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GHC Commentary: Software Transactional Memory (STM)

This document gives an overview of the runtime system (RTS) support for GHC's STM implementation. We will focus on the case where fine grain locking is used (STM_FG_LOCKS).

Some details about the implementation can be found in the papers Composable Memory Transactions and Transactional memory with data invariants. Additional details can be found in the Harris et al book Transactional memory. Some analysis on performance can be found in the paper The Limits of Software Transactional Memory though this work only looks at the coarse grain lock version. Many of the other details here are gleaned from the comments in the source code.

Background

This document assumes the reader is familiar with some general details of GHC's execution and memory layout. A good starting point for this information is can be found here: Generated Code.

Definitions

Useful RTS terms

Capability

Corresponds to a CPU. The number of capabilities should match the number of CPUs. See Capabilities.

TSO

Thread State Object. The state of a Haskell thread. See Thread State Objects.

Heap object

Objects on the heap all take the form of an StgClosure structure with a header pointing and a payload of data. The header points to code and an info table. See Heap Objects.

Transactional Memory terms

Read set

The set of TVars that are read, but not written to durring a transaction.

Write set

The set of TVars that are written to durring a transaction. In the code each written TVar is called an "update entry" in the transactional record.

Access set

All TVars accessed durring the transaction.

While GHC's STM does not have a separate read set and write set these terms are useful for discussion.

Retry

Here we will use the term retry exclusively for the blocking primitive in GHC's STM. This should not be confused with the steps taken when a transaction detects that it has seen an inconsistent view of memory and must start again from the beginning.

Failure

A failed transaction is one that has seen inconsistent state. This should not be confused with a successful transaction that executes the retry primitive.


Overview of Features

At the high level, transactions are computations that read and write to TVars with changes only being committed atomically after seeing a consistent view of memory. Transactions can also be composed together, building new transactions out of existing transactions. In the RTS each transaction keeps a record of its interaction with the TVars it touches in a TRec. A pointer to this record is stored in the TSO that is running the transaction.

Reading and Writing

The semantics of a transaction require that when a TVar is read in a transaction, ts value will stay the same for the duration of execution. Similarly a write to a TVar will keep the same value for the duration of the transaction. The transaction itself, however, from the perspective of other threads can apply all of its effects in one moment. That is, other threads cannot see intermediate states of the transaction, so it is as if all the effects happen in a single moment.

As a simple example we can consider a transaction that transfers value between two accounts:

transfer :: Int -> TVar Int -> TVar Int -> STM ()
transfer v a b = do
    x <- readTVar a
    y <- readTVar b
    writeTVar a (x - v)
    writeTVar b (y + v)

No other thread can observe the value x - v in a without also observing y + v in b.

Blocking

Transactions can choose to block until changes are made to TVars that allow it to try again. This is enabled with an explicit retry. Note that when changes are made the transaction is restarted from the beginning.

Continuing the example, we can choose to block when there are insufficient funds:

transferBlocking :: Int -> TVar Int -> TVar Int -> STM ()
transferBlocking v a b = do
    x <- readTVar a
    y <- readTVar b
    if x < v
      then retry
      else do
              writeTVar a (x - v)
              writeTVar b (y + v)

Choice

Any blocking transaction can be composed with orElse to choose an alternative transaction to run instead of blocking. The orElse primitive operation creates a nested transaction and if this first transaction executes retry, the effects of the nested transaction are rolled back and the alternative transaction is executed. This choice is biased towards the first parameter. A validation failure in the first branch aborts the entire transaction, not just the nested part. An explicit retry is the only mechanism that gives partial rollback.

We now can choose the account that has enough funds for the transfer:

transferChoice :: Int -> TVar Int -> TVar Int -> TVar Int -> STM ()
transferChoice v a a' b = do
    transferBlocking v a b `orElse` transferBlocking v a' b

Data Invariants

Invariants support checking global data invariants beyond the atomicity transactions demand. For instance, a transactional linked list (written correctly) will never have an inconsistent structure due to the atomicity of updates. It is no harder to maintain this property in a concurrent setting then in a sequential one with STM. It may be desired, however, to make statements about the consistency of the data in a particular a sorted linked list is sorted, not because of the structure (where the TVars point to) but instead because of the data in the structure (the relation between the data in adjacent nodes). Global data invariant checks can be introduced with the always operation which demands that the transaction it is given results in True and that it continues to hold for every transaction that is committed globally.

We can use data invariants to guard against negative balances:

newNonNegativeAccount :: STM (TVar Int)
newNonNegativeAccount = do
    t <- newTVar 0
    always $ do
        x <- readTVar t
        return (x > 0)
    return t

Exceptions

Exceptions inside transactions should only propagate outside if the transaction has seen a consistent view of memory. Note that the semantics of exceptions allow the exception itself to capture the view of memory from inside the transaction, but this transaction is not committed.


Overview of the Implementation

We will start this section by considering building GHC's STM with only the features of reading and writing. Then we will add retry then orElse and finally data invariants. Each of the subsequent features adds more complexity to the implementation. Taken all at once it can be difficult to understand the subtlety of some of the design choices.


Transactions that Read and Write.

With this simplified view we only support newTVar, readTVar, and writeTVar as well as all the STM type class instances except Alternative.

Transactional Record

The overall scheme of GHC's STM is to perform all the effects of a transaction locally in the transactional record or TRec. Once the transaction has finished its work locally, a value based consistency check determines if the values read for the entire access set are consistent. This only needs to consider the TRec and the main memory view of the access set as it is assumed that main memory is always consistent. This check also obtains locks for the write set and with those locks we can update main memory and unlock. Rolling back the effects of a transaction is just forgetting the current TRec and starting again.

The transactional record itself will have an entry for each transactional variable that is accessed. Each entry has a pointer to the TVar heap object and a record of the value that the TVar held when it was first accessed.

Starting

A transaction starts by initializing a new TRec (stmStartTransaction) assigning the TSO's trec pointer to the new TRec then executing the transaction's code.

(See rts/PrimOps.cmm stg_atomicallyzh and rts/STM.c stmStartTransaction).

Reading

When a read is attempted we first search the TRec for an existing entry. If it is found, we use that local view of the variable. On the first read of the variable, a new entry is allocated and the value of the variable is read and stored locally. The original TVar does not need to be accessed again for its value until a validation check is needed.

In the coarse grain version, the read is done without synchronization. With the fine grain lock, the lock variable is the current_value of the TVar structure. While reading an inconsistent value is an issue that can be resolved later, reading a value that indicates a lock and handing that value to code that expects a different type of heap object will almost certainly lead to a runtime failure. To avoid this the fine grain lock version of the code will spin if the value read is a lock, waiting to observe the lock released with an appropriate pointer to a heap object.

(See rts/STM.c stmReadTVar)

Writing

Writing to a TVar requires that the variable first be in the TRec. If it is not currently in the TRec, a read of the TVar's value is stored in a new entry (this value will be used to validate and ensure that no updates were made concurrently to this variable).

In both the fine grain and coarse grain lock versions of the code no synchronization is needed to perform the write as the value is stored locally in the TRec until commit time.

(See rts/STM.c stmWriteTVar)

Validation

Before a transaction can make its effects visible to other threads it must check that it has seen a consistent view of memory while it was executing. Most of the work is done in validate_and_acquire_ownership by checking that TVars hold their expected values.

For the coarse grain lock version the lock is held before entering validate_and_acquire_ownership through the writing of values to TVars. With the fine grain lock, validation acquires locks for the write set and reads a version number consistent with the expected value for each TVar in the read set. After all the locks for writes have been acquired, The read set is checked again to see if each value is still the expected value and the version number still matches (check_read_only).

(See rts/STM.c validate_and_acquire_ownership and check_read_only)

Committing

Before committing, each invariant associated with each accessed TVar needs to be checked by running the invariant transaction with its own TRec. The read set for each invariant is merged into the transaction as those reads must be included in the consistency check. The TRec is then validated. If validation fails, the transaction must start over from the beginning after releasing all locks. In the case of the coarse grain lock validation and commit are in a critical section protected by the global STM lock. Updates to TVars proceeds while holding the global lock.

With the fine grain lock version when validation, including any read-only phase, succeeds, two properties will hold simultaneously that give the desired atomicity:

  • Validation has witnessed all TVars with their expected value.
  • Locks are held for all of the TVars in the write set.

Commit can proceed to increment each locked TVar's num_updates field and unlock by writing the new value to the current_value field. While these updates happen one-by-one, any attempt to read from this set will spin while the lock is held. Any reads made before the lock was acquired will fail to validate as the number of updates will change.

(See rts/PrimOps.cmm stg_atomically_frame and rts/STM.c stmCommitTransaction)

Aborting

Aborting is simply throwing away changes that are stored in the TRec.

(See rts/STM.c stmAbortTransaction)

Exceptions

An exception in a transaction will only propagate outside of the transaction if the transaction can be validated. If validation fails, the whole transaction will abort and start again from the beginning. Nothing special needs to be done to support the semantics allowing the view inside the aborted transaction.

(See rts/Exception.cmm which calls stmValidateNestOfTransactions from rts/STM.c).


Blocking with retry

We will now introduce the blocking feature. To support this we will add a watch queue to each TVar where we can place a pointer to a blocked TSO. When a transaction commits we will now wake up the TSOs on watch queues for TVars that are written.

The mechanism for retry is similar to exception handling. In the simple case of only supporting blocking and not supporting choice, an encountered retry should validate, and if valid, add the TSO to the watch queue of every accessed TVar (see rts/STM.c stmWait and build_watch_queue_entries_for_trec). Locks are acquired for all TVars when validating to control access to the watch queues and prevent missing an update to a TVar before the thread is sleeping. In particular if validation is successful the locks are held after the return of stmWait, through the return to the scheduler, after the thread is safely paused (see rts/HeapStackCheck.cmm stg_block_stmwait), and until stmWaitUnlock is called. This ensures that no updates to the TVars are made until the TSO is ready to be woken. If validation fails, the TRec is discarded and the transaction is started from the beginning. (See rts/PrimOps.cmm stg_retryzh)

When a transaction is committed, each write that it makes to a TVar is preceded by waking up each TSO in the watch queue. Eventually these TSOs will be run, but before restarting the transaction its TRec is validated again if valid then nothing has changed that will allow the transaction to proceed with a different result. If invalid, some other transaction has committed and progress may be possible (note there is the additional case that some other transaction is merely holding a lock temporarily, causing validation to fail). The TSO is not removed from the watch queues it is on until the transaction is aborted (at this point we no longer need the TRec) and the abort happens after the failure to validate on wakeup. (See rts/STM.c stmReWait and stmAbortTransaction)


Choice with orElse

When retry# executes it searches the stack for either a CATCH_RETRY_FRAME or the outer ATOMICALLY_FRAME (the boundary between normal execution and the transaction). The former is placed on the stack by an orElse (see rts/PrimOps.cmm stg_catchRetryzh) and if executing the first branch we can partially abort and switch to the second branch, otherwise we propagate the retry further. In the latter case this retry represents a transaction that should block and the behavior is as above with only retry.

How do we support a "partial abort"? This introduces the need for a nested transaction. Our TRec will now have a pointer to an outer TRec (the enclosing_trec field). This allows us to isolate effects from the branch of the orElse that we might need to abort. Let's revisit the features that need to take this into account.

  • Reading -- Reads now search the chain of nested transactions in addition to the local TRec. When an entry is found in a parent it is copied into the local TRec. Note that there is still only a single access to the actual TVar through the life of the transaction (until validation).
  • Writing -- Writes, like reads, now search the parent TRecs and the write is stored in the local copy.
  • Retry -- As described above, we now need to search the stack for a CATCH_RETRY_FRAME and if found, aborting the nested transaction and attempting the alternative or propagating the retry instead of immediately working on blocking.
  • Validation -- If we are validating in the middle of a running transaction we will need to validate the whole nest of transactions.
    (See rts/STM.c stmValidateNestOfTransactions and its uses in rts/Exception.cmm and rts/Schedule.c)
  • Committing -- Just as we now have a partial abort, we need a partial commit when we finish a branch of an orElse. This commit is done with stmCommitNestedTransaction which validates just the inner TRec and merges updates back into its parent. Note that an update is distinguished from a read only entry by value. This means that if a nested transaction performs a write that reverts a value this is a change and must still propagate to the parent (see ticket #7493).
  • Aborting -- There is another subtle issue with how choice and blocking interact. When we block we need to wake up if there is a change to any accessed TVar. Consider a transaction:
    t = t1 `orElse` t2
    If both t1 and t2 execute retry then even though the effects of t1 are thrown away, it could be that a change to a TVar that is only in the access set of t1 will allow the whole transaction to succeed when it is woken.
    To solve this problem, when a branch on a nested transaction is aborted the access set of the nested transaction is merged as a read set into the parent TRec. Specifically if the TVar is in any TRec up the chain of nested transactions it must be ignored, otherwise it is entered as a new entry (retaining just the read) in the parent TRec.
    (See again ticket #7493 and rts/STM.c merge_read_into)
  • Exceptions -- The only change needed here each CATCH_RETRY_FRAME on the stack represents a nested transaction. As the stack is searched for a handler, at each encountered CATCH_RETRY_FRAME the nested transaction is aborted. When the ATOMICALLY_FRAME is encountered we then know that there is no nested transaction.
    (See rts/Exception.cmm stg_raisezh)

(See rts/PrimOps.cmm stg_retryzh and stg_catch_retry_frame)


Invariants

We will start this section with an overview of some of the details then review with notes on the changes from the choice case.

Details

As a transaction is executing it can collect dynamically checked data invariants. These invariants are transactions that are never committed, but if they raise an exception when executed successfully that exception will propagate out of the atomic frame.

check#

Primitive operation that adds an invariant (transaction to run) to the queue of the current TRec by calling stmAddInvariantToCheck.

checkInv :: STM a -> STM ()

A wrapper for check# (to give it the STM type).

alwaysSucceeds :: STM a -> STM ()

This is the check from the "Transactional memory with data invariants" paper. The action immediately runs, wrapped in a nested transaction so that it will never commit but will have an opportunity to raise an exception. If successful, the originally passed action is added to the invariant queue.

always :: STM Bool -> STM ()

Takes an STM action that results in a Bool and adds an invariant that throws an exception when the result of the transaction is False.

The bookkeeping for invariants is in each TRecs invariants_to_check queue and the StgAtomicallyFrames next_invariant_to_check field. Each invariant is in a StgAtomicInvariant structure that includes the STM action, the TRec where it was last executed, and a lock. This is added to the current TRecs queue when check# is executed.

When a transaction completes, execution will reach the stg_atomically_frame and the TRecs enclosing_trec will be NO_TREC (a nested transaction would have a stg_catch_retry_frame before the stg_atomically_frame to handle cases of non-empty enclosing_trec). The frame will then check the invariants by collecting the invariants it needs to check with stmGetInvariantsToCheck, dequeuing each, executing, and when (or if) we get back to the frame, aborting the invariant action. If the invariant failed to hold, we would not get here due to an exception and if it succeeds we do not want its effects. Once all the invariants have been checked, the frame will to commit.

Which invariants need to be checked for a given transaction? Clearly invariants introduced in the transaction will be checked these are added to the TRecs invariants_to_check queue directly when check# is executed. In addition, once the transaction has finished executing, we can look at each entry in the write set and search its watch queue for any invariants.

Note that there is a check in the stm package in Control.Monad.STM which matches the check from the beauty chapter of "Beautiful code":

check :: Bool -> STM ()
check b = if b then return () else retry

It requires no additional runtime support. If it is a transaction that produces the Bool argument it will be committed (when True) and it is only a one time check, not an invariant that will be checked at commits.

Changes from Choice

With the addition of data invariants we have the following changes to the implementation:

  • Retrying -- A retry in an invariant indicates that the invariant could not proceed and the whole transaction should block. This special case is detected when an ATOMICALLY_FRAME is encountered with a nest of transactions (i.e. when the enclosing_trec field is not NO_TREC). The invariant is simply aborted and execution proceeds to stmWait (see rts/PrimOps.cmm stg_retryzh).
  • Commiting -- Commit now needs a phase where it runs invariants after the code of the transaction has completed but before commit. The implementation recycles the structure already in place for this phase so special cases are needed in the ATOMICALLY_FRAME that collects invariants and works through them one at a time then moves on to committing (see rts/PrimOps.cmm stg_atomically_frame).
    To efficiently handle invariants they need to only be checked when a relevant data dependency changes. This means we can associate them with the TRec of the last commit that needed to check the invariant at the cost of serializing invariant handling commits. This is enforced by the lock on each invariant. If it cannot be acquired the whole transaction must start over.
    At commit time, each invariant is locked and the read set for the last commited transaction of each invariant is merged into the TRec.
    Validation acuqires lock for all entries in the TRec (not just the writes). After validation, each invariant is removed from the watch queue of each TVar it previously depended on, then the TRec that was used when executing the invariant code is updated to reflect the values from the final execution of the main transaction and each TVar, being a data depenency of the invariant, has the invariant added to its watch queue.
    (See rts/STM.c stmCommitTransaction, disconnect_invariant and connect_invariant_to_trec)
  • Exceptions -- When an exception propagates to the ATOMICALLY_FRAME there are now two states that it could encounter. If there is no enclosing TRec we are not dealing with an exception from an invariant and it proceeds as above. Seeing a nest of transactions indicates that the transaction was checking an invariant when it encountered the exception. The effect of a failed invariant is this exception so nothing special needs to be done except to validate and abort both the outer transaction and the nested transaction (see rts/Exception.cmm stg_raisezh).

Other Details

This section describes some details that can be discussed largely in isolation from the rest of the system.

Detecting Long Running Transactions

While the type system enforces STM actions to be constrained to STM side effects, pure computations in Haskell can be non-terminating. It could be that a transaction sees inconsistent data that leads to non-termination that would never happen in a program that only saw consistent data. To detect this problem, every time a thread yields it is validated. A validation failure causes the transaction to be condemned.

Transaction State

Each TRec has a state field that holds the status of the transaction. It can be one of the following:

TREC_ACTIVE

The transaction is actively running.

TREC_CONDEMNED

The transaction has seen an inconsistency.

TREC_COMMITTED

The transaction has committed and is in the process of updating TVar values.

TREC_ABORTED

The transaction has aborted and is working to release locks.

TREC_WAITING

The transaction has hit a retry and is waiting to be woken.

If a TRec state is TREC_CONDEMNED (some inconsistency was seen) validate does nothing. When a top-level transaction is aborted in stmAbortTransaction, if the state is TREC_WAITING it will remove the watch queue entries for the TRec. Similarly if a waiting TRec is condemned via an asynchronous exception when a validation failure is observed after a thread yield, its watch queue entries are removed. Finally a TRec in the TREC_WAITING state is not condemned by a validation. In this case the TRec is already waiting for a wake up from a TVar that changes and observing an inconsistency merely indicates that this will happen soon.

In the work of Keir Fraser a transaction state is used for cooperative efforts of transactions to give lock-free properties for STM systems. The design of GHC's STM is clearly influenced by this work and seems close to some of the algorithms in Fraser's work. It does not, however, implement what would be required to be lock-free or live-lock free (in the fine grain lock code). For instance, if two transactions T1 and T2 are committing at the same time and T1 has read A and written B while T2 has read B and written A, both the transactions can fail to commit. For example, consider the interleaving:

T1 TVar T2 Action
A 0 0 A 0 T1 read A
B 0 B 0 0 T2 read B
B 0 1 T1 write B 1
A 0 1 T2 write A 1
A 0 0 0 A 0 T1 Validation Part 1 (read A)
A T2 T2 Validation (Lock A)
B 0 B 0 0 0 T2 Validation (Read B)
B T1 T1 Validation Part 2 (Lock B)

Note: the first and third columns are the local state of the TRecs and the second column is the values of the TVar structures. Each TRec entry has the expected value followed by the new value and a number of updates field when it is read for validation.

At this point T1 and T2 both perform their read_only_check and both could (at least one will) discover that a TVar in their read set is now locked. This leads to both transactions aborting. The chances of this are narrow but not impossible (see ticket #7815). Fraser's work avoids this by using the transaction status and the fact that locks point back to the TRec holding the lock to detect other transactions in a read only check (read phase) and resolving conflicts so that at least one of the transactions can commit.

A simpler example can also cause both transactions to abort. Consider two transactions with the same write set, but the writes entered the TRecs in a different order. Both transactions could encounter a lock from the other before they have a chance to release locks and get out of the way. Having an ordering on lock could avoid this problem but would add a little more complexity.

GC and ABA

GHC's STM does comparisons for validation by value. Since these are always pure computations these values are represented by heap objects and a simple pointer comparison is sufficient to know if the same value is in place. This presents an ABA problem however if the location of some value is recycled it could appear as though the value has not changed when, in fact, it is a different value. This is avoided by making the expected_value fields of the TRec entries pointers into the heap followed by the garbage collector. As long as a TRec is still alive it will keep the original value it read for a TVar alive.

Management of TRecs

The TRec structure is built as a list of chunks to give better locality and amortize the cost of searching and allocating entries. Additionally TRecs are recycled to aid locality further when a transaction is aborted and started again. Both of these details add a little complexity to the implementation that is abated with some macros such as FOR_EACH_ENTRY and BREAK_FOR_EACH.

Tokens and Version Numbers.

When validating a transaction each entry in the TRec is checked for consistency. Any entry that is an update (in the write set) is locked. This locking is a visible effect to the rest of the system and prevents other committing transactions from progress. Reads, however, are not going to be updated. Instead we check that a read to the value matches our expected value, then we read a version number (the num_updates field) and check again that the expected value holds. This gives us a read of num_updates that is consistent with the TVar holding the expected value. Once all the locks for the write set are acquired we know that only our transaction can have an effect on the write set. All that remains is to rule out some change to the read set while we were still acquiring locks for the writes. This is done in the read phase (with read_only_check) which checks first if the value matches the expectation then checks if the version numbers match. If this holds for each entry in the read set then there must have existed a moment, while we held the locks for all the write set, where the read set held all its values. Even if some other transaction committed a new value and yet another transaction committed the expected value back the version number will have been incremented.

All that remains is managing these version numbers. When a TVar is updated its version number is incremented before the value is updated with the lock release. There is the unlikely case that the finite version numbers wrap around to an expected value while the transaction is committing (even with a 32-bit version number this is highly unlikely to happen). This is, however, accounted for by allocating a batch of tokens to each capability from a global max_commits variable. Each time a transaction is started it decrements it's batch of tokens. By sampling max_commits at the beginning of commit and after the read phase the possibility of an overflow can be detected (when more then 32-bits worth of commits have been allocated out).

(See rts/STM.c validate_and_acquire_ownership, check_read_only, getToken, stmStartTransaction, and stmCommitTransaction)

Implementation Invariants

Some of the invariants of the implementation:

  • Locks are only acquired in rts/STM.c and are always released before the end of a function call (with the exception of stmWait which must release locks after the thread is safe).
  • When running a transaction each TVar is read exactly once and if it is a write, is updated exactly once.
  • Main memory (TVars) always holds consistent values or locks of a partially updated commit. That is a set of reads at any moment from TVars will result in consistent data if none of the values are locks.
  • A nest of TRecs has a matching nest of CATCH_RETRY_FRAMEs ending with an ATOMICALLY_FRAME on the stack. One exception to this is when checking data invariants the invariant's TRec is nested under the top level TRec without a CATCH_RETRY_FRAME.

Fine Grain Locking

The locks in fine grain locking (STM_FG_LOCKS) are at the TVar level and are implemented by placing the locking thread's TRec in the TVars current value using a compare and swap (lock_tvar). The value observed when locking is returned by lock_tvar. To test if a TVar is locked the value is inspected to see if it is a TRec (checking that the closure's info table pointer is to stg_TREC_HEADER_info). If a TRec is found lock_tvar will spin reading the TVars current value until it is not a TRec and then attempt again to obtain the lock. Unlocking is simply a write of the current value of the TVar. There is also a conditional lock cond_lock_tvar which will obtain the lock if the TVars current value is the given expected value. If the TVar is already locked this will not be the case (the value would be a TRec) and if the TVar has been updated to a new (different) value then locking will fail because the value does not match the expected value. A compare and swap is used for cond_lock_tvar.

This arrangement is useful for allowing a transaction that encounters a locked TVar to know which particular transaction is locked (used in algorithms in from Fraser). GHC's STM does not, however, use this information.

Bibliography

Fraser, Keir. Practical lock-freedom. Diss. PhD thesis, University of Cambridge Computer Laboratory, 2004.

Jones, Simon Peyton. "Beautiful concurrency." Beautiful Code: Leading Programmers Explain How They Think (2007): 385-406.

Harris, Tim, et al. "Composable memory transactions." Proceedings of the tenth ACM SIGPLAN symposium on Principles and practice of parallel programming. ACM, 2005.

Harris, Tim, James Larus, and Ravi Rajwar. "Transactional memory." Synthesis Lectures on Computer Architecture 5.1 (2010): 1-263.

Harris, Tim, and Simon Peyton Jones. "Transactional memory with data invariants." First ACM SIGPLAN Workshop on Languages, Compilers, and Hardware Support for Transactional Computing (TRANSACT'06), Ottowa. 2006.