Command:def or eval

The "def" and "eval" commands are identical. The syntax for them is as follows:

def <name> <predicate>

Results saved in: Result/, Automata Library/.

For example, to create and save an automaton that accepts an input of "a" if and only if a is the msd_2 representation of 4 (i.e. it belongs to 0*100), one can create the following automaton:

def four "a=4";

In previous versions of Walnut, word automata names in eval/def commands could not begin with A, E, or I. This restriction has now been lifted using a new delimiter for word automata: putting "." (without quotation marks) before the name of a word automaton now signals that the following string of characters is the name of the word automaton. If there is a word automaton named AUTOMATON, you can write ".AUTOMATON" (without quotation marks) to refer to it in eval/def commands. For example, the following is now valid:

def test ".AUTOMATON[n] = @1";

There is also a "headless mode" option, if you don't wish to save the automaton. For example,

def "E x x > x+1";

will not create an automaton file, but will still build and evaluate. Headless eval/def can also print the output of a word automaton or word expression directly. For example:

def "F[1]";

prints the value F[1].

To print an expression over a finite range of values, place one or more variable bindings before the quoted expression. Ranges are inclusive. For example:

def n=1..10 "F[n]";
def n=1..10 "F[2*n+5]";

For an ordinary automaton, the corresponding Boolean values are printed as 0 and 1. All free variables of the expression must be bound. Multiple bindings give multidimensional output, which is displayed as indented slices. For example:

def i=1..10 j=2..5 k=1..4 "multi_example[i][j][k]";

A binding may also specify a single value, for example n=5.

Please refer to section 7 of the Arxiv manual for a more detailed description of the "def"/"eval" commands and what one can do with them.