Hatt is a command-line program which prints truth tables for expressions in classical propositional logic, and a library allowing its parser, evaluator, truth table generator and other functionality to be used in other programs.
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.
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. Note that Hatt accepts Unicode symbols for logical connectives. This is practical for example when wanting to copy-paste formulae from web browser - no need to rewrite to corresponding ASCII representations.
- Variables:
P,Q,a,betc.---basically anything in the character class[a-zA-Z] - Negation:
~ϕor¬ϕ - Conjunction:
(ϕ & ψ)or(ϕ ∧ ψ) - Disjunction:
(ϕ | ψ)or(ϕ ∨ ψ) - Conditional:
(ϕ -> ψ)or(ϕ → ψ) - Biconditional:
(ϕ <-> ψ)or(ϕ ↔ ψ)
Parentheses are not required around top-level formulae, regardless of whether
the primary connective is binary. For example, the expression a | b is valid
and will be parsed correctly, as would p <-> (q & ~r), although the
parenthesised versions of both these expressions ((a | b) and
(p <-> (q & ~r))) are also fine.
Standard operator precedence for logical operators is supported. All the
binary connectives associate to the right, so a -> b -> c is interpreted as
a -> (b -> c). To override these rules, use parentheses as normal. Note that
right-associativity only matters for the material conditional: all the other
logical operators are associative, so a * (b * c) is equivalent to
(a * b) * c where * is conjunction, disjunction or the biconditional.
The default mode is interactive: you start the program, enter expressions at the prompt, and their truth tables are printed. Here's an example session.
$ hatt
Entering interactive mode. Type `help` if you don't know what to do!
> A | B
A B | (A | B)
-------------
T T | T
T F | T
F T | T
F F | F
> p -> (q & ~r)
p q r | (p -> (q & ~r))
-----------------------
T T T | F
T T F | T
T F T | F
T F F | F
F T T | T
F T F | T
F F T | T
F F F | T
> e <-> f
e f | (e <-> f)
---------------
T T | T
T F | F
F T | F
F F | T
> exit
The --evaluate flag lets you pass a single expression to be evaluated
directly.
$ 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
By default, hatt will print ASCII representations of expressions. If you have
a Unicode-capable terminal, try passing the --pretty option to pretty-print
expressions using the the more common logical symbols.
$ hatt --evaluate="P -> (Q | ~R)" --pretty
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
You can enable pretty-printing while in interactive mode by using the pretty
command.
If you pass the --coloured flag, hatt will colour the truth values in the
tables which it prints: green for true, red for false. You can enable colouring
during interactive mode by using the colour command.
You can print out the normal forms of expressions too, by prefixing an
expression with nnf, dnf or cnf.
$ hatt --pretty
> nnf ~(P -> (Q & R))
(P ∧ (¬Q ∨ ¬R))
The three supported normal forms are negation normal form, conjunctive normal form and disjunctive normal form.
Hatt exposes the Data.Logic.Propositional module, which provides a simple API
for parsing, evaluating, and printing truth tables. It also includes the
Data.Logic.Propositional.NormalForms module which exports functions to convert
logical expressions into normal forms. Details of the foregoing can be found in
the library documentation.