Compute the before-state of diffs.

This is `Optional`, as some diffs have unrecoverable before states. For
example, the insertion of a term has no before state, but can still
produce a valid before state if it occurs within the context of an
`Indexed` or `Keyed` node.

However, certain malformed diffs (such as `.Pure(.Insert(…))` in
isolation) may lack a valid before state, and thus the public API has
to reflect this.

prototype/Doubt/Free.swift

@@ -90,6 +90,19 @@ public enum Free<A, B>: CustomDebugStringConvertible {
 
 extension Free where B: PatchConvertible, B.Info == A {
 	public typealias Term = Fix<A>
+
+	public var before: Term? {
+		return map { $0.patch.state.before }.iterate { syntax -> Term? in
+			switch syntax {
+			case let .Leaf(a):
+				return .In(.Leaf(a))
+			case let .Indexed(a):
+				return .In(.Indexed(a.flatMap(id)))
+			case let .Keyed(a):
+				return .In(.Keyed(Dictionary(elements: a.flatMap { k, v in v.map { (k, $0) } })))
+			}
+		}
+	}
 }