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6 Marpa::XS::Semantics::Infinite - How Marpa Deals with Infinite Cycles
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9 Marpa will parse using an infinitely ambiguous grammar. (In the
10 technical literature, an infinite ambiguity is more usually called a
11 cycle or a loop.)
12 An example of an infinitely ambiguous grammar is the following:
14 S ::= A
16 A ::= B
17 B ::= A
18 B :: 'x'
19 Given the input 'x', this grammar will produce these parses
21 S -> A -> B -> x
23 S -> A -> B -> A -> B -> x
24 S -> A -> B -> A -> B -> A -> B -> x
25 .
26 .
27 .
28 Because of the two rules "A ::= B" and "B ::= A", this list of parses
30 could go on forever. The two rules "A ::= B" and "B ::= A" form what
31 is called a cycle.
32 Typically, if a user has written an grammar with an infinite cycle, it
34 was a mistake and he wants to rewrite it before proceeding. By
35 default, an infinitely ambiguous grammar is a fatal error. This is the
36 behavior most users will want.
37 To produce parse results from an infinitely ambiguous grammar, the user
39 must set the grammar's "infinite_action" named argument to a value
40 other than ""fatal"". The other choices are ""warn"" and ""quiet"".
41
43 Obviously, Marpa cannot list all of an infinite number of parse
44 results. Marpa deals with potentially infinite parses by limiting the
45 cycle length. Cycle length is the number of times a parse derivation
46 goes around a potentially infinite cycle.
47 Marpa limits all cycles to a length of 1. There will always be a
49 finite number of these parse results.
50 Above I showed a set of parses from an example of an infinitely
52 ambiguous grammar. Here are those parses again, this time labeled with
53 their cycle length.
54 Cycle length 1: S -> A -> B -> x
56 Cycle length 2: S -> A -> B -> A -> B -> x
57 Cycle length 3: S -> A -> B -> A -> B -> A -> B -> x
58 Marpa would return a parse result only for the first parse tree in the
60 list above, the one whose cycle length is 1.
61
63 The precise behavior of Marpa's cycle detection is, at this point, not
64 strictly defined and applications should avoid relying on the details
65 of its semantics. The exact point at which a cycle is broken varies
66 among implementations.
67 In future releases, Marpa's cycle detection may be more carefully
69 defined. But cycles at this point are universally considered useless,
70 and there seems to be literally nobody who cares about the details of
71 their semantics. The quality of the present implementation seems to be
72 completely adequate in terms of the present interest.
73 At this point it seems that a cycle should be broken when it is about
75 to loop back to the "same rule". But in current Marpa implementations,
76 the "same rule" means the same rule after Marpa's rewriting of the
77 grammar, not the same rule as in the original grammar. If a more
78 careful semantics is created, it probably should be defined in terms of
79 the rules as the user sees them, rather than in terms of the rules as
80 rewritten by Marpa's internals.
81
83 Copyright 2012 Jeffrey Kegler
84 This file is part of Marpa::XS. Marpa::XS is free software: you can
85 redistribute it and/or modify it under the terms of the GNU Lesser
86 General Public License as published by the Free Software Foundation,
87 either version 3 of the License, or (at your option) any later version.
88 Marpa::XS is distributed in the hope that it will be useful,
90 but WITHOUT ANY WARRANTY; without even the implied warranty of
91 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
92 Lesser General Public License for more details.
93 You should have received a copy of the GNU Lesser
95 General Public License along with Marpa::XS. If not, see
96 http://www.gnu.org/licenses/.
97perl v5.32.0 2020-07-28 Marpa::XS::Semantics::Infinite(3)