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@@ -143,3 +143,53 @@ I was then able to create a demo program by defining a dummy evaluator
 that simply returns the input expression unmodified, and running a
 REPL using that, connected to stdin and stdout.  This demonstrated a
 full round trip through the parsing and printing procedures.
+
+## Evaluator
+
+Rather than trying to handle everything in one complex evaluator, I
+decided to implement a multi-pass evaluator.  This essentially means
+that the expressions run through multiple different passes that apply
+different transformations to them, thereby keeping the complexity of
+each pass more managable.  This is a common method used when
+implementing compilers and interpreters.
+
+### Normalisation
+
+The first preliminary pass I implemented was a normalisation pass.
+This transforms things like `x - y` into `x + (-1)y`, and `x/y` into
+`xy^(-1)`.  The main benefit of this is to make it easier for the
+later differentiation pass as it will only have to handle sums,
+products and exponents (not differences and quotients).  I decided to
+leave quotients of integers as-is since these will be untouched by the
+differentiation process anyway, and "1/2" reads far better than
+"1*2^(-1)".
+
+### Constant Folding
+
+The purpose of this pass is to combine constants together as much as
+possible, such as transforming `1 + 2*3` into `6`, or `x + 1 + 2` into
+`x + 3`.  This is mostly a nice-to-have rather than an essential
+feature, though it will make the output much more readable.
+
+Implementing this pass did get a little hairy, as the binary tree
+structure I used for the AST made handling cases like `x + 1 + 2`
+(which is represented in the AST as `(x + 1) + 2` quite complex.  The
+module implementing this therefore ended up being somewhat messy,
+especially since Rust's move/borrow semantics made flattening trees of
+sums and products more complex than it would otherwise be.  However, I
+decided to move on rather than spend a great deal of time tidying this
+up since, as previously mentioned, this was more of a nice-to-have
+feature rather than core functionality.
+
+### Evaluator Composition
+
+I then implemented a mechanism to compose evaluators together, and
+build a pipeline of arbitrarily many of them.  This was simple to do
+since I was implementing the `Evaluator` trait for each pass, so
+supporting composition simply meant creating a struct containing two
+evaluators, and implementing the `Evaluator` trait for this such that
+the evaluators were run in sequence on any input expression.
+
+To combine more than two evaluators, I created a `pipeline` macro that
+constructs nested compositions of evaluators with Rust's `macro_rules`
+system.