Truth Table

This is a simple truth table generator. For more information about truth tables, please see the relevant Wikipedia article.

There is an instance of the web version of this program hosted here: tt.zander.im

This repository contains three things: a Common Lisp library to parse and manipulate propositional logic expressions, a command line truth table generator, and a web-based truth table generator.

To build the CLI version, just run make. You will need SBCL, ASDF, and Quicklisp. Quicklisp is used to load uiop and with-user-abort.

To run the web server, execute ./truth-table-web-wrapper. If you want to run it in the background, I recommend using something like GNU Screen. The web server supports -h and --help, you can use them to see all the options it supports. It should be noted, however, that it does not support HTTPS. If you want to use HTTPS, run the web server behind something like Nginx or HAProxy.

The format of the input propositions is fairly free-form. The above Wikipedia article has some information about their format, as well as possible symbols for operators. You can also take a look at the table near the top of parse.lisp for all the variations supported by this program.

CLI Usage

Here is the help output from the CLI (not web) program:

usage: truth-table [options] <propositions...>

  -h, --help          print this message, then exit
  -f, --format=<arg>  specify the output format (*unicode*, ascii, latex, or html)
  -s, --subexps       include sub-expressions in the output table
  -n, --no-vars       do not include variables in the output table
  -m, --multi-char    allow multi-character variable names
  -i, --no-implicit   do not use implicit 'and' operations
  -p, --pretty        pretty print latex, html, etc. output
  -l, --latin         use the Latin T and F characters for truth values

The choice surrounded by '*' is the default. Arguments to long
options are also required for their short variant.

Here is an example truth table:

$ truth-table '(a /\ b) -> ~b'
┌───┬───┬────────────┐
│ a │ b │ a ∧ b → ¬b │
├───┼───┼────────────┤
│ ⊤ │ ⊤ │     ⊥      │
│ ⊤ │ ⊥ │     ⊤      │
│ ⊥ │ ⊤ │     ⊤      │
│ ⊥ │ ⊥ │     ⊤      │
└───┴───┴────────────┘