Modification to the current specifications. I. Order -- Sequential order (SO): Some total order that is consistent with the union of happens-before and SC relation. II. State Previously, we keep a sequential state throughout the process of executing the sequential history. In our model, we keep a state local to each method call. Conceptually, this state is the accumulative side effects of the subset of method calls that happen before the current method call. To evaluate the state of each method call, an obvious approach is to execute the subset of methods that happen before the current method in the sequential order from the initial state. A optimization we can make is that we start to evaluate the state from the most recent deviding node which every other node in that subset is either hb before or after. III. Specifications Our specification language supports using the following primitives to access the state of method calls so that users can use those to write specifications with different level of tightness. To support tighter specifications, we introduce the concept of concurrent set of method calls, meaning that for a specific method call, it can basically see the effect of two different categories of method calls --- one that happens before it, and one that concurrently execute with it. It is worth noting that when two two method calls execute concurrently, in general there can be the following two effects: 1) those concurrent methods can happen in either order, and the final result remains the same. A concurrent FIFO is an example, in which concurrent enqueue and dequeue methods can happen in a random order; and 2) the order of those concurrent methods will affect the final result. The C/C++11 atomics is an example, in which when concurrent stores to the same location execute in different order, a later store will have different result. 1. CONCURRENT: This primitive extracts all the methods that executes "concurrently" with the current method --- neither hb/SC before nor after the current method --- and returns as a set. It is worth noting that in order to preserve composability, when evaluating the state, the concurrent method calls' information cannot be used. That is to say, the concurrent set of mehtods are only used for assertions. 2. PREV: This primitive extracts all the methods that execute right before the current method in the execution graph --- most recent method calls that are hb/SC before the current method call --- and returns as a set. For each method in this set, the current method's specification can access their state. 3. NEXT: This primitive extracts all the methods that execute right after the current method in the execution graph, and returns as a set. For each method in this set, the current method's specification CANNOT access their state (for preserving composability). // FIXME: This might break composability!!??!! 4. FINAL: This is the function that allows users to specify some final check on the state. This will enable to users to use the graph model (the relaxed atomics can be specified) although the complxity of using that can get quite complex. Our specifications allow two ways of evaluating the state of method calls. One way is to define "@Transition" on method calls, and then our checker executes the method calls that are hb/SC before me in the sequential order starting from the initial state. The other way is to define "@EvaluateState" after "@Transition", which can only access the states of method calls that are hb/SC before it. Usually users calculate the state by using the PREV primitive to access the state of previous method calls. IV. Specification Details /// Global specification @State: // Declare the state structure @Initial: // How do we initialize the state @Commutativity: Method1 <-> Method2 (Guard) // Guard can only access the return // value and the arguments of the two method calls /// Interface specification @Interface: InterfaceName // Required; a label to represent the interface @Transition: // Optional; the transitional side effect from the initial state to // the current method call by executing such effect on method calls // that are hb/SC before me in sequential order. When this field is // omitted, the current state seen before checking is the same as // the initial state. @EvaluateState: // Optional; to calculate the state before this // method call is checked in a customized fashion. This is // evaluated after "@Transition". If omitted, the state we would // see is the effect after the "@Transition". @PreCondition: // Optional; checking code @SideEffect: // Optional; to calculate the side effect this method call // have on the state after the "@PreCondition". @PostCondition: // Optional; checking code /// Convienient operations We define a struct called MethodCall to represent the data we would collect and communicate between the real execution and the checking process. STATE(field) // A primitive to access the current state in the interface // specification by the name of the field. We can use this as a // lvalue & rvalue ==> "STATE(x) = 1" and "int i = STATE(x)" are // both okay // This can also be used to refer to the state of a method item // in the Subset operation (see Subset) NAME // Used to refer to the name of a method item in the Subset // operation (see Subset) RET(type) // Used to refer to the return value of a method item in the // Subset operation (see Subset) ARG(type, arg) // Used to refer to the argument of a method item in the // Subset operation (see Subset) PREV // Represent the set of previous method calls of the current method // call CONCURRENT // Represent the set of concurrent method calls of the current // method call NEXT // Represent the set of next method calls of the current method // call Name(method) // The interface label name of the specific method State(method, field) // A primitive to access a specific state field of a // specific method. Also used as lvalue and rvalue Ret(method, type) // The return value of the specific method; type should // be the name of the interface label Arg(method, type, arg) // The arguement by name of the specific method; type should // be the name of the interface label, and arg should be // the name of the argument Prev(method) // Represent the set of previous method calls of the // specific method call Next(method) // Represent the set of next method calls of the specific // method call ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ForEach(item, container) { ... } // Useful iteration primitive NewMethodSet // Create a new method set (set*) MakeSet(type, oldset, newset, field); // Construct a new set from an // old set. We extract a specific field of that set item // and form a new set. Specifically we expect users to // use this on MethodSet. For example, if we want to // construct an integer set from the state "x" of // the previous methods, we use "MakeSet(int, PREV, // newset, STATE(x))", and the newset contains the new // set Subset(set, condition) // A generic subset operation that takes a condition and // returns all the item for which the boolean guard // holds. The condition can be specified with GUARD or // GeneralGuard shown as follow. HasItem(set, condition) // A generic set operation that takes a condition and // returns if there exists any item in "set" for which // the condition holds. Its syntax is similar to that of // Subset() operation Size(container) // Return the size of a container type Belong(container, item) // Return if item is in the container Union(set1, set2) // Union of two sets Intesection(set1, set2) // Intersection of two sets Subtract(set1, set2) // Returns the new set that represents the result of // set1-set2 Insert(set, item) // Insert item to set Insert(set, others) // Insert the whole set "others" to "set" ITEM // Used to refer to the set item in the GeneralGuard shown below GeneralGuard(type, expression) // Used as a condition for any set type. We // use "ITEM" to refer to a set item. For // example, a subset of positive elements on an // IntSet "s" would be // "Subset(s, GeneralGuard(int, ITEM > 0))" Guard(expression) // Used specifically for MethodSet(set). An // example to extract the subset of method calls in the PREV // set that is a "Store" method and whose state "x" is equal // to "val" and the return value is 5 would be // "Subset(PREV, Guard(STATE(x) == val && NAME == "Store" && // RET(Store) == 5))" ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ To make things easier, we have the following helper macros. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ /** This is a common macro that is used as a constant for the name of specific variables. We basically have two usage scenario: 1. In Subset operation, we allow users to specify a condition to extract a subset. In that condition expression, we provide NAME, RET(type), ARG(type, field) and STATE(field) to access each item's (method call) information. 2. In general specification (in pre- & post- conditions and side effects), we would automatically generate an assignment that assign the current MethodCall* pointer to a variable namedd _M. With this, when we access the state of the current method, we use STATE(field) (this is a reference for read/write). */ #define ITEM _M #define _M ME #define CAT(a, b) CAT_HELPER(a, b) /* Concatenate two symbols for macros! */ #define CAT_HELPER(a, b) a ## b #define X(name) CAT(__##name, __LINE__) /* unique variable */ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ***************************************************************************** typedef struct MethodCall { string name; // The interface label name void *value; // The pointer that points to the struct that have the return // value and the arguments void *state; // The pointer that points to the struct that represents // the state set *prev; // Method calls that are hb right before me set *concurrent; // Method calls that are concurrent with me set *next; // Method calls that are hb right after me } MethodCall; typedef MethodCall *Method; typedef set *MethodSet; typedef vector IntVector; typedef list IntList; typedef set IntSet; ***************************************************************************** We will automatically generate two types of struct. One is the state struct, and we will call it StateStruct. The other one is a per interface struct, and it wraps the return value (RET) and the arguments as its field. We will name those struct with the interface label name. ----------------------------------------------------------------------------- For example, if we declare an ordered integer list in the specification state , we will generate a struct as follow. @State: IntList *queue; @Initial: queue = new IntList; @... ===> typedef struct StateStruct { IntList *queue; } StateStruct; ----------------------------------------------------------------------------- If we have two interface whose specifications are as follow, we would generate two struct accordingly. @Interface: Store @... void store(atomic_int *loc, int val) ... @Interface: Load @... int load(atomic_int *loc) ... ===> typedef struct Store { atomic_int *loc; int val; } Store; typedef struct Load { int RET; atomic_int *loc; } Load; ----------------------------------------------------------------------------- We will put all these generated struct in a automatically-generated header file called "generated.h". This file also includes header files that have commonly used data types that interface (return value and arguments) accesses. In order to make things work, users should include "generated.h" file in the end for using our specification checker. ***************************************************************************** /// Ordering point specification @OPDefine: condition // If the specified condition satisfied, the atomic // operation right before is an ordering point @PotentialOP(Label): condition // If the specified condition satisfied, the // atomic operation right before is a potential // ordering point, and we label it with a tag @OPCheck(Label): condition // If the specified condition satisfied, the // potential ordering point defined earlier with the // same tag becomes an ordering point @OPClear: condition // If the specified condition satisfied, all the // ordering points and potential ordering points will be // cleared @OPClearDefine: condition // If the specified condition satisfied, all the // ordering points and potential ordering points will // be cleared, and the atomic operation right before // becomes an ordering point. This is a syntax sugar // as the combination of an "OPClear" and "OPDefine" // statement V. Examples !!!!!!! The register example should be extended to commute if we think of their transitional effects as set operations --- a set operation that will only mask out side the effects of its own previous behavior (things that are hb/SC before it) ---- VERY IMPORTANT note here!! 1. The register examples: Basically, we can think of registers as the cache on a memory system. The effect of a load or store basically tells us what the current value in the cache line is, and a load can read from values that can be potentially in the cache --- either one of the concurrent store update the cache or it inherites one of the the previous state in the execution graph. ---------- Interfae ---------- void init(atomic_int &loc, int initial); int load(atomic_int &loc); void store(atomic_int &loc, int val); ---------- Interfae ---------- a. The SC atomics --- the classic linearizability approach b. The RA (release/acquire) C/C++ atomics // For RA atomics, a load must read its value from a store that happens before // it. ---------- Specification ---------- @State: int x; @Initial: x = 0; @Commutativity: Store <-> Store(true) @Commutativity: Load <-> Load(true) @Commutativity: Store <-> Load(true) /** No @Transition */ @Interface: Store @SideEffect: STATE(x) = val; void store(int *loc, int val); @Interface: Load @PreCondition: return HasItem(PREV, STATE(x) == RET); @SideEffect: STATE(x) = RET; int load(int *loc); c. The C/C++ atomics (a slightly loose specification) // Actually, any concurrent data structures that rely modification-order to be // correct would not have a precicely tight specification under our model, and // C/C++ relaxed atomics is an example. See the following read-read coherence // example. // T1 // T2 x = 1; x = 2; // T3 r1 = x; // r1 == 1 r2 = x; // r2 == 2 r3 = x; // r3 == 1 Our model cannot prevent such a case from happening. However, we can still have a slightly loose specification which basically states that a load can read from any store that either immediately happens before it or concurrently executes. ---------- Specification ---------- @State: int x; @Initial: x = 0; @Interface: Store @SideEffect: STATE(x) = val; void store(int *loc, int val); @Interface: Load @PreCondition: // Auto generated code // MethodCall *ME = ((SomeTypeConversion) info)->method; return HasItem(Prev, STATE(x) == RET) || + HasItem(CONCURRENT, NAME == "Store" && ARG(Store, val) == RET) @SideEffect: STATE(x) = RET; int load(int *loc); d. The C/C++ normal memory accesses - Use the admissibility requirement, then the classic linearizability approach on the admissible executions 2. The FIFO queue example. ---------- Specification ---------- // A FIFO queue should have the following properties held: // 1. The enq() methods should conflict // 2. The deq() methods that succeed should conflict // 3. Corresponding enq() and deq() methods should conflict // 4. An enqueued item can be dequeued by at most once // 5. A dequeued item must have a corresponding enqueued item // 6. When a queue is NOT "empty" (users can tightly or loosely define // emptiness), and there comes a deq() method, the deq() method should succeed @DeclareVar: vector *q; @InitVar: q = new voctor; @Copy: New.q = new vector(Old.q); // Fails to dequeue @Commutativity: Deq <-> Deq (!_M1.RET || !_M2.RET) @Commutativity: Enq <-> Deq (true) @Interface: Enq @Transition: q->push_back(val); void enq(queue_t *q, int val); @Interface: Deq @Transition: if (RET) q->pop_back(); @PreCondition: // Check whether the queue is really empty // Either the state is an empty queue, or for all those remaining // elements in the queue, there should be some concurrent dequeuers to // dequeue them if (!RET) { // State is empty if (STATE(q)->size() == 0) return true; // Otherwise check there must be other concurrent dequeuers ForEach (item, State(q)) { // Check there's some concurrent dequeuer for this item if (!HasItem(CONCURRENT, NAME == "Deq" && RET(Deq) && *ARG(Deq, res) == item)) return false; } return true; } else { // Check the global queue state return q->back() == *res; } bool deq(queue_t *q, int *res); ******************************************************************************* A good example to simulate a queue data structure is as follows. Suppose we have a special structure typedef struct Q { atomic_int x; atomic_int y; } Q; , and we have two interface on Q, read() and write(), where the write and read method calls are synchronized by themselves, and they have to read and write the x and y fields in turn.