Hatt

Hatt is a command-line program which prints truth tables for expressions in classical propositional logic, and a library allowing its parser, evaluator and truth table generator to be used in other programs.

Installation

Hatt is available from Hackage. To install it with cabal-install, update your list of known packages and then install Hatt.

$ cabal update
$ cabal install hatt

To build it from source, cd into the directory containing the Hatt source files, including hatt.cabal, and run cabal install.

Valid Hatt expressions

The following are all valid expression forms which can be parsed by Hatt, where ϕ and ψ are metalinguistic variables standing in for any valid expression. The parser isn't as smart about parentheses as it could be, so you have to follow these rules quite literally. This shouldn't be a great hardship, but it does mean that, for example, while (A -> B) is a valid expression, A -> B isn't.

• Variables: P, Q, R etc.---basically anything in the character class [A-Z]
• Negation: ~ϕ
• Conjunction: (ϕ & ψ)
• Disjunction: (ϕ | ψ)
• Conditional: (ϕ -> ψ)
• Biconditional: (ϕ <-> ψ)

Using the hatt command-line program

The --evaluate flag lets you pass an expression to be evaluated directly. Here's an example session doing just that.

$ hatt --evaluate="(P -> (Q | ~R))"
P Q R | (P → (Q ∨ ¬R))
----------------------
T T T | F
T T F | F
T F T | F
T F F | F
F T T | F
F T F | F
F F T | T
F F F | F

Note that while you need to use ASCII symbols to interact with hatt, it pretty-prints expressions using the more common logical symbols. The Hatt library exposes the showAscii function which will print expressions in the format in which they're entered.

Using Hatt in other programs

Hatt exposes the Data.Logic.Propositional module, which provides a simple API for parsing, evaluating, and printing truth tables.