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# grammar::me_vm(n) 0.2 tcllib "Grammar operations and usage"

## Name

grammar::me_vm - Virtual machine for parsing token streams

## Description

Please go and read the document grammar::me_intro first for an overview of the various documents and their relations.

This document specifies a virtual machine for the controlled matching and parsing of token streams, creating an abstract syntax tree (short AST) reflecting the structure of the input. Special machine features are the caching and reuse of partial results, caching of the encountered input, and the ability to backtrack in both input and AST creation.

These features make the specified virtual machine especially useful to packrat parsers based on parsing expression grammars. It is however not restricted to this type of parser. Normal LL and LR parsers can be implemented with it as well.

The following sections will discuss first the abstract state kept by ME virtual machines, and then their instruction set.

## MACHINE STATE

A ME virtual machine manages the following state:

Current token CT

  The token from the input under consideration by the machine.

  This information is used and modified by the instructions defined in the section TERMINAL MATCHING.

Current location CL

  The location of the current token in the input stream, as offset relative to the beginning of the stream. The first token is considered to be at offset 0.

  This information is implicitly used and modified by the instructions defined in the sections TERMINAL MATCHING and NONTERMINAL MATCHING, and can be directly queried and modified by the instructions defined in section INPUT LOCATION HANDLING.

Location stack LS

  In addition to the above a stack of locations, for backtracking. Locations can put on the stack, removed from it, and removed with setting the current location.

  This information is implicitly used and modified by the instructions defined in the sections TERMINAL MATCHING and NONTERMINAL MATCHING, and can be directly queried and modified by the instructions defined in section INPUT LOCATION HANDLING.

Match status OK

  A boolean value, the result of the last attempt at matching input. It is set to true if that attempt was successful, and false otherwise.

  This information is influenced by the instructions defined in the sections TERMINAL MATCHING, NONTERMINAL MATCHING, and UNCONDITIONAL MATCHING. It is queried by the instructions defined in the section CONTROL FLOW.

Semantic value SV

  The semantic value associated with (generated by) the last attempt at matching input. Contains either the empty string or a node for the abstract syntax tree constructed from the input.

  This information is influenced by the instructions defined in the sections SEMANTIC VALUES, and AST STACK HANDLING.

AST stack AS

  A stack of partial abstract syntax trees constructed by the machine during matching.

  This information is influenced by the instructions defined in the sections SEMANTIC VALUES, and AST STACK HANDLING.

AST Marker stack MS

  In addition to the above a stack of stacks, for backtracking. This is actually a stack of markers into the AST stack, thus implicitly snapshooting the state of the AST stack at some point in time. Markers can be put on the stack, dropped from it, and used to roll back the AST stack to an earlier state.

  This information is influenced by the instructions defined in the sections SEMANTIC VALUES, and AST STACK HANDLING.

Error status ER

  Error information associated with the last attempt at matching input. Contains either the empty string or a list of 2 elements, a location in the input and a list of error messages associated with it, in this order.

  Note that error information can be set even if the last attempt at matching input was successful. For example the *-operator (matching a sub-expression zero or more times) in a parsing expression grammar is always successful, even if it encounters a problem further in the input and has to backtrack. Such problems must not be forgotten when continuing to match.

  This information is queried and influenced by the instructions defined in the sections TERMINAL MATCHING, NONTERMINAL MATCHING, and ERROR HANDLING.

Error stack ES

  In addition to the above a stack of error information, to allow the merging of current and older error information when performing backtracking in choices after an unsucessful match.

  This information is queried and influenced by the instructions defined in the sections TERMINAL MATCHING, NONTERMINAL MATCHING, and ERROR HANDLING.

Return stack RS

  A stack of program counter values, i.e. locations in the code controlling the virtual machine, for the management of subroutine calls, i.e. the matching of nonterminal symbols.

  This information is queried and influenced by the instructions defined in the section NONTERMINAL MATCHING.

Nonterminal cache NC

  A cache of machine states (A 4-tuple containing a location in the input, match status OK, semantic value SV, and error status ER) keyed by name of nonterminal symbol and location in the input stream.

  The key location is where machine started the attempt to match the named nonterminal symbol, and the location in the value is where machine ended up after the attempt completed, independent of the success of the attempt.

  This status is queried and influenced by the instructions defined in the section NONTERMINAL MATCHING.

## MACHINE INSTRUCTIONS

With the machine state specified it is now possible to explain the instruction set of ME virtual machines. They are grouped roughly by the machine state they influence and/or query.

### TERMINAL MATCHING

First the instructions to match tokens from the input stream, and by extension all terminal symbols.

These instructions are the only ones which may retrieve a new token from the input stream. This is a may and not a will because the instructions will a retrieve new token if, and only if the current location CL is at the head of the stream. If the machine has backtracked (see icl_rewind) the instructions will retrieve the token to compare against from the internal cache.

ict_advance message

  This instruction tries to advance to the next token in the input stream, i.e. the one after the current location CL. The instruction will fail if, and only if the end of the input stream is reached, i.e. if there is no next token.

  The sucess/failure of the instruction is remembered in the match status OK. In the case of failure the error status ER is set to the current location and the message message. In the case of success the error status ER is cleared, the new token is made the current token CT, and the new location is made the current location CL.

  The argument message is a reference to the string to put into the error status ER, if such is needed.

ict_match_token tok message

  This instruction tests the current token CT for equality with the argument tok and records the result in the match status OK. The instruction fails if the current token is not equal to tok.

  In case of failure the error status ER is set to the current location CL and the message message, and the current location CL is moved one token backwards. Otherwise, i.e. upon success, the error status ER is cleared and the current location CL is not touched.

ict_match_tokrange tokbegin tokend message

  This instruction tests the current token CT for being in the range of tokens from tokbegin to tokend (inclusive) and records the result in the match status OK. The instruction fails if the current token is not inside the range.

  In case of failure the error status ER is set to the current location CL and the message message, and the current location CL is moved one token backwards. Otherwise, i.e. upon success, the error status ER is cleared and the current location CL is not touched.

ict_match_tokclass code message

  This instruction tests the current token CT for being a member of the token class code and records the result in the match status OK. The instruction fails if the current token is not a member of the specified class.

  In case of failure the error status ER is set to the current location CL and the message message, and the current location CL is moved one token backwards. Otherwise, i.e. upon success, the error status ER is cleared and the current location CL is not touched.

  Currently the following classes are legal:

  alnum

    A token is accepted if it is a unicode alphabetical character, or a digit.

  alpha

    A token is accepted if it is a unicode alphabetical character.

  digit

    A token is accepted if it is a unicode digit character.

  xdigit

    A token is accepted if it is a hexadecimal digit character.

  punct

    A token is accepted if it is a unicode punctuation character.

  space

    A token is accepted if it is a unicode space character.

### NONTERMINAL MATCHING

The instructions in this section handle the matching of nonterminal symbols. They query the nonterminal cache NC for saved information, and put such information into the cache.

The usage of the cache is a performance aid for backtracking parsers, allowing them to avoid an expensive rematch of complex nonterminal symbols if they have been encountered before.

inc_restore branchlabel nt

  This instruction checks if the nonterminal cache NC contains information about the nonterminal symbol nt, at the current location CL. If that is the case the instruction will update the machine state (current location CL, match status OK, semantic value SV, and error status ER) with the found information and continue execution at the instruction refered to by the branchlabel. The new current location CL will be the last token matched by the nonterminal symbol, i.e. belonging to it.

  If no information was found the instruction will continue execution at the next instruction.

  Together with icf_ntcall it is possible to generate code for memoized and non-memoized matching of nonterminal symbols, either as subroutine calls, or inlined in the caller.

inc_save nt

  This instruction saves the current state of the machine (current location CL, match status OK, semantic value SV, and error status ER), to the nonterminal cache NC. It will also pop an entry from the location stack LS and save it as the start location of the match.

  It is expected to be called at the end of matching a nonterminal symbol, with nt the name of the nonterminal symbol the code was working on. This allows the instruction inc_restore to check for and retrieve the data, should we have to match this nonterminal symbol at the same location again, during backtracking.

icf_ntcall branchlabel

  This instruction invokes the code for matching the nonterminal symbol nt as a subroutine. To this end it stores the current program counter PC on the return stack RS, the current location CL on the location stack LS, and then continues execution at the address branchlabel.

  The next matching icf_ntreturn will cause the execution to continue at the instruction coming after the call.

icf_ntreturn

  This instruction will pop an entry from the return stack RS, assign it to the program counter PC, and then continue execution at the new address.

### UNCONDITIONAL MATCHING

The instructions in this section are the remaining match operators. They change the match status OK directly and unconditionally.

iok_ok

  This instruction sets the match status OK to true, indicating a successful match.

iok_fail

  This instruction sets the match status OK to false, indicating a failed match.

iok_negate

  This instruction negates the match status OK, turning a failure into a success and vice versa.

### CONTROL FLOW

The instructions in this section implement both conditional and unconditional control flow. The conditional jumps query the match status OK.

icf_jalways branchlabel

  This instruction sets the program counter PC to the address specified by branchlabel and then continues execution from there. This is an unconditional jump.

icf_jok branchlabel

  This instruction sets the program counter PC to the address specified by branchlabel. This happens if, and only if the match status OK indicates a success. Otherwise it simply continues execution at the next instruction. This is a conditional jump.

icf_jfail branchlabel

  This instruction sets the program counter PC to the address specified by branchlabel. This happens if, and only if the match status OK indicates a failure. Otherwise it simply continues execution at the next instruction. This is a conditional jump.

icf_halt

  This instruction halts the machine and blocks any further execution.

### INPUT LOCATION HANDLING

The instructions in this section are for backtracking, they manipulate the current location CL of the machine state. They allow a user of the machine to query and save locations in the input, and to rewind the current location CL to saved locations, making them one of the components enabling the implementation of backtracking parsers.

icl_push

  This instruction pushes a copy of the current location CL on the location stack LS.

icl_rewind

  This instruction pops an entry from the location stack LS and then moves the current location CL back to this point in the input.

icl_pop

  This instruction pops an entry from the location stack LS and discards it.

### ERROR HANDLING

The instructions in this section provide read and write access to the error status ER of the machine.

ier_push

  This instruction pushes a copy of the current error status ER on the error stack ES.

ier_clear

  This instruction clears the error status ER.

ier_nonterminal message

  This instruction checks if the error status ER contains an error whose location is just past the location found in the top entry of the location stack LS. Nothing happens if no such error is found. Otherwise the found error is replaced by an error at the location found on the stack, having the message message.

ier_merge

  This instruction pops an entry from the error stack ES, merges it with the current error status ER and stores the result of the merge as the new error status ER.

  The merge is performed as described below:

  If one of the two error states is empty the other is chosen. If neither error state is empty, and refering to different locations, then the error state with the location further in the input is chosen. If both error states refer to the same location their messages are merged (with removing duplicates).

### SEMANTIC VALUES

The instructions in this section manipulate the semantic value SV.

isv_clear

  This instruction clears the semantic value SV.

isv_terminal

  This instruction creates a terminal AST node for the current token CT, makes it the semantic value SV, and also pushes the node on the AST stack AS.

isv_nonterminal_leaf nt

  This instruction creates a nonterminal AST node without any children for the nonterminal nt, and makes it the semantic value SV.

  This instruction should be executed if, and only if the match status OK indicates a success. In the case of a failure isv_clear should be called.

isv_nonterminal_range nt

  This instruction creates a nonterminal AST node for the nonterminal nt, with a single terminal node as its child, and makes this AST the semantic value SV. The terminal node refers to the input string from the location found on top of the location stack LS to the current location CL (both inclusive).

  This instruction should be executed if, and only if the match status OK indicates a success. In the case of a failure isv_clear should be called.

isv_nonterminal_reduce nt

  This instruction creates a nonterminal AST node for the nonterminal nt and makes it the semantic value SV.

  All entries on the AST stack AS above the marker found in the top entry of the AST Marker stack MS become children of the new node, with the entry at the stack top becoming the rightmost child. If the AST Marker stack MS is empty the whole stack is used. The AST marker stack MS is left unchanged.

  This instruction should be executed if, and only if the match status OK indicates a success. In the case of a failure isv_clear should be called.

### AST STACK HANDLING

The instructions in this section manipulate the AST stack AS, and the AST Marker stack MS.

ias_push

  This instruction pushes the semantic value SV on the AST stack AS.

ias_mark

  This instruction pushes a marker for the current state of the AST stack AS on the AST Marker stack MS.

ias_mrewind

  This instruction pops an entry from the AST Marker stack MS and then proceeds to pop entries from the AST stack AS until the state represented by the popped marker has been reached again. Nothing is done if the AST stack AS is already smaller than indicated by the popped marker.

ias_mpop

  This instruction pops an entry from the AST Marker stack MS and discards it.

## Bugs, Ideas, Feedback

This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category grammar_me of the Tcllib Trackers. Please also report any ideas for enhancements you may have for either package and/or documentation.

When proposing code changes, please provide unified diffs, i.e the output of diff -u.

Note further that attachments are strongly preferred over inlined patches. Attachments can be made by going to the Edit form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar.

## Keywords

grammar, parsing, virtual machine

## Category

Grammars and finite automata

## Copyright

Copyright © 2005 Andreas Kupries <andreas_kupries@users.sourceforge.net>