CFG Checker searches for ambiguities in context-free grammars. It is only semi-decidable to determine whether an arbitrary context-free grammar is ambiguous. The best we can do is generate all derivations in a breadth-first fashion and look for two which produce the same sentential form. So that's exactly what CFG Checker does. If the input grammar is ambiguous, CFG Checker will eventually find a minimal ambiguous sentential form. If the grammar is unambiguous, CFG Checker will either reach this conclusion or loop forever.
Here's how it works. You specify the grammar as a series of production rules:
expression = number | sum sum = expression + expression
Then you run CFG Checker on it:
$ cfg-checker example.cfg .... Found a sentential form with two different derivations: expression + expression + expression Derivation 1: 0: expression 1: sum 2: expression + expression 3: expression + sum 4: expression + expression + expression Derivation 2: 0: expression 1: sum 2: expression + expression 3: sum + expression 4: expression + expression + expression
If it doesn't finish within a few seconds, the grammar is probably unambiguous unless you gave it some pathological input.
Each line is a production rule. A production rule specifies that a symbol may be rewritten as one of several alternatives separated by pipes (
|). An alternative is a (possibly empty) sequence of symbols separated by whitespace. Consider this example:
S = a S a | b S b | c
This rule says
S can be rewritten to
a S a,
b S b, or
A symbol can be any non-whitespace string except a pipe (
|). All of the following are valid symbols:
The first rule in the grammar determines the start symbol.
How to build and install
make from the root of this repository. A binary called
cfg-checker will be produced. You can run
make install to install it to
make install PREFIX=/custom/path to change the installation prefix.
CFG Checker is written in C++ and has no dependencies.
Copyright (c) 2017 Stephan Boyer
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