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Alice 2023-10-23 21:28:40 +01:00
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commit 341d411882
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49
4a1s/MFES/PL - Aula 5.md
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@ -49,7 +49,7 @@ pred Invs {
//all x, y: Node | x.key.hash != y.key.hash implies (x.prox != y and y.prox != x)
//keys are unique to a single node
all k: Key | one x: Node | x.key = k
all x: Key | one y: Node | y.key = x
//heads are unique to a single bucket (UNNECESSARY)
all x: Bucket | lone x.head
@ -68,4 +68,49 @@ pred Invs {
}
```
```
// SOLVED
```c
sig Bucket {
head : lone Node
}
sig Node {
key : one Key,
prox : lone Node
}
sig Key {
hash : one Hash
}
sig Hash {}
pred Invs {
// no node links to itself and its children don't link to it (no loops)
all x: Node | x not in x.^prox
//for all nodes sequentially linked, they must have the same hash
all x, y: Node | (x.prox = y) implies x.key.hash = y.key.hash
//keys are unique to a single node
all x: Key | one y: Node | y.key = x
//nodes must be prox to another node or be the head of a bucket
all x: Node | (x in Bucket.head) or (x in Node.prox)
//different buckets must have different heads
all x, y: Bucket, z : Node | x != y and x.head = z implies y.head!=z
//keys must have a hash
all x: Key | some y: Hash | x.hash = y
//nodes(heads) associated to different buckets, must differ in hash
all x, y: Bucket | (x != y and x.head != none and y.head != none ) implies x.head.key.hash != y.head.key.hash
}
```
http://alloy4fun.inesctec.pt/5yb5zPPJWP29SDSbD