edits

[cdsspec-compiler.git] / notes / nondeterm-spec.txt

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. Examples

/// 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<MethodCall*>*)

MakeSet(NewSetType, oldset, newset, field);             // 

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.

ITEM    // Used to refer to the set item in the GeneralGuard shown below

GeneralGuard(type, expression)  // Used as a condition for any set<T> 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<MethodCall*>). 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 LOCAL(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
        local state of the current method, we use LOCAL(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<MethodCall*> *prev; // Method calls that are hb right before me
        set<MethodCall*> *concurrent; // Method calls that are concurrent with me
        set<MethodCall*> *next; // Method calls that are hb right after me
} MethodCall;

typedef MethodCall *Method;
typedef set<Method> *MethodSet;

typedef vector<int> IntVector;
typedef list<int> IntList;
typedef set<int> 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.

*****************************************************************************


// Some nice C/C++ macro definition to make specifications easier to write

-----------------------------------------------------------------------------
#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 */



-----------------------------------------------------------------------------
1. ForEach  --> to iterate a set, list or vector (containers that support using
iterator to iterate)

#define ForEach(item, container) \
        auto X(_container) = (container); \
        auto X(iter) = X(_container)->begin(); \
        for (auto item = *X(iter); X(iter) != X(_container)->end(); item = ((++X(iter)) != \
                X(_container)->end()) ? *X(iter) : 0)

-----------------------------------------------------------------------------

/**
        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 LOCAL(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
        local state of the current method, we use LOCAL(field) (this is a reference
        for read/write).
*/
#define ITEM _M
#define _M ME


-----------------------------------------------------------------------------

// 1.1 Subset(set, guard)  --> to get a subset of method calls by a boolean
// expression; This takes advantage of C++11 std::function features and C macros.

// 1.2 Size(set) --> to get the size of a method set
#define Size(set) set->size()

// 1.3 Belong(set, method) --> whether method belongs to set
#define Belong(set, method) std::find(set->begin(), set->end(), method) != set->end()

// 1.4 Intersect(set1, set2) --> the intersection of two method sets
inline MethodSet Intersect(MethodSet set1, MethodSet set2) {
        MethodSet res = NewSet;
        ForEach (m, set1) {
                if (Belong(set2, m))
                        res->push_back(m);
        }
        return res;
}

// 1.5 Union(set1, set2) --> the union of two method sets
inline MethodSet Union(MethodSet set1, MethodSet set2) {
        MethodSet res = NewSet(set1);
        ForEach (m, set2) {
                if (!Belong(set1, m))
                        res->push_back(m);
        }
        return res;
}

// 1.6 Insert(set, method) --> add a method to the set
inline bool Insert(MethodSet set, Method m) {
        if (Belong(set, m))
                return false;
        else {
                set->push_back(m);
                return true;
        }
}

// 1.7 Subtract(set1, set2) --> subtract set2 from set1 
inline MethodSet Subtract(MethodSet set1, MethodSet set2) {
        MethodSet res = NewSet;
        ForEach (m, set1) {
                if (!Belong(set2, m))
                        res->push_back(m);
        }
        return res;
}

// 1.8 MakeSet(count, ...) --> Make a set from the arguments

        
// 2. Local(method, field)
#define Local(method, field) ((StateStruct*) method->localState)->field

// 3. Value(method, type, field)
#define Value(method, type, field) ((type*) method->value)->field
3.1 Return
#define Ret(method, type) Value(method, type, RET)
3.2 Arguments
#define Arg(method, type, arg) Value(method, type, arg)


// 4. Name(mehtod)
#defien Lable(method) method->interfaceName

// 5. Prev(method)
#define Prev(method) mehtod->prev

// 6. Next(method)
#define Next(method) mehtod->next

// 7. Concurrent(method)
#define Concurrent(method) mehtod->concurrent


/// 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


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 local 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   ----------
@DeclareVar: int x;
@InitVar: x = 0;

@Interface: Store
@SideEffect: LOCAL(x) = val;
void store(int *loc, int val);

@Interface: Load
@PreCondition:
        Size(Subset(PREV, LOCAL(x) == RET)) > 0;
@SideEffect: LOCAL(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   ----------
@DeclareVar: int x;
@InitVar: x = 0;

@Interface: Store
@SideEffect: LOCAL(x) = val;
void store(int *loc, int val);


@Interface: Load
@PreCondition:
        // Auto generated code
        // MethodCall *ME = ((SomeTypeConversion) info)->method;
        
        int count = Size(Subset(Prev, LOCAL(x) == RET)) 
                + Size(Subset(CONCURRENT, NAME == "Store" && ARG(Store, val) == RET))
        return count > 0;
@SideEffect: LOCAL(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<int> *q;
@InitVar: q = new voctor<int>;
@Copy: New.q = new vector<int>(Old.q);
// Fails to dequeue
@Commutativity: Deq <-> Deq (!_M1.RET || !_M2.RET)
// The dequeuer doesn't dequeue from that enqueuer
@Commutativity: Enq <-> Deq (!_M2.RET || (_M2.RET && Enq.val != *Deq.res))

@Interface: Enq
@SideEffect: q->push_back(val);
void enq(queue_t *q, int val);

@Interface: Deq
@PreCondition:
        // Check whether the queue is really empty
        // Either the local state is an empty queue, or for all those remaining
        // elements in the local queue, there should be some concurrent dequeuers to
        // dequeue them
        if (!RET) {
                // Local state is empty
                if (Local(q)->size() == 0) return true;
                // Otherwise check there must be other concurrent dequeuers
                ForEach (item, Local(q)) {
                        // Check there's some concurrent dequeuer for this item
                        if (Size(Subset(CONCURRENT, NAME == "Deq" && RET(Deq) &&
                                *ARG(Deq, res) == item)) == 0) return false;
                }
                return true;
        } else { // Check the global queue state
                return q->back() == *res;
        }
@SideEffect:
        if (RET) q->pop_back();
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.



















----------------------------------------------------------------------------------------
We also need to think about the non-ordered queue.

####
Combiming Data Structures --- 
For example, a queue, a -hb->c, b -hb-> e.

// T1
enq(1) -> {1} - {$}    // a
enq(2) -> {1, 2} - {$}   // b

// T2
deq(1) -> {$} - {1}   // c
deq($) -> {$} - {1}   // d

// State before this method  
JOIN ({1, 2} - {$}, {$} - {1}) = {2} - {1}
deq(2) -> {$} - {1, 2}