A simple CAS and language for computations in boolean algebra

What this is

Boolean is a small programming language designed specifically to manipulate boolean expressions. It can generate truth tables, evaluate simplification rules, and do a little bit of inference.

Mess around with a demo (compiled from Rust to WebAssembly):


Boolean can parse the following expressions and operations:

  • Literals (T for true, F for false)
  • Symbolic variables (e.g. a, thing)
  • Negation (e.g. !x, !(a & b))
  • Conjunction (AND) (a & b)
  • Disjunction (OR) (a | b)
  • Implication (p => q)
  • Biconditional implication (p <=> q)

It also understands some of its own syntax:

  • Commands (Table (a & b | c), Satisfy (p => q))
  • Strings ("Some text")


The language allows commands to control the evaluation of their own arguments. This mechanism is somewhat similar to the Hold* family of function attributes in the Wolfram Language--each function gets to control how its children in the AST are handled.

Boolean understands the following functions:


Usage: With expr assumptions

With substitutes a set of concrete assumptions into expr.

For example:

> With (a | b) a

> With (a & b) (!a)

> With (a & b & !c & d) (b & !c)
a & d


Usage: Table expr [var...]

Table generates truth tables for expr, in disjunctive normal form (e.g. a | !b).

For example:

> Table (a | b)
a & !b | !a & b | b & a

> Table ( (a & b) => q ) a b
!a & !b | b & !a | !b & a


Usage: Satisfy expr

Satisfy finds a set of bindings which satisfy expr.

For example:

> Satisfy (a & b & (!a | b))
b & a

Running it

Boolean has both a CLI (in ./cli) and a web UI (in ./www). For the web UI, a server isn't required--the core is compiled to WebAssembly, and shipped directly to the browser.

  # running the CLI
$ cd cli && cargo run

  # build the web UI (requires cargo-web and cross)
$ cd www && yarn install && make