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Difference between revisions of "SCI/Specifications/SCI in action/Parser"
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SCI/Specifications/SCI in action/Parser (view source)
Revision as of 19:13, 18 January 2009
, 19:13, 18 January 2009Merging of the SCI documentation. Work in progress.
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(Merging of the SCI documentation. Work in progress.) |
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==The Parse tree== | ==The Parse tree== | ||
This and the two following sections borrow some ideas and structures from abstract language theory. Readers might want to consider related literature. | This and the two following sections borrow some ideas and structures from abstract language theory. Readers might want to consider related literature. | ||
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|} | |} | ||
With the notable exception of the first rule, these rules constitute <span style="white-space:nowrap"><i>P. V := {χ|∃R ∈ P.χ &exist | With the notable exception of the first rule, these rules constitute <span style="white-space:nowrap"><i>P. V := {χ|∃R ∈ P.χ &exist R}</i></span>; typically, <span style="white-space:nowrap"><i> V = {0χ12ƒ…0χ13ƒ⋅ s = m<sub>0</sub></i></span> of the first rule encountered; in all games observed, it was set to 0x13c. Σ contains all word groups and class masks. For the sake of simplicity, we will consider rules matching composite class masks to be several rules. Here is a simplified example of what such a grammar might look like (the hexadecimal prefix '0x' is omitted for brevity): | ||
In addition to this grammar, each right-hand non-terminal <i>m<sub>i</sub></i> carries its semantic value <i>ρ<sub>i</sub></i> , which is not relevant for constructing a syntax tree, but must be considered for the semantic tree <i>T</i><sub>π</sub>. These values were omitted in the example above. As in the example above, the grammar is a context-free (type 2) grammar, almost in Chomsky Normal Form (CNF) in SCI; constructing a grammar with CNF rules from it would be trivial.<ref>FreeSCI constructs a GNF (Greibach Normal Form) representation from these rules for parsing.</ref> | In addition to this grammar, each right-hand non-terminal <i>m<sub>i</sub></i> carries its semantic value <i>ρ<sub>i</sub></i> , which is not relevant for constructing a syntax tree, but must be considered for the semantic tree <i>T</i><sub>π</sub>. These values were omitted in the example above. As in the example above, the grammar is a context-free (type 2) grammar, almost in Chomsky Normal Form (CNF) in SCI; constructing a grammar with CNF rules from it would be trivial.<ref>FreeSCI constructs a GNF (Greibach Normal Form) representation from these rules for parsing.</ref> | ||
Obviously, G is an ambiguous grammar. In SCI, rule precedence is implied by rule order, so the resulting left derivation tree is well-defined (in the example, it would be defined by <i>D<sub>0</sub>.<ref>In FreeSCI, you can use the ”parse” console command to retreive all possible left derivation trees.</ref> | Obviously, G is an ambiguous grammar. In SCI, rule precedence is implied by rule order, so the resulting left derivation tree is well-defined (in the example, it would be defined by <i>D<sub>0</sub></i>.<ref>In FreeSCI, you can use the ”parse” console command to retreive all possible left derivation trees.</ref> | ||
<br> | |||
====Parser grammar example==== | |||
<span style="white-space:nowrap">G = ⟨{⟩12ƒ…13e,(C<sub>1</sub>,C<sub>2</sub>,C<sub>4</sub>,…,C<sub>1</sub>00},P,13c)</span> | |||
{| <i> | |||
|---- | |||
| | |||
|13c | |||
|↦ | |||
|13b 134 | |||
|---- | |||
| | |||
|13c | |||
|↦ | |||
|13b 13d 133 | |||
|---- | |||
| | |||
|13c | |||
|↦ | |||
|13b 13d | |||
|---- | |||
| | |||
|13c | |||
|↦ | |||
|13c | |||
|---- | |||
| | |||
|13c | |||
|↦ | |||
|13b 13d 13b 13d | |||
|---- | |||
| | |||
|13b | |||
|↦ | |||
|131 134 | |||
|---- | |||
| | |||
|13b | |||
|↦ | |||
|131 13d 13d | |||
|---- | |||
|rowspan=2| P = { | |||
|13b | |||
|↦ | |||
|131 | |||
|---- | |||
|13d | |||
|↦ | |||
|134 | |||
|---- | |||
| | |||
|131 | |||
|↦ | |||
|C<sub>8</sub>0 | |||
|---- | |||
| | |||
|133 | |||
|↦ | |||
|C<sub>2</sub>0 | |||
|---- | |||
| | |||
|134 | |||
|↦ | |||
|C<sub>1</sub>0} | |||
|---- | |||
|}</i> | |||
===Semantics=== | |||
This is important, since the parser does much more than just accept or discard input. Using the semantic tags applied to each non-terminal on the right-hand side of a rule, it constructs what I will call the semantic parse tree <i>T</i><sub>π</sub> , which attempts to describe what the input means. For each non-terminal rule | |||
<i>r = υ<sub>0</sub> ↦ υ<sub>1</sub>υ<sub>2</sub>…υ<sub>n</sub></i> | |||
there are semantic tags <i>σ<sub>r,1</sub>,σ<sub>r,2</sub>…σ<sub>r,n</sub> ∈ S</i> , as explained above. <i>T</i><sub>π</sub> is now constructed from the resulting derivation and the semantic tags assiociated with each non-terminal of the rule used. The construction algorithm is explained below with <i>T</i><sub>π</sub> being constructed from nodes, which have the following structure: | |||
<i>NODE = {◇} ∪ S × V × (NODE ∪ Γ);*</i> | |||
Where S is the set of possible semantic values, and V is the set of non-terminals as defined in the grammar. We will also use the sequence <i>γ<sub>0</sub>,&gamma<sub>1</sub>,&gamma<sub>2</sub> … &gamma<sub>k-1</sub></i> which will represent the word groups the input tokens belonged to (in the exact order they were accepted), and the sequence <i>r<sub>0</sub>,r<sub>1</sub>,r<sub>2</sub> … r<sub>l-1</sub></i> , which will be the list of rules used to create the left derivation tree as described in the previous section. | |||
<syntax type="?"> | |||
Helper function sci_said_recursive: S \times V \times (V \cup \Sigma)* \to \Node | |||
Parameters: s \in S, Rule r \in V \times (V \cup \Sigma): v0 \to v1 v2 ... vi | |||
cnmr = cnr | |||
\Node n := s, v0 | |||
FOR j := 1 TO i | |||
IF (vj \in \Sigma) THEN | |||
n := n, \gammacn\gamma | |||
cn\gamma := cn\gamma + 1 | |||
ELSE | |||
cnoldr := cnr | |||
cnr := cnr + 1 | |||
n := n, sci_said_recursive(\sigmarmr,j, rcnoldr) | |||
FI | |||
ROF | |||
RETURN (n) | |||
Helper function get_children: \Node \to \Node* | |||
get_children((s, v, n0, n1 ... nm)) := n0, n1 ... nm | |||
Algorithm SCI-SAID-TREE | |||
cn\gamma := 0; | |||
cnr := 1; | |||
ntemp := ntemp, SCI-SAID-RECURSIVE(0, r0) | |||
root(T\Pi) := (141, 13f, get_children(ntemp)) | |||
</syntax> | |||
Here is an example, based on the previous one: | |||
====Example: Semantic tree example==== | |||
<i> | |||
* k = 2 | |||
* γ<sub>0</sub> = 842 | |||
* γ<sub>1</sub> = 917 | |||
* l = 4 | |||
* r<sub>0</sub> = 13c ↦ 13b 134 | |||
* σ<sub>r<sub>0</sub>,1</sub> = 141 | |||
* σ<sub>r<sub>0</sub>,2</sub> = 142 | |||
* r<sub>1</sub> = 13b ↦ 131 | |||
* σ<sub>1<sub>1</sub>,1</sub> = 141 | |||
* r<sub>2</sub> = 131 ↦ C<sub>80</sub> | |||
* r<sub>3</sub> = 134 ↦ C<sub>10</sub> | |||
</i> | |||
The resulting tree would look like this: | |||
<tt><pre> | |||
(141 13f | |||
	(141 13b | |||
		(141 131 842) | |||
	) | |||
	(142 134 917) | |||
) | |||
</tt></pre> | |||
==Notes== | |||
<references/> | |||