updates

Author: queelius

README.md

@@ -1,53 +1,85 @@
-Disjoint Interval Set
-=====================
+# Disjoint Interval Set
 
 The Disjoint Interval Set (DIS) equipped with a few operations
 satisfies the concept of a Boolean algebra over sets of disjoint
 intervals equipped with all the standard set-theoretic operations,
 like intersection (*), union (+), and complement (~).
 
-### Boolean Algebra
+## Concept: Boolean Algebra
+
 A Boolean algebra provides a powerful conceptual and mathematical framework.
 It is a set of elements equipped with a few operations that satisfy
 a few axioms. The operations are usually called union (+), intersection (*),
 and complement (~). The axioms are usually called the Boolean laws.
 
-## DIS Operations
-The DIS supports the following operations:
+## Constructors
+
+The DIS supports the following constructors:
+
+- **Empty Constructor**: `disjoint_interval_set()`
+
+  Create an empty DIS.
+
+- **Constructor From Iterable**: `disjoint_interval_set(intervals)`
+
+  Create a DIS from an iterable of intervals.
+
+- **Copy Constructor**: `disjoint_interval_set(disjoint_interval_set)`
+
+  Create a copy of a DIS.
+
+## Set-Theoretic Operations
+
+The DIS supports the following set-theoretic operations:
+
+- **Union**: `operator+(disjoint_interval_set, disjoint_interval_set)`
 
-1. `disjoint_interval_set()`: Create an empty DIS.
-2. `disjoint_interval_set(intervals)`: Create a DIS from an iterable of intervals.
-3. `disjoint_interval_set(disjoint_interval_set)`: Create a copy of a DIS.
-4. `operator+(disjoint_interval_set, disjoint_interval_set)`: Union of two DIS.
-5. `operator*(disjoint_interval_set, disjoint_interval_set)`: Intersection of two DIS.
-6. `operator~(disjoint_interval_set)`: Complement of a DIS.
+  Create a DIS that is the union of two DIS.
+
+- **Intersection**: `operator*(disjoint_interval_set, disjoint_interval_set)`
+
+  Create a DIS that is the intersection of two DIS.
+
+- **Complement**: `operator~(disjoint_interval_set)`
+
+  Create a DIS that is the complement of a DIS.
+
+- **Set-Difference**: `operator-(disjoint_interval_set, disjoint_interval_set)`
+
+  Create a DIS that is the set difference of two DIS.
+
+- **Symmetric Difference**: `operator^(disjoint_interval_set, disjoint_interval_set)`
+
+  Create a DIS that is the symmetric difference of two DIS.
+
+## Predicates
 
-## DIS Predicates
 The DIS supports the following predicates:
 
-1. `is_empty(disjoint_interval_set)`: Check if a DIS is empty.
+- **Empty**: `is_empty(disjoint_interval_set)`: Check if a DIS is empty.
 
-2. relational predicates `==`, `!=`, `<`, `<=`, `>`, `>=`:
+- **Relational Predicates**: `==`, `!=`, `<`, `<=`, `>`, `>=`:
 
-   Compare two DIS for equality, inequality, subset, proper subset, superset,
-   and proper superset.
+  Compare two DIS for equality, inequality, subset, proper subset, superset,
+  and proper superset.
 
-   These also work with intervals and values. For example, `DIS == interval`,
-   since an interval can be considered a DIS with a single interval and a
-   value can be considered an interval with a single value, `[value, value]`.
+  These also work with intervals and values. For example, `DIS == interval`,
+  since an interval can be considered a DIS with a single interval and a
+  value can be considered an interval with a single value, `[value, value]`.
 
-3. `contains(disjoint_interval_set, value)`: Check if a DIS contains a value.
+- **Set Membership**: `contains(disjoint_interval_set, value)`
 
+  Check if a DIS contains a value.
 
-## Generic Programming
+## Interval Type
 
 The DIS is parameterized by the interval type. The interval type must
-satisfy the concept of an interval:
-
+satisfy the concept of an interval.
 
 ### Interval Concept
+
 An interval is a pair of values that satisfy the following axioms:
 
-1. `lower(interval)`: Return the lower bound of the interval.
-2. `upper(interval)`: Return the upper bound of the interval.
-3. `contains(interval, value)`: Check if the interval contains a value. 
+- `infimum(interval)`: Return the infimum of the interval.
+- `supremum(interval)`: Return the supremum of the interval.
+- `contains(interval, value)`: Check if the interval contains a value.