Add Pausable FV (#4117)

Co-authored-by: Hadrien Croubois <hadrien.croubois@gmail.com>

certora/specs/Pausable.spec

@@ -0,0 +1,96 @@
+import "helpers.spec"
+
+methods {
+    paused() returns (bool) envfree
+    pause()
+    unpause()
+    onlyWhenPaused()
+    onlyWhenNotPaused()
+}
+
+/*
+┌─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
+│ Function correctness: _pause pauses the contract                                                                    │
+└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
+*/
+rule pause(env e) {
+    require nonpayable(e);
+
+    bool pausedBefore = paused();
+
+    pause@withrevert(e);
+    bool success = !lastReverted;
+
+    bool pausedAfter = paused();
+    
+    // liveness
+    assert success <=> !pausedBefore, "works if and only if the contract was not paused before";
+
+    // effect
+    assert success => pausedAfter, "contract must be paused after a successful call";
+}
+
+/*
+┌─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
+│ Function correctness: _unpause unpauses the contract                                                                │
+└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
+*/
+rule unpause(env e) {
+    require nonpayable(e);
+
+    bool pausedBefore = paused();
+
+    unpause@withrevert(e);
+    bool success = !lastReverted;
+
+    bool pausedAfter = paused();
+    
+    // liveness
+    assert success <=> pausedBefore, "works if and only if the contract was paused before";
+
+    // effect
+    assert success => !pausedAfter, "contract must be unpaused after a successful call";
+}
+
+/*
+┌─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
+│ Function correctness: whenPaused modifier can only be called if the contract is paused                              │
+└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
+*/
+rule whenPaused(env e) {
+    require nonpayable(e);
+
+    onlyWhenPaused@withrevert(e);
+    assert !lastReverted <=> paused(), "works if and only if the contract is paused";
+}
+
+/*
+┌─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
+│ Function correctness: whenNotPaused modifier can only be called if the contract is not paused                       │
+└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
+*/
+rule whenNotPaused(env e) {
+    require nonpayable(e);
+    
+    onlyWhenNotPaused@withrevert(e);
+    assert !lastReverted <=> !paused(), "works if and only if the contract is not paused";
+}
+
+/*
+┌─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
+│ Rules: only _pause and _unpause can change paused status                                                            │
+└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
+*/
+rule noPauseChange(env e) {
+    method f;
+    calldataarg args;
+
+    bool pausedBefore = paused();
+    f(e, args);
+    bool pausedAfter = paused();
+
+    assert pausedBefore != pausedAfter => (
+        (!pausedAfter && f.selector == unpause().selector) ||
+        (pausedAfter && f.selector == pause().selector)
+    ), "contract's paused status can only be changed by _pause() or _unpause()";
+}