Match specifications in Erlang

## 1 Match specifications in Erlang

A "match specification" (match_spec) is an Erlang term describing a small "program" that will try to match something (either the parameters to a function as used in the `erlang:trace_pattern/2` BIF, or the objects in an ETS table.). The match_spec in many ways works like a small function in Erlang, but is interpreted/compiled by the Erlang runtime system to something much more efficient than calling an Erlang function. The match_spec is also very limited compared to the expressiveness of real Erlang functions.

Match specifications are given to the BIF `erlang:trace_pattern/2` to execute matching of function arguments as well as to define some actions to be taken when the match succeeds (the `MatchBody` part). Match specifications can also be used in ETS, to specify objects to be returned from an `ets:select/2` call (or other select calls). The semantics and restrictions differ slightly when using match specifications for tracing and in ETS, the differences are defined in a separate paragraph below.

The most notable difference between a match_spec and an Erlang fun is of course the syntax. Match specifications are Erlang terms, not Erlang code. A match_spec also has a somewhat strange concept of exceptions. An exception (e.g., `badarg`) in the `MatchCondition` part, which resembles an Erlang guard, will generate immediate failure, while an exception in the `MatchBody` part, which resembles the body of an Erlang function, is implicitly caught and results in the single atom `'EXIT'`.

### 1.1 Grammar

A match_spec can be described in this informal grammar:

- MatchExpression ::= [ MatchFunction, ... ]
- MatchFunction ::= { MatchHead, MatchConditions, MatchBody }
- MatchHead ::= MatchVariable | `'_'` | [ MatchHeadPart, ... ]
- MatchHeadPart ::= term() | MatchVariable | `'_'`
- MatchVariable ::= '$<number>'
- MatchConditions ::= [ MatchCondition, ...] | `[]`
- MatchCondition ::= { GuardFunction } | { GuardFunction, ConditionExpression, ... }
- BoolFunction ::= `is_atom` | `is_constant` | `is_float` | `is_integer` | `is_list` | `is_number` | `is_pid` | `is_port` | `is_reference` | `is_tuple` | `is_binary` | `is_function` | `is_record` | `is_seq_trace` | `'and'` | `'or'` | `'not'` | `'xor'` | `andalso` | `orelse`
- ConditionExpression ::= ExprMatchVariable | { GuardFunction } | { GuardFunction, ConditionExpression, ... } | TermConstruct
- ExprMatchVariable ::= MatchVariable (bound in the MatchHead) | `'$_'` | `'$$'`
- TermConstruct = {{}} | {{ ConditionExpression, ... }} | `[]` | [ConditionExpression, ...] | NonCompositeTerm | Constant
- NonCompositeTerm ::= term() (not list or tuple)
- Constant ::= {`const`, term()}
- GuardFunction ::= BoolFunction | `abs` | `element` | `hd` | `length` | `node` | `round` | `size` | `tl` | `trunc` | `'+'` | `'-'` | `'*'` | `'div'` | `'rem'` | `'band'` | `'bor'` | `'bxor'` | `'bnot'` | `'bsl'` | `'bsr'` | `'>'` | `'>='` | `'<'` | `'=<'` | `'=:='` | `'=='` | `'=/='` | `'/='` | `self` | `get_tcw`
- MatchBody ::= [ ActionTerm ]
- ActionTerm ::= ConditionExpression | ActionCall
- ActionCall ::= {ActionFunction} | {ActionFunction, ActionTerm, ...}
- ActionFunction ::= `set_seq_token` | `get_seq_token` | `message` | `return_trace` | `process_dump` | `enable_trace` | `disable_trace` | `trace` | `display` | `caller` | `set_tcw` | `silent`

### 1.2 Function descriptions

#### 1.2.1 Functions allowed in all types of match specifications

The different functions allowed in `match_spec` work like this:

is_atom, is_constant, is_float, is_integer, is_list, is_number, is_pid, is_port, is_reference, is_tuple, is_binary, is_function: Like the corresponding guard tests in Erlang, return `true` or `false`.

is_record: Takes an additional parameter, which SHALL be the result of `record_info(size, <record_type>)`, like in `{is_record, '$1', rectype, record_info(size, rectype)}`.

'not': Negates its single argument (anything other than `false` gives `false`).

'and': Returns `true` if all its arguments (variable length argument list) evaluate to `true`, else `false`. Evaluation order is undefined.

'or': Returns `true` if any of its arguments evaluates to `true`. Variable length argument list. Evaluation order is undefined.

andalso: Like `'and'`, but quits evaluating its arguments as soon as one argument evaluates to something else than true. Arguments are evaluated left to right.

orelse: Like `'or'`, but quits evaluating as soon as one of its arguments evaluates to `true`. Arguments are evaluated left to right.

'xor': Only two arguments, of which one has to be true and the other false to return `true`; otherwise `'xor'` returns false.

abs, element, hd, length, node, round, size, tl, trunc, '+', '-', '*', 'div', 'rem', 'band', 'bor', 'bxor', 'bnot', 'bsl', 'bsr', '>', '>=', '<', '=<', '=:=', '==', '=/=', '/=', self: Work as the corresponding Erlang bif's (or operators). In case of bad arguments, the result depends on the context. In the `MatchConditions` part of the expression, the test fails immediately (like in an Erlang guard), but in the `MatchBody`, exceptions are implicitly caught and the call results in the atom `'EXIT'`.

#### 1.2.2 Functions allowed only for tracing

is_seq_trace: Returns `true` if a sequential trace token is set for the current process, otherwise `false`.

set_seq_token: Works like `seq_trace:set_token/2`, but returns `true` on success and `'EXIT'` on error or bad argument. Only allowed in the `MatchBody` part and only allowed when tracing.

get_seq_token: Works just like `seq_trace:get_token/0`, and is only allowed in the `MatchBody` part when tracing.

message: Sets an additional message appended to the trace message sent. One can only set one additional message in the body; subsequent calls will replace the appended message. As a special case, `{message, false}` disables sending of trace messages ('call' and 'return_to') for this function call, just like if the match_spec had not matched, which can be useful if only the side effects of the `MatchBody` are desired. Another special case is `{message, true}` which sets the default behavior, as if the function had no match_spec, trace message is sent with no extra information (if no other calls to `message` are placed before `{message, true}`, it is in fact a "noop").

Takes one argument, the message. Returns `true` and can only be used in the `MatchBody` part and when tracing.

return_trace: Causes a `return_from` trace message to be sent upon return from the current function. Takes no arguments, returns `true` and can only be used in the `MatchBody` part when tracing. If the process trace flag `silent` is active the `return_from` trace message is inhibited.

NOTE! If the traced function is tail recursive, this match spec function destroys that property. Hence, if a match spec executing this function is used on a perpetual server process, it may only be active for a limited time, or the emulator will eventually use all memory in the host machine and crash. If this match_spec function is inhibited using the `silent` process trace flag tail recursiveness still remains.

exception_trace: Same as return_trace, plus; if the traced function exits due to an exception, an `exception_from` trace message is generated, whether the exception is caught or not.

process_dump: Returns some textual information about the current process as a binary. Takes no arguments and is only allowed in the `MatchBody` part when tracing.

enable_trace: With one parameter this function turns on tracing like the Erlang call `erlang:trace(self(), true, [P2])`, where `P2` is the parameter to `enable_trace`. With two parameters, the first parameter should be either a process identifier or the registered name of a process. In this case tracing is turned on for the designated process in the same way as in the Erlang call `erlang:trace(P1, true, [P2])`, where P1 is the first and P2 is the second argument. The process `P1` gets its trace messages sent to the same tracer as the process executing the statement uses. `P1` can not be one of the atoms `all`, `new` or `existing` (unless, of course, they are registered names). `P2` can not be `cpu_timestamp` nor `{tracer,_}`. Returns `true` and may only be used in the `MatchBody` part when tracing.

disable_trace: With one parameter this function disables tracing like the Erlang call `erlang:trace(self(), false, [P2])`, where `P2` is the parameter to `disable_trace`. With two parameters it works like the Erlang call `erlang:trace(P1, false, [P2])`, where P1 can be either a process identifier or a registered name and is given as the first argument to the match_spec function. `P2` can not be `cpu_timestamp` nor `{tracer,_}`. Returns `true` and may only be used in the `MatchBody` part when tracing.

trace: With two parameters this function takes a list of trace flags to disable as first parameter and a list of trace flags to enable as second parameter. Logically, the disable list is applied first, but effectively all changes are applied atomically. The trace flags are the same as for `erlang:trace/3` not including `cpu_timestamp` but including `{tracer,_}`. If a tracer is specified in both lists, the tracer in the enable list takes precedence. If no tracer is specified the same tracer as the process executing the match spec is used. With three parameters to this function the first is either a process identifier or the registered name of a process to set trace flags on, the second is the disable list, and the third is the enable list. Returns `true` if any trace propery was changed for the trace target process or `false` if not. It may only be used in the `MatchBody` part when tracing.

caller: Returns the calling function as a tuple {Module, Function, Arity} or the atom `undefined` if the calling function cannot be determined. May only be used in the `MatchBody` part when tracing.

Note that if a "technically built in function" (i.e. a function not written in Erlang) is traced, the `caller` function will sometimes return the atom `undefined`. The calling Erlang function is not available during such calls.

display: For debugging purposes only; displays the single argument as an Erlang term on stdout, which is seldom what is wanted. Returns `true` and may only be used in the `MatchBody` part when tracing.

get_tcw: Takes no argument and returns the value of the node's trace control word. The same is done by `erlang:system_info(trace_control_word)`.

The trace control word is a 32-bit unsigned integer intended for generic trace control. The trace control word can be tested and set both from within trace match specifications and with BIFs. This call is only allowed when tracing.

set_tcw: Takes one unsigned integer argument, sets the value of the node's trace control word to the value of the argument and returns the previous value. The same is done by `erlang:system_flag(trace_control_word, Value)`. It is only allowed to use `set_tcw` in the `MatchBody` part when tracing.

silent: Takes one argument. If the argument is `true`, the call trace message mode for the current process is set to silent for this call and all subsequent, i.e call trace messages are inhibited even if `{message, true}` is called in the `MatchBody` part for a traced function.

This mode can also be activated with the `silent` flag to `erlang:trace/3`.

If the argument is `false`, the call trace message mode for the current process is set to normal (non-silent) for this call and all subsequent.

If the argument is neither `true` nor `false`, the call trace message mode is unaffected.

Note that all "function calls" have to be tuples, even if they take no arguments. The value of `self` is the atom() `self`, but the value of `{self}` is the pid() of the current process.

### 1.3 Variables and literals

Variables take the form `'$<number>'` where `<number>` is an integer between 0 (zero) and 100000000 (1e+8), the behavior if the number is outside these limits is undefined. In the `MatchHead` part, the special variable `'_'` matches anything, and never gets bound (like `_` in Erlang). In the `MatchCondition/MatchBody` parts, no unbound variables are allowed, why `'_'` is interpreted as itself (an atom). Variables can only be bound in the `MatchHead` part. In the `MatchBody` and `MatchCondition` parts, only variables bound previously may be used. As a special case, in the `MatchCondition/MatchBody` parts, the variable `'$_'` expands to the whole expression which matched the `MatchHead` (i.e., the whole parameter list to the possibly traced function or the whole matching object in the ets table) and the variable `'$$'` expands to a list of the values of all bound variables in order (i.e. `['$1','$2', ...]`).

In the `MatchHead` part, all literals (except the variables noted above) are interpreted as is. In the `MatchCondition/MatchBody` parts, however, the interpretation is in some ways different. Literals in the `MatchCondition/MatchBody` can either be written as is, which works for all literals except tuples, or by using the special form `{const, T}`, where `T` is any Erlang term. For tuple literals in the match_spec, one can also use double tuple parentheses, i.e., construct them as a tuple of arity one containing a single tuple, which is the one to be constructed. The "double tuple parenthesis" syntax is useful to construct tuples from already bound variables, like in `{{'$1', [a,b,'$2']}}`. Some examples may be needed:

Literals in the MatchCondition/MatchBody parts of a match_spec
Expression | Variable bindings | Result
{{'$1','$2'}} | '$1' = a, '$2' = b | {a,b}
{const, {'$1', '$2'}} | doesn't matter | {'$1', '$2'}
a | doesn't matter | a
'$1' | '$1' = [] | []
['$1'] | '$1' = [] | [[]]
[{{a}}] | doesn't matter | [{a}]
42 | doesn't matter | 42
"hello" | doesn't matter | "hello"
$1 | doesn't matter | 49 (the ASCII value for the character '1')

### 1.4 Execution of the match

The execution of the match expression, when the runtime system decides whether a trace message should be sent, goes as follows:

For each tuple in the `MatchExpression` list and while no match has succeeded:

- Match the `MatchHead` part against the arguments to the function, binding the `'$<number>'` variables (much like in `ets:match/2`). If the `MatchHead` cannot match the arguments, the match fails.
- Evaluate each `MatchCondition` (where only `'$<number>'` variables previously bound in the `MatchHead` can occur) and expect it to return the atom `true`. As soon as a condition does not evaluate to `true`, the match fails. If any BIF call generates an exception, also fail.
- - If the match_spec is executing when tracing:
    Evaluate each `ActionTerm` in the same way as the `MatchConditions`, but completely ignore the return values. Regardless of what happens in this part, the match has succeeded.
  - If the match_spec is executed when selectiing objects from an ETS table:
    Evaluate the expressions in order and return the value of the last expression (typically there is only one expression in this context)

### 1.5 Differences between match specifications in ETS and tracing

ETS match specifications are there to produce a return value. Usually the expression contains one single `ActionTerm` which defines the return value without having any side effects. Calls with side effects are not allowed in the ETS context.

When tracing there is no return value to produce, the match specification either matches or doesn't. The effect when the expression matches is a trace messsage rather then a returned term. The `ActionTerm`'s are executed as in an imperative language, i.e. for their side effects. Functions with side effects are also allowed when tracing.

In ETS the match head is a `tuple()` (or a single match variable) while it is a list (or a single match variable) when tracing.

### 1.6 Examples

Match an argument list of three where the first and third arguments are equal:

    [{['$1', '_', '$1'],
      [],
      []}]

Match an argument list of three where the second argument is a number greater than three:

    [{['_', '$1', '_'],
      [{ '>', '$1', 3}],
      []}]

Match an argument list of three, where the third argument is a tuple containing argument one and two or a list beginning with argument one and two (i. e. `[a,b,[a,b,c]]` or `[a,b,{a,b}]`):

    [{['$1', '$2', '$3'],
      [{orelse,
          {'=:=', '$3', {{'$1','$2'}}},
          {'and',
            {'=:=', '$1', {hd, '$3'}},
            {'=:=', '$2', {hd, {tl, '$3'}}}}}],
      []}]

The above problem may also be solved like this:

    [{['$1', '$2', {'$1', '$2}], [], []},
     {['$1', '$2', ['$1', '$2' | '_']], [], []}]

Match two arguments where the first is a tuple beginning with a list which in turn begins with the second argument times two (i. e. [{[4,x],y},2] or [{[8], y, z},4])

    [{['$1', '$2'], [{'=:=', {'*', 2, '$2'}, {hd, {element, 1, '$1'}}}],
      []}]

Match three arguments. When all three are equal and are numbers, append the process dump to the trace message, else let the trace message be as is, but set the sequential trace token label to 4711.

    [{['$1', '$1', '$1'],
      [{is_number, '$1'}],
      [{message, {process_dump}}]},
     {'_', [], [{set_seq_token, label, 4711}]}]

As can be noted above, the parameter list can be matched against a single `MatchVariable` or an `'_'`. To replace the whole parameter list with a single variable is a special case. In all other cases the `MatchHead` has to be a proper list.

Match all objects in an ets table where the first element is the atom 'strider' and the tuple arity is 3 and return the whole object.

    [{{strider,'_'.'_'},
      [],
      ['$_']}]

Match all objects in an ets table with arity > 1 and the first element is 'gandalf', return element 2.

    [{'$1',
      [{'==', gandalf, {element, 1, '$1'}},{'>=',{size, '$1'},2}],
      [{element,2,'$1'}]}]

In the above example, if the first element had been the key, it's much more efficient to match that key in the `MatchHead` part than in the `MatchConditions` part. The search space of the tables is restricted with regards to the `MatchHead` so that only objects with the matching key are searched.

Match tuples of 3 elements where the second element is either 'merry' or 'pippin', return the whole objects.

    [{{'_',merry,'_'},
      [],
      ['$_']},
     {{'_',pippin,'_'},
      [],
      ['$_']}]

The function `ets:test_ms/2` can be useful for testing complicated ets matches.

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