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Marpa::R2::Advanced::Input_Models - Alternative input models
About this document
The alternative input models described in this document are an advanced technique. While you are starting out with Marpa, you probably want to ignore this document. If you are an experienced Marpa user, it is still safe to ignore this document, but you might find the possibilities it discusses interesting.
This document describes the input models at a conceptual, rather than an implementation level. The reader should be familiar with the recognizer's external scanning capability. A reader interested in implementation is assumed to be familiar with the methods described in "Mutators for external scanning" in Marpa::R2::Scanless::R,
Marpa has two different ideas of location
In the other Marpa documentation, we have spoken of "location", and assumed the standard input model. The locations actually in use by the methods described for the standard input model were Earley set ordinals. (An Earley set's ordinal is also its ID.)
Marpa actually has two different ideas of location -- Earley set ordinal and earleme. This is ignored in the other Marpa documents, and it can be, because they assume the standard input model. Use of the standard input model guarantees that earleme and Earley set ordinal will always be exactly the same.
This document introduces methods which make it possible (and in fact likely) that earleme and Earley set ordinal will differ. From here on, the reader will need to pay careful attention to the distinction.
What is an alternative input model?
An alternative input model is anything that is not the default, token-stream model. More helpfully, Marpa allows variable-length tokens and ambiguous tokens, and an alternative input model is any input model which
Allows a token whose length is not exactly 1, or
Allows locations which have more than one token.
To do either of these things, a user must use external scanning and the recognizer'x external scanning methods. In particular, if an application is not directly using the recognizer's lexeme_read or lexeme_alternative method calls, that application is not using an alternative input method.
Many concepts, such as parsing location, parse exhaustion, and the end of parsing, are somewhat more complicated when alternative input models are involved. These concepts were explained in the main document for the recognizer on the assumption that the default input model was in use. This document revises those explanations as necessary to take into account the alternative input models.
Token streams
Marpa's default input model is the traditional one -- a token stream. Token streams are very standard in parsing applications -- so much so that most texts do not take the trouble of defining the term. A token stream is input structured as a sequence of tokens, where each token occupies one location and every location has a token. In the token stream model, all tokens are of the same length.
Conventionally, all tokens are of length 1, and the token stream starts at location 0. Following this convention, the Nth token would start at location N-1 and end at location N. For example, the first token would start at location 0 and end at location 1. The second token would start at location 1 and end at location 2.
Earlemes
For most parsers, position is location in a token stream. To deal with variable-length and overlapping tokens, Marpa needs a more flexible idea of location.
Marpa's tracks position in terms of earlemes. Earlemes are named after Jay Earley, the inventor of the first algorithm in Marpa's lineage. Every token has a start earleme and an end earleme.
The token stream model may also be called the token-per-earleme model. In the token stream model, token location and earleme location are exactly identical. More formally, in the token stream model, if the token location is N, then the earleme location is also N. If a user's application uses the token stream model, the user can ignore the existence of earlemes, and can think entirely in terms of tokens and their position in a token stream. Because of this, the main Marpa documents often speak simply of the "location" in the parse.
The furthest earleme
The furthest earleme is the last earleme at which a token ends. In the default input model, the furthest earleme and the current earleme are always the same. As a result, in the default input model, the furthest earleme is not an important concept.
In alternative input models, tokens may be longer than 1 earleme, and the furthest earleme and the current earleme may be far apart. This becomes an issue when parsing is finished. Alternative input models use one or more calls to the recognizer's lexeme_complete() method to ensure that processing of input catches up to the furthest earleme.
The latest Earley set and latest earleme
The latest earleme is the earleme location of the latest Earley set. In the default input model, the latest earleme is always the same as the current earleme.
In alternative input models, there may not be an Earley set at a given earleme location. When that is the case for the current earleme, then the latest Earley set is not at the current earleme, and the latest earleme and current earlemes are different.
Ambiguous lexing
Marpa allows ambiguous tokens. Several Marpa tokens can start at a single parsing location. Ambiguous tokens can be of various lengths. Tokens can also overlap.
Potentially ambiguous lexing occurs when more than one token starts at a single earleme. When potentially ambiguous lexing occurs, it becomes possible for there to be more than one sequence of tokens.
An actual lexical ambiguity only occurs if more than one of the potential token sequences is consistent with the grammar. If there is no actual lexical ambiguity, Marpa will use the only token choice that is consistent with the grammar.
When lexing is actually ambiguous, Marpa will use all the alternatives consistent with the grammar. When the lexing in a parse is actually ambiguous, the parse will be ambiguous. From the point of view of Marpa's semantics, ambiguities caused by lexing look the same as ambiguities caused by an ambiguous grammar.
In the standard terminology, if a grammar produces more than one parse tree for any input, then that grammar must be ambiguous. In Marpa this is not strictly true. In Marpa, if the input is ambiguous, even an unambiguous grammar can produce more than one parse.
Duplicate tokens
A duplicate token is a token of the same type and the same length as another that was read at the same earleme. Duplicate tokens are impossible in the default, token-stream, model. This is because in the token-stream model only one token can be read at each earleme.
In alternative models, more than one token may be read at an earleme, and duplicates are possible. Marpa detects duplicate tokens and treats them as "hard errors" -- Marpa throws an exception when it sees a duplicate token. Marpa's assumption is that duplicate tokens indicate an error at the application level.
An application can retry input after a duplicate token, if it catches the exception. In the future, if recovery from duplicate tokens is found to be a useful technique, Marpa may provide an option to change its behavior, so that a soft failure is returned when there is a duplicate token.
Earlemes: the details
While scanning, Marpa keeps track of the current earleme. Earlemes in a parse start at earleme 0 and increase numerically. The earleme immediately following earleme 0 is earleme 1, the earleme immediately following earleme 1 is earleme 2, and so on. The earleme immediately following earleme N is always earleme N+1.
Distance in the earleme stream is what you would intuitively expect it to be. The distance between earleme X and earleme Y is the absolute value of the difference between X and Y, |X-Y|. The distance from earleme 3 to earleme 6, for example, is 3 earlemes.
Whenever a token is given to Marpa to be scanned, it starts at the current earleme. In addition to the type and value of the token, Marpa must be told the token's length in earlemes. The length of a Marpa token must be greater than zero.
This earleme length will become the distance from the start of the token to the end of the token. If the length of the token is L, and the current earleme is C, the end of the token will be at earleme C+L.
The character-per-earleme model
Many different models of the relationship between tokens and earlemes are possible, but two are particularly important. One is the one-token-per-earleme model, which is the default, and which has already been described. The other is the one-character-per-earleme model.
In the one-character-per-earleme model, every character will be treated as being exactly one earleme in length. If a token is more than one character in length, that token will span earlemes. When the lexing is ambiguous, tokens may overlap.
When a one-character-per-earleme model of input is used, there may be many earlemes at which no tokens start. For example, in a straightforward character-per-earleme implementation of a grammar for a language that allows comments, no tokens will start at any earlemes which correspond to character locations inside a comment.
Other input models
So far only the token-per-earleme and character-per-earleme models have seen any real use in Marpa programs. But other models are certainly possible. Using earlemes, you can structure your input in almost any way you like.
There are only three restrictions:
Scanning always starts at earleme 0.
All tokens starting at earleme N must be scanned before any tokens starting at earleme N+1. In other words, the tokens must be scanned in non-decreasing order by start earleme.
Every token must have a length, in earlemes, which is greater than zero. In other words, token length can never be zero or negative.
Copyright and License
Copyright 2022 Jeffrey Kegler
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