define the atoms

I took a stab at some names. Not sure if I like them all.

book/src/rules/atoms.md

@@ -1 +1,74 @@
-**To be written**
+Polonius defines the following **atoms**. To Polonius, these are
+opaque identifiers that identify particular things within the input
+program (literally they are newtype'd integers). Their meaning and
+relationships come entirely from the input relations.
+
+## Example
+
+We'll use this snippet of Rust code to illustrate the various kinds of
+atoms that can exist.
+
+```rust
+let x = (vec![22], vec![44]);
+let y = &x.1;
+let z = x.0;
+drop(y);
+```
+
+## Variables
+
+A **variable** represents a user variable defined by the Rust source
+code. In our snippet, `x`, `y`, and `z` are variables. Other kinds of
+variables include parameters.
+
+## Path
+
+A **path** indicates a path through memory to a memory location --
+these roughly correspond to **places** in MIR, although we only
+support a subset of the full places (that is, every MIR place maps to
+a Path, but sometimes a single Path maps back to multiple MIR places).
+
+Each path begins with a variable (e.g., `x`) but can be extended with
+fields (e.g., `x.1`), with an "index" (e.g., `x[]`) or with a deref `*x`.
+Note that the index paths (`x[]`) don't track the actual index that was
+accessed, since the borrow check treats all indices as equivalent.
+
+The grammar for paths would thus look something like this:
+
+```
+Path = Variable
+     | Path "." Field // field access
+     | Path "[" "]"   // index
+     | "*" Path
+```
+
+Each path has a distinct atom associated with it. So there would be an
+atom P1 for the path `x` and another atom P2 for the path `x.0`.
+These atoms are related to one another through the `path_parent`
+relation.
+
+## Node
+
+Nodes are, well, *nodes* in the control-flow graph. They are related
+to one another by the `cfg_edge` relation.
+
+For each statement (resp. terminator) S in the MIR, there are actually
+two associated nodes. One represents the "start" of S -- before S has
+begun executing -- the other is called the "mid node" -- which
+represents the point where S "takes effect". Each start node has
+exactly one successor, the mid node.
+
+## Loans
+
+A **loan** represents some borrow that occurs in the source.  Each
+loan has an associated path that was borrowed along with a mutability.
+So, in our example, there would be a single loan, for the `&x.1`
+expression.
+
+## Origins
+
+An **origin** is what it typically called in Rust a **lifetime**. In
+Polonius, an **origin** refers to the set of loans from which a
+reference may have been created.
+
+