Existential and universal quantification used redundant data
representations, while they actually share the same structure. This
unifies both into a single QuantifiedFormula type.
For convenience, support biconditionals with more than one argument.
An n-ary “if and only if” statement
F_1 <-> F_2 <-> ... <-> F_n
is to be interpreted as
F_1 <-> F_2 and F2 <-> F3 and ... and F_(n - 1) <-> F_n
As the absolute value operation has its own type of parentheses, it
never needs to take precedence over other terms in order to be displayed
correctly. To avoid extraneous parentheses around absolute value
operations, set its precedence level to 0.
The precedence rules of binary operations are a bit trickier than
expected. The fact that a parent and a child term have the same
precedence level doesn’t automatically mean that parentheses can be
omitted. This is the case, for example, with
a - (b + c)
While addition and subtraction have the same precedence level, the
parenthesis cannot be omitted. In general, this happens on the right-
hand side of the subtraction, division, and modulo operators if the
right-hand side has the same precedence level.
This patch fixes the output of binary operations accordingly.
Booleans are supposed to be formatted without a leading hash sign in
both terms and formulas. By mistake, the formula formatter added leading
hash signs though.
This adds Debug and Display trait implementations for the SpecialInteger
enum to make it possible to format its values without having to wrap it
in a Term variant.
Provided that the latest version of this crate is always published on
crates.io and tagged as a release on GitHub.com, the crates.io and the
GitHub.com release badges will always show the same version.
Consequently, remove the GitHub.com release badge to avoid redundancy.
This provides an abstract syntax tree for first-order logic with integer
arithmetics. Initially, the following types of formulas are supported:
- Booleans values (true and false)
- predicates
- negated formulas
- comparisons of terms (<, ≤, >, ≥, =, ≠)
- implications and biconditionals
- conjunctions and disjunctions of formulas
- existentially and universally quantified formulas
In addition, these types of terms are provided:
- Boolean values (true and false)
- integers
- strings
- special integers (infimum and supremum)
- symbolic functions
- variables
- binary operations (addition, subtraction, multiplication, division,
modulo, exponentiation)
- unary operations (absolute value, numeric negation)
