ago
by
Ralf Jung
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sProp → siProp
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98a3e89c
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iris/base_logic/upred.v
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@@ -18,9 +18,9 @@ Local Hint Extern 10 (_ ≤ _) => lia : core.
monotonicity has to be stated in the SProp logic. Together with the
usual closedness property of SProp, this gives exactly uPred_mono.
Then, we quotient uPred0 *in the sProp logic* with respect to
Then, we quotient uPred0 *in the s
i
Prop logic* with respect to
equivalence on valid elements of M. That is, we quotient with
respect to the following *sProp* equivalence relation:
respect to the following *s
i
Prop* equivalence relation:
P1 ≡ P2 := ∀ x, ✓ x → (P1(x) ↔ P2(x)) (1)
When seen from the ambiant logic, obtaining this quotient requires
definig both a custom Equiv and Dist.
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@@ -30,7 +30,7 @@ Local Hint Extern 10 (_ ≤ _) => lia : core.
representatives. More precisely, one can show that every
equivalence class contains exactly one element P0 such that:
∀ x, (✓ x → P0(x)) → P0(x) (2)
(Again, this assertion has to be understood in sProp). Intuitively,
(Again, this assertion has to be understood in s
i
Prop). Intuitively,
this says that P0 trivially holds whenever the resource is invalid.
Starting from any element P, one can find this canonical
representative by choosing:
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@@ -38,7 +38,7 @@ Local Hint Extern 10 (_ ≤ _) => lia : core.
Hence, as an alternative definition of uPred, we could use the set
of canonical representatives (i.e., the subtype of monotonous
sProp predicates that verify (2)). This alternative definition would
s
i
Prop predicates that verify (2)). This alternative definition would
save us from using a quotient. However, the definitions of the various
connectives would get more complicated, because we have to make sure
they all verify (2), which sometimes requires some adjustments. We
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