3 files changed, 552 insertions, 0 deletions
diff --git a/fib/tm/fib-desc.txt b/fib/tm/fib-desc.txt
new file mode 100644
index 0000000..b98b324
--- /dev/null
+++ b/fib/tm/fib-desc.txt
@@ -0,0 +1,219 @@
+The following is a low-level description of a Turing machine that will write
+the Fibonacci sequence (represented in binary, separated by $) without halting.
+
+A Turing machine is a 7-tuple T = (Q,Σ,Γ,δ,qI,qA,qR) where:
+- Q is the set of states; non-empty and finite
+- Σ is the input alphabet; non-empty and finite
+- Γ is the tape alphabet; non-empty and finite
+- δ is the transition function: δ(Q, Γ) -> (Q, Γ, {L, R})
+- qI ∈ Q is the initial state
+- qA ∈ Q is the accept state
+- qR ∈ Q is the reject state
+
+- Q: {
+  ca, cb, cc, cd, ce, cf, cg, ch, ci,
+  sa, sb, sc, sd,
+  aa, ab, ac,
+  aaa, aab, aac, aad, aae, aaf,
+  aba, abb, abc, abd, abe, abf,
+  ba, bb, bc,
+  baa, bab, bac, bad, bae, baf,
+  bba, bbb, bbc, bbd, bbe, bbf,
+  za, zb, zc, zd
+}
+- Σ: not relevant as we entirely disregard the input to begin with.
+- Γ: {_, $, X, 0, 1, 0*, 1*} (_ means the blank symbol)
+- δ: described below. a note on syntax:
+  - no entry in the output parameter means do not write a character to the tape.
+  - similarly, no entry in the position parameter means do not move the tape head.
+  - numerous "possible" transition functions are not stated. those are thought by the author to be inaccessible in normal operation of this machine (and if they are, it is probably a bug).
+- qI: the initial state is ca.
+- qA: the machine does not accept.
+- qR: the machine does not reject.
+
+Overview:
+1. We clear the tape and write our initial state: the first three Fibonacci numbers
+2. We write a number of Xs to the end of the tape for convenience
+3. We add the last two numbers of the sequence digit-by-digit to create another number
+  - Effort/pain is taken to ensure carrying works: including when the next number is a digit larger
+4. Upon having created the new Fibonacci number, we write a $ and repeat from step 3, ad nauseam
+
+states c*: clearing the initial tape
+- clear the tape: write $0$1$1$, then write _ until reading a _
+
+δ(ca, Γ) -> (cb, $, R)
+δ(cb, Γ) -> (cc, 0, R)
+δ(cc, Γ) -> (cd, $, R)
+δ(cd, Γ) -> (ce, 1*, R)
+δ(ce, Γ) -> (cf, $, R)
+δ(cf, Γ) -> (cg, 1, R)
+δ(cg, Γ) -> (ch, $, R)
+δ(ch, Γ \ _) -> (ci, _, R)
+δ(ch, _) -> (sa, , )
+
+
+states s*: making space for the next number
+- from the end: append XX...X where len(XX...X) = len(previous_number)
+
+δ(sa, {_,X}) -> (sa, , L)
+δ(sa, $) -> (sb, , L)
+
+δ(sb, {0*,1*}) -> (sb, , L)
+δ(sb, 0) -> (sc, 0*, R)
+δ(sb, 1) -> (sc, 1*, R)
+δ(sb, $) -> (sd, , R)
+
+δ(sc, Γ \ _) -> (sc, , R)
+δ(sc, _) -> (sa, X, L)
+
+δ(sd, {$,X}) -> (sd, , R)
+δ(sd, 0*) -> (sd, 0, R)
+δ(sd, 1*) -> (sd, 1, R)
+δ(sd, _) -> (aa, , L)
+
+
+states a*: add the last digit of both numbers without carrying
+- read left until $, then read left until:
+  - 0: replace with 0*, goto state (aaa)
+  - 1: replace with 1*, goto state (aba)
+  - $: do not replace, read right until _, write $, goto state (s)
+
+δ(aa, {X,0,1}) -> (aa, , L)
+δ(aa, $) -> (ab, , L)
+
+δ(ab, {0*,1*}) -> (ab, , L)
+δ(ab, 0) -> (aaa, 0*, L)
+δ(ab, 1) -> (aba, 1*, L)
+
+δ(ab, $) -> (ac, , R)
+δ(ac, Γ \ _) -> (ac, , R)
+δ(ac, _) -> (sa, $, R)
+
+states aa*
+- read left until $, then read left until:
+  - 0*: replace with 0, read right until _, then read left until X and replace with 0
+  - 1*: replace with 1, read right until _, then read left until X and replace with 1
+
+δ(aaa, {0,1}) -> (aaa, , L)
+δ(aaa, $) -> (aab, , L)
+
+δ(aab, 0*) -> (aac, 0, R)
+δ(aac, Γ \ _) -> (aac, , R)
+δ(aac, _) -> (aad, , L)
+δ(aad, {0,1}) -> (aad, , L)
+δ(aad, X) -> (aa, 0, L)
+
+δ(aab, 1*) -> (aae, 1, R)
+δ(aae, Γ \ _) -> (aae, , R)
+δ(aae, _) -> (aaf, , L)
+δ(aaf, {0,1}) -> (aaf, , L)
+δ(aaf, X) -> (aa, 1, L)
+
+δ(aab, {0,1}) -> (aab, , L)
+
+states ab*
+- read left until $, then read left until:
+  - 0*: replace with 0, read right until _, then read left until X and replace with 1
+  - $: do not replace, read right until _, then read left until X and replace with 1
+  - 1*: replace with 1, read right until _, then read left until X and replace with 0, goto state (b)
+
+δ(aba, {0,1}) -> (aba, , L)
+δ(aba, $) -> (abb, , L)
+
+δ(abb, 0*) -> (abc, 0, R)
+δ(abc, Γ \ _) -> (abc, , R)
+δ(abc, _) -> (abd, , L)
+δ(abd, {0,1}) -> (abd, , L)
+δ(abd, X) -> (aa, 1, L)
+
+δ(abb, 1*) -> (abe, 1, R)
+δ(abe, Γ \ _) -> (abe, , R)
+δ(abe, _) -> (abf, , L)
+δ(abf, {0,1}) -> (abf, , L)
+δ(abf, X) -> (ba, 0, L)
+
+δ(abb, $) -> (abc, , R)
+
+δ(abb, {0,1}) -> (abb, , L)
+
+
+states b*: add the last digit of both numbers while carrying a one
+- read left from end of tape, after reading $, until reading:
+  - 0: replace with 0*, goto state (baa)
+  - 1: replace with 1*, goto state (bba)
+  - $: do not replace, read right until _, goto state (za)
+
+δ(ba, {X,0,1}) -> (ba, , L)
+δ(ba, $) -> (bb, , L)
+
+δ(bb, {0*,1*}) -> (bb, , L)
+δ(bb, 0) -> (baa, 0*, L)
+δ(bb, 1) -> (bba, 1*, L)
+
+δ(bb, $) -> (bc, , R)
+δ(bc, Γ \ _) -> (bc, , R)
+δ(bc, _) -> (za, , L)
+
+states ba*
+- read left until $, then read left until:
+  - 0*: replace with 0, read right until _, then read left until X and replace with 1, then goto state (aa)
+  - 1*: replace with 1, read right until _, then read left until X and replace with 0, then goto state (ba)
+
+δ(baa, {0,1}) -> (baa, , L)
+δ(baa, $) -> (bab, , L)
+
+δ(bab, 0*) -> (bac, 0, R)
+δ(bac, Γ \ _) -> (bac, , R)
+δ(bac, _) -> (bad, , L)
+δ(bad, {0,1}) -> (bad, , L)
+δ(bad, X) -> (aa, 1, L)
+
+δ(bab, 1*) -> (bae, 1, R)
+δ(bae, Γ \ _) -> (bae, , R)
+δ(bae, _) -> (baf, , L)
+δ(baf, {0,1}) -> (baf, , L)
+δ(baf, X) -> (ba, 0, L)
+
+δ(bab, {0,1}) -> (bab, , L)
+
+states bb*
+- read left until $, then read left until:
+  - 0*: replace with 0, read right until _, then read left until X and replace with 0, goto state (ba)
+  - 1*: replace with 1, read right until _, then read left until X and replace with 1, goto state (ba)
+
+δ(bba, {0,1}) -> (bba, , L)
+δ(bba, $) -> (bbb, , L)
+
+δ(bbb, 0*) -> (bbc, 0, R)
+δ(bbc, Γ \ _) -> (bbc, , R)
+δ(bbc, _) -> (bbd, , L)
+δ(bbd, {0,1}) -> (bbd, , L)
+δ(bbd, X) -> (ba, 0, L)
+
+δ(bbb, 1*) -> (bbe, 1, R)
+δ(bbe, Γ \ _) -> (bbe, , R)
+δ(bbe, _) -> (bbf, , L)
+δ(bbf, {0,1}) -> (bbf, , L)
+δ(bbf, X) -> (ba, 1, L)
+
+δ(bbb, $) -> (bbc, , R)
+
+δ(bbb, {0,1}) -> (bbb, , L)
+
+states c*: scooting over the computed number to make space for a carried digit
+- read left until $, then:
+  - read right, noting the current number and writing the previous number
+  - then go to state (sa)
+
+δ(za, {0,1}) -> (za, , L)
+δ(za, $) -> (zb, , R)
+
+δ(zb, 0) -> (zc, 1, R)
+δ(zb, 1) -> (zb, 1, R)
+δ(zb, _) -> (zd, 1, R)
+
+δ(zc, 0) -> (zc, 0, R)
+δ(zc, 1) -> (zb, 0, R)
+δ(zc, _) -> (zd, 0, R)
+
+δ(zd, _) -> (sa, $, R)
diff --git a/fib/tm/fib.txt b/fib/tm/fib.txt
new file mode 100644
index 0000000..402db15
--- /dev/null
+++ b/fib/tm/fib.txt
@@ -0,0 +1,144 @@
+The following is a low-level description of a Turing machine that will write
+the Fibonacci sequence (represented in binary, separated by $) without halting.
+
+A Turing machine is a 7-tuple T = (Q,Σ,Γ,δ,qI,qA,qR) where:
+- Q is the set of states; non-empty and finite
+- Σ is the input alphabet; non-empty and finite
+- Γ is the tape alphabet; non-empty and finite
+- δ is the transition function: δ(Q, Γ) -> (Q, Γ, {L, R})
+- qI ∈ Q is the initial state
+- qA ∈ Q is the accept state
+- qR ∈ Q is the reject state
+
+- Q: {
+  ca, cb, cc, cd, ce, cf, cg, ch, ci,
+  sa, sb, sc, sd,
+  aa, ab, ac,
+  aaa, aab, aac, aad, aae, aaf,
+  aba, abb, abc, abd, abe, abf,
+  ba, bb, bc,
+  baa, bab, bac, bad, bae, baf,
+  bba, bbb, bbc, bbd, bbe, bbf,
+  za, zb, zc, zd
+}
+- Σ: not relevant as we entirely disregard the input to begin with.
+- Γ: {_, $, X, 0, 1, 0*, 1*} (_ means the blank symbol)
+- δ: described below. a note on syntax:
+  - no entry in the output parameter means do not write a character to the tape.
+  - similarly, no entry in the position parameter means do not move the tape head.
+  - numerous "possible" transition functions are not stated. those are thought by the author to be inaccessible in normal operation of this machine (and if they are, it is probably a bug).
+- qI: the initial state is ca.
+- qA: the machine does not accept.
+- qR: the machine does not reject.
+
+δ(ca, Γ) -> (cb, $, R)
+δ(cb, Γ) -> (cc, 0, R)
+δ(cc, Γ) -> (cd, $, R)
+δ(cd, Γ) -> (ce, 1*, R)
+δ(ce, Γ) -> (cf, $, R)
+δ(cf, Γ) -> (cg, 1, R)
+δ(cg, Γ) -> (ch, $, R)
+δ(ch, Γ \ _) -> (ci, _, R)
+δ(ch, _) -> (sa, , )
+
+δ(sa, {_,X}) -> (sa, , L)
+δ(sa, $) -> (sb, , L)
+δ(sb, {0*,1*}) -> (sb, , L)
+δ(sb, 0) -> (sc, 0*, R)
+δ(sb, 1) -> (sc, 1*, R)
+δ(sb, $) -> (sd, , R)
+δ(sc, Γ \ _) -> (sc, , R)
+δ(sc, _) -> (sa, X, L)
+δ(sd, {$,X}) -> (sd, , R)
+δ(sd, 0*) -> (sd, 0, R)
+δ(sd, 1*) -> (sd, 1, R)
+δ(sd, _) -> (aa, , L)
+
+δ(aa, {X,0,1}) -> (aa, , L)
+δ(aa, $) -> (ab, , L)
+δ(ab, {0*,1*}) -> (ab, , L)
+δ(ab, 0) -> (aaa, 0*, L)
+δ(ab, 1) -> (aba, 1*, L)
+δ(ab, $) -> (ac, , R)
+δ(ac, Γ \ _) -> (ac, , R)
+δ(ac, _) -> (sa, $, R)
+
+δ(aaa, {0,1}) -> (aaa, , L)
+δ(aaa, $) -> (aab, , L)
+δ(aab, 0*) -> (aac, 0, R)
+δ(aac, Γ \ _) -> (aac, , R)
+δ(aac, _) -> (aad, , L)
+δ(aad, {0,1}) -> (aad, , L)
+δ(aad, X) -> (aa, 0, L)
+δ(aab, 1*) -> (aae, 1, R)
+δ(aae, Γ \ _) -> (aae, , R)
+δ(aae, _) -> (aaf, , L)
+δ(aaf, {0,1}) -> (aaf, , L)
+δ(aaf, X) -> (aa, 1, L)
+δ(aab, {0,1}) -> (aab, , L)
+
+δ(aba, {0,1}) -> (aba, , L)
+δ(aba, $) -> (abb, , L)
+δ(abb, 0*) -> (abc, 0, R)
+δ(abc, Γ \ _) -> (abc, , R)
+δ(abc, _) -> (abd, , L)
+δ(abd, {0,1}) -> (abd, , L)
+δ(abd, X) -> (aa, 1, L)
+δ(abb, 1*) -> (abe, 1, R)
+δ(abe, Γ \ _) -> (abe, , R)
+δ(abe, _) -> (abf, , L)
+δ(abf, {0,1}) -> (abf, , L)
+δ(abf, X) -> (ba, 0, L)
+δ(abb, $) -> (abc, , R)
+δ(abb, {0,1}) -> (abb, , L)
+
+δ(ba, {X,0,1}) -> (ba, , L)
+δ(ba, $) -> (bb, , L)
+δ(bb, {0*,1*}) -> (bb, , L)
+δ(bb, 0) -> (baa, 0*, L)
+δ(bb, 1) -> (bba, 1*, L)
+δ(bb, $) -> (bc, , R)
+δ(bc, Γ \ _) -> (bc, , R)
+δ(bc, _) -> (za, , L)
+
+δ(baa, {0,1}) -> (baa, , L)
+δ(baa, $) -> (bab, , L)
+δ(bab, 0*) -> (bac, 0, R)
+δ(bac, Γ \ _) -> (bac, , R)
+δ(bac, _) -> (bad, , L)
+δ(bad, {0,1}) -> (bad, , L)
+δ(bad, X) -> (aa, 1, L)
+δ(bab, 1*) -> (bae, 1, R)
+δ(bae, Γ \ _) -> (bae, , R)
+δ(bae, _) -> (baf, , L)
+δ(baf, {0,1}) -> (baf, , L)
+δ(baf, X) -> (ba, 0, L)
+δ(bab, {0,1}) -> (bab, , L)
+
+δ(bba, {0,1}) -> (bba, , L)
+δ(bba, $) -> (bbb, , L)
+δ(bbb, 0*) -> (bbc, 0, R)
+δ(bbc, Γ \ _) -> (bbc, , R)
+δ(bbc, _) -> (bbd, , L)
+δ(bbd, {0,1}) -> (bbd, , L)
+δ(bbd, X) -> (ba, 0, L)
+δ(bbb, 1*) -> (bbe, 1, R)
+δ(bbe, Γ \ _) -> (bbe, , R)
+δ(bbe, _) -> (bbf, , L)
+δ(bbf, {0,1}) -> (bbf, , L)
+δ(bbf, X) -> (ba, 1, L)
+δ(bbb, $) -> (bbc, , R)
+δ(bbb, {0,1}) -> (bbb, , L)
+
+δ(za, {0,1}) -> (za, , L)
+δ(za, $) -> (zb, , R)
+
+δ(zb, 0) -> (zc, 1, R)
+δ(zb, 1) -> (zb, 1, R)
+δ(zb, _) -> (zd, 1, R)
+
+δ(zc, 0) -> (zc, 0, R)
+δ(zc, 1) -> (zb, 0, R)
+δ(zc, _) -> (zd, 0, R)
+
+δ(zd, _) -> (sa, $, R)
diff --git a/fib/tm/tm.nim b/fib/tm/tm.nim
new file mode 100644
index 0000000..71debe4
--- /dev/null
+++ b/fib/tm/tm.nim
@@ -0,0 +1,189 @@
+# A simple Turing machine simulator implemented in Nim.
+
+import std/enumerate
+
+type Symbol = enum
+  `_`, `$`, `X`, `0`, `1`, `0*`, `1*`,
+  noop
+
+type Tape = seq[Symbol]
+
+type Direction = enum
+  L, R, S
+
+type State = enum
+  ca, cb, cc, cd, ce, cf, cg, ch, ci
+  sa, sb, sc, sd,
+  aa, ab, ac,
+  aaa, aab, aac, aad, aae, aaf,
+  aba, abb, abc, abd, abe, abf,
+  ba, bb, bc,
+  baa, bab, bac, bad, bae, baf,
+  bba, bbb, bbc, bbd, bbe, bbf,
+  za, zb, zc, zd
+
+type Transition = object
+  current_state: State
+  read_symbol: set[Symbol]
+  next_state: State
+  write_symbol: Symbol
+  move_direction: Direction
+
+# convenience constructor
+func δ(a: State, b: set[Symbol], c: State, d: Symbol, e: Direction): Transition =
+  return Transition(current_state: a, read_symbol: b, next_state: c, write_symbol: d, move_direction: e)
+
+# safe get for an infinite tape: pretty, right?
+func get(tape: var Tape, i: int): Symbol =
+  for j in tape.len .. i:
+    tape.add(`_`)
+  return tape[i]
+
+# safe set for an infinite tape
+func set(tape: var Tape, i: int, s: Symbol) =
+  for j in tape.len .. i:
+    tape.add(`_`)
+  tape[i] = s
+
+let turing_machine = @[
+  δ(ca, {`_`}, cb, `$`, R),
+  δ(cb, {`_`}, cc, `0`, R),
+  δ(cc, {`_`}, cd, `$`, R),
+  δ(cd, {`_`}, ce, `1*`, R),
+  δ(ce, {`_`}, cf, `$`, R),
+  δ(cf, {`_`}, cg, `1`, R),
+  δ(cg, {`_`}, ch, `$`, R),
+  δ(ch, {`_`}, sa, noop, S),
+
+  δ(sa, {`_`, `X`}, sa, noop, L),
+  δ(sa, {`$`}, sb, noop, L),
+  δ(sb, {`0*`, `1*`}, sb, noop, L),
+  δ(sb, {`0`}, sc, `0*`, R),
+  δ(sb, {`1`}, sc, `1*`, R),
+  δ(sb, {`$`}, sd, noop, R),
+  δ(sc, {`$`, `X`, `0*`, `1*`}, sc, noop, R),
+  δ(sc, {`_`}, sa, `X`, L),
+  δ(sd, {`$`, `X`}, sd, noop, R),
+  δ(sd, {`0*`}, sd, `0`, R),
+  δ(sd, {`1*`}, sd, `1`, R),
+  δ(sd, {`_`}, aa, noop, L),
+
+  δ(aa, {`X`, `0`, `1`}, aa, noop, L),
+  δ(aa, {`$`}, ab, noop, L),
+  δ(ab, {`0*`, `1*`}, ab, noop, L),
+  δ(ab, {`0`}, aaa, `0*`, L),
+  δ(ab, {`1`}, aba, `1*`, L),
+  δ(ab, {`$`}, ac, noop, R),
+  δ(ac, {`$`, `X`, `0`, `1`, `0*`, `1*`}, ac, noop, R),
+  δ(ac, {`_`}, sa, `$`, R),
+
+  δ(aaa, {`0`, `1`}, aaa, noop, L),
+  δ(aaa, {`$`}, aab, noop, L),
+  δ(aab, {`0*`}, aac, `0`, R),
+  δ(aac, {`$`, `X`, `0`, `1`, `0*`, `1*`}, aac, noop, R),
+  δ(aac, {`_`}, aad, noop, L),
+  δ(aad, {`0`, `1`}, aad, noop, L),
+  δ(aad, {`X`}, aa, `0`, L),
+  δ(aab, {`1*`}, aae, `1`, R),
+  δ(aae, {`$`, `X`, `0`, `1`, `0*`, `1*`}, aae, noop, R),
+  δ(aae, {`_`}, aaf, noop, L),
+  δ(aaf, {`0`, `1`}, aaf, noop, L),
+  δ(aaf, {`X`}, aa, `1`, L),
+  δ(aab, {`0`, `1`}, aab, noop, L),
+
+  δ(aba, {`0`, `1`}, aba, noop, L),
+  δ(aba, {`$`}, abb, noop, L),
+  δ(abb, {`0*`}, abc, `0`, R),
+  δ(abc, {`$`, `X`, `0`, `1`, `0*`, `1*`}, abc, noop, R),
+  δ(abc, {`_`}, abd, noop, L),
+  δ(abd, {`0`, `1`}, abd, noop, L),
+  δ(abd, {`X`}, aa, `1`, L),
+  δ(abb, {`1*`}, abe, `1`, R),
+  δ(abe, {`$`, `X`, `0`, `1`, `0*`, `1*`}, abe, noop, R),
+  δ(abe, {`_`}, abf, noop, L),
+  δ(abf, {`0`, `1`}, abf, noop, L),
+  δ(abf, {`X`}, ba, `0`, L),
+  δ(abb, {`$`}, abc, noop, R),
+  δ(abb, {`0`, `1`}, abb, noop, L),
+
+  δ(ba, {`X`, `0`, `1`}, ba, noop, L),
+  δ(ba, {`$`}, bb, noop, L),
+  δ(bb, {`0*`, `1*`}, bb, noop, L),
+  δ(bb, {`0`}, baa, `0*`, L),
+  δ(bb, {`1`}, bba, `1*`, L),
+  δ(bb, {`$`}, bc, noop, R),
+  δ(bc, {`$`, `X`, `0`, `1`, `0*`, `1*`}, bc, noop, R),
+  δ(bc, {`_`}, za, noop, L),
+
+  δ(baa, {`0`, `1`}, baa, noop, L),
+  δ(baa, {`$`}, bab, noop, L),
+  δ(bab, {`0*`}, bac, `0`, R),
+  δ(bac, {`$`, `X`, `0`, `1`, `0*`, `1*`}, bac, noop, R),
+  δ(bac, {`_`}, bad, noop, L),
+  δ(bad, {`0`, `1`}, bad, noop, L),
+  δ(bad, {`X`}, aa, `1`, L),
+  δ(bab, {`1*`}, bae, `1`, R),
+  δ(bae, {`$`, `X`, `0`, `1`, `0*`, `1*`}, bae, noop, R),
+  δ(bae, {`_`}, baf, noop, L),
+  δ(baf, {`0`, `1`}, baf, noop, L),
+  δ(baf, {`X`}, ba, `0`, L),
+  δ(bab, {`0`, `1`}, bab, noop, L),
+
+  δ(bba, {`0`, `1`}, bba, noop, L),
+  δ(bba, {`$`}, bbb, noop, L),
+  δ(bbb, {`0*`}, bbc, `0`, R),
+  δ(bbc, {`$`, `X`, `0`, `1`, `0*`, `1*`}, bbc, noop, R),
+  δ(bbc, {`_`}, bbd, noop, L),
+  δ(bbd, {`0`, `1`}, bbd, noop, L),
+  δ(bbd, {`X`}, ba, `0`, L),
+  δ(bbb, {`1*`}, bbe, `1`, R),
+  δ(bbe, {`$`, `X`, `0`, `1`, `0*`, `1*`}, bbe, noop, R),
+  δ(bbe, {`_`}, bbf, noop, L),
+  δ(bbf, {`0`, `1`}, bbf, noop, L),
+  δ(bbf, {`X`}, ba, `1`, L),
+  δ(bbb, {`$`}, bbc, noop, R),
+  δ(bbb, {`0`, `1`}, bbb, noop, L),
+
+  δ(za, {`0`, `1`}, za, noop, L),
+  δ(za, {`$`}, zb, noop, R),
+
+  δ(zb, {`0`}, zc, `1`, R),
+  δ(zb, {`1`}, zb, `1`, R),
+  δ(zb, {`_`}, zd, `1`, R),
+
+  δ(zc, {`0`}, zc, `0`, R),
+  δ(zc, {`1`}, zb, `0`, R),
+  δ(zc, {`_`}, zd, `0`, R),
+
+  δ(zd, {`_`}, sa, `$`, R)
+]
+
+proc print(state: State, tape: Tape, position: int) =
+  stdout.write($state)
+  for i, s in enumerate(tape):
+    if i == position:
+      stdout.write("[" & $s & "]")
+    elif s == `$`:
+      stdout.write(" ")
+    else:
+      stdout.write($s)
+  stdout.write("\n")
+
+var state = ca
+var position = 0
+var tape = @[`_`]
+
+proc step() =
+  # print(state, tape, position)
+  for δ in turing_machine:
+    if state == δ.current_state and tape.get(position) in δ.read_symbol:
+      state = δ.next_state
+      if δ.write_symbol != noop: tape.set(position, δ.write_symbol)
+      if δ.move_direction == L: position.dec
+      elif δ.move_direction == R: position.inc
+      return
+  echo "Invalid state! crashing"
+  quit()
+
+while true:
+  step()