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CERT-6936: Update init axioms for some specs #126

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Aug 12, 2024
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CERT-6936: Update init axioms for some specs #126

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9 changes: 6 additions & 3 deletions CVLByExample/QuantifierExamples/DoublyLinkedList/certora/spec/dll-linkedcorrectly.spec
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Original file line number Diff line number Diff line change
Expand Up @@ -18,9 +18,12 @@ ghost mapping(address => address) ghostPrev {
ghost mapping(address => uint256) ghostValue {
init_state axiom forall address x. ghostValue[x] == 0;
}
ghost address ghostHead;
ghost address ghostTail;
ghost uint256 ghostLength;
ghost address ghostHead {
init_state axiom ghostHead == 0;
}
ghost address ghostTail {
init_state axiom ghostTail == 0;
}
ghost nextstar(address, address) returns bool {
init_state axiom forall address x. forall address y. nextstar(x, y) == (x == y);
}
Expand Down
7 changes: 4 additions & 3 deletions CVLByExample/QuantifierExamples/EnumerableSet/certora/spec/set.spec
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Expand Up @@ -22,12 +22,13 @@ ghost mapping(bytes32 => uint256) ghostIndexes {
}
// ghost field for the length of the values array (stored in offset 0)
ghost uint256 ghostLength {
init_state axiom ghostLength == 0;
// assumption: it's infeasible to grow the list to these many elements.
axiom ghostLength < max_uint256;
}

// HOOKS
// Store hook to synchronize ghostLength with the length of the set._inner._values array.
// Store hook to synchronize ghostLength with the length of the set._inner._values array.
hook Sstore currentContract.set._inner._values.length uint256 newLength {
ghostLength = newLength;
}
Expand All @@ -48,7 +49,7 @@ hook Sstore currentContract.set._inner._indexes[KEY bytes32 value] uint256 newIn
// By following this simple pattern it is ensured that the ghost state and the storage are always the same
// and that the solver can use this knowledge in the proofs.

// Load hook to synchronize ghostLength with the length of the set._inner._values array.
// Load hook to synchronize ghostLength with the length of the set._inner._values array.
hook Sload uint256 length currentContract.set._inner._values.length {
require ghostLength == length;
}
Expand All @@ -67,7 +68,7 @@ hook Sload uint256 index currentContract.set._inner._indexes[KEY bytes32 value]

invariant setInvariant()
(forall uint256 index. 0 <= index && index < ghostLength => to_mathint(ghostIndexes[ghostValues[index]]) == index + 1)
&& (forall bytes32 value. ghostIndexes[value] == 0 ||
&& (forall bytes32 value. ghostIndexes[value] == 0 ||
(ghostValues[ghostIndexes[value] - 1] == value && ghostIndexes[value] >= 1 && ghostIndexes[value] <= ghostLength));

// DEFINITION
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18 changes: 10 additions & 8 deletions CVLByExample/QuantifierExamples/SinglyLinkedList/certora/spec/list-reach.spec
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Expand Up @@ -29,25 +29,27 @@ ghost mapping(bytes32 => bytes32) ghostSucc {
}

// Our ghost copy of the list head.
ghost bytes32 ghostHead;
ghost bytes32 ghostHead {
init_state axiom ghostHead == to_bytes32(0);
}

definition isSucc(bytes32 a, bytes32 b) returns bool = reach(a, b) && a != b && (forall bytes32 X. reach(a, X) && reach(X, b) => (a == X || b == X));

definition reachSuccInvariant(bytes32 key) returns bool =
(key == to_bytes32(0) && ghostSucc[key] == to_bytes32(0))
|| (key != to_bytes32(0) && isSucc(key, ghostSucc[key]));

definition updateSucc(bytes32 a, bytes32 b) returns bool = forall bytes32 X. forall bytes32 Y. reach@new(X, Y) ==
definition updateSucc(bytes32 a, bytes32 b) returns bool = forall bytes32 X. forall bytes32 Y. reach@new(X, Y) ==
(X == Y ||
(reach@old(X, Y) && !(reach@old(X, a) && a != Y && reach@old(a, Y))) ||
(reach@old(X, a) && reach@old(b, Y)));

hook Sstore currentContract.list.elements[KEY bytes32 key].nextKey bytes32 newNextKey {
bytes32 otherKey;

require reachSuccInvariant(otherKey);
assert !reach(newNextKey,key), "Setting next introduces cycle";

// update ghost successor
ghostSucc[key] = newNextKey;
// update ghost reachability
Expand Down Expand Up @@ -87,21 +89,21 @@ invariant inListIffValid()
}

invariant reach_invariant()
forall bytes32 X. forall bytes32 Y. forall bytes32 Z. (
forall bytes32 X. forall bytes32 Y. forall bytes32 Z. (
reach(X, X)
&& (reach(X,Y) && reach (Y, X) => X == Y)
&& (reach(X,Y) && reach (Y, Z) => reach(X, Z))
&& (reach(X,Y) && reach (X, Z) => (reach(Y,Z) || reach(Z,Y)))
)
{
{
preserved {
requireInvariant inListIffValid();
}
}

invariant reach_succ(bytes32 key)
reachSuccInvariant(key)
{
{
preserved {
requireInvariant reach_invariant();
requireInvariant inListIffValid();
Expand Down Expand Up @@ -191,4 +193,4 @@ rule checkInsertSucceedsOtherwise {

insertAfter@withrevert(key, afterKey);
assert !lastReverted, "insert should not revert";
}
}