truthtable - truth table to logical formula

About

The truthtable library generates a truth table from a logical formula written in Ruby. The truth table can be converted to a logical formula.

Home Page

http://www.a-k-r.org/truthtable/

Feature

• generate a truth table from a given block written in Ruby.
• generate a formula from the table:
  • minimal one (obtained by Quine-McCluskey algorithm)
  • disjunctive normal form
  • conjunctive normal form

Usage

• require

  require 'truthtable'

• puts, p and pp shows truth table

  puts TruthTable.new {|v| v[0] & v[1] }
  #=>
  v[0] v[1] | 
  ----------+--
   f    f   | f
   f    t   | f
   t    f   | f
   t    t   | t
  
  p TruthTable.new {|v| v[0] & v[1] }
  #=> #<TruthTable: !v[0]&!v[1]=>false !v[0]&v[1]=>false v[0]&!v[1]=>false v[0]&v[1]=>true>
  
  require 'pp'
  pp TruthTable.new {|v| v[0] & v[1] }
  #=>
  #<TruthTable:
   !v[0]&!v[1]=>false
   !v[0]& v[1]=>false
    v[0]&!v[1]=>false
    v[0]& v[1]=>true>

• '?' is shown for non-evaluated variable

  puts TruthTable.new {|v| v[0] && v[1] }'
  #=>
  v[0] v[1] | 
  ----------+--
   f    ?   | f
   t    f   | f
   t    t   | t
  
  puts TruthTable.new {|v| v[0] || v[1] }'
  #=>
  v[0] v[1] | 
  ----------+--
   f    f   | f
   f    t   | t
   t    ?   | t
  
  puts TruthTable.new {|v| !v[0] ? !v[1] : !v[2] }'
  #=>
  v[0] v[1] v[2] | 
  ---------------+--
   f    f    ?   | t
   f    t    ?   | f
   t    ?    f   | t
   t    ?    t   | f

• formula generation

  p TruthTable.new {|v| !v[0] }.formula        #=> "!v[0]"
  p TruthTable.new {|v| v[0] & v[1] }.formula  #=> "v[0]&v[1]"
  p TruthTable.new {|v| v[0] | v[1] }.formula  #=> "v[0] | v[1]"
  p TruthTable.new {|v| v[0] ^ v[1] }.formula  #=> "!v[0]&v[1] | v[0]&!v[1]"
  p TruthTable.new {|v| v[0] == v[1] }.formula #=> "!v[0]&!v[1] | v[0]&v[1]"

• shortcuts, && and ||, are not preserved

  p TruthTable.new {|v| v[0] && v[1] }.formula #=> "v[0]&v[1]"
  p TruthTable.new {|v| v[0] || v[1] }.formula #=> "v[0] | v[1]"

• actually any expression (without side effect)

  p TruthTable.new {|v| v[0] ? !v[1] : v[1] }.formula #=> "!v[0]&v[1] | v[0]&!v[1]"

• any number of inputs

  p TruthTable.new {|v| [v[0], v[1], v[2], v[3]].grep(true).length <= 3 }.formula
  #=> "!v[0] | !v[1] | !v[2] | !v[3]"

Requirements

• ruby : http://www.ruby-lang.org/

Download

• latest release: truthtable-0.1.tar.gz (sha256)
• development version: http://github.com/akr/truthtable

Install

% ruby install.rb

Reference Manual

See rdoc/TruthTable.html.

License

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. The name of the author may not be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

(The modified BSD licence)