Let T be a TM.

Let Sigma be the input alphabet of T.
let Gamma be the tape alphabet of T.  We assume Sigma is a subset of Gamma,
and that Gamma contains "_", the "blank."

Let Q be the set of states of T.
Let <0> be the start state of T.
Let <h> be the halt state of T.  (Accept)

We define a configuration of T to be a string of the form

alpha q beta

where q is a state of T, and alpha and beta are strings over Gamma,
and beta has at least one symbol.  (If the head is over a blank and
there are no non-blank symbols to the right of the head, beta consists
of a single blank.)  The state is a halt configuration if q = <h>.

We write x |- y to mean that configuration x yields configuration y
in one step.  We say that M accepts a string w over Sigma
if <0>w yields a halt configuration in any number of steps.

We now define an unrestricted grammar G which generates L(M).

The input terminal of G is Sigma.
The grammar alphabet of G is Gamma + Q + {$}

The start symbol of G is <h>

There are three kinds of productions of G:

Starting productions: We have the production
<h> -> $<h>$
and for each g in Gamma, we have productions
<h> -> g<h>
<h> -> <h>g

Emulation productions: For each trasition rule of M, we have one
emulation production of G.  If the transition rule is

<i> a b R <j>

then the production is b<j> -> <i>a
If the transition rule is

<i> a b L <j>

Ending productions:  There is only one, namely
$<0> -> emptystring