1 files changed, 189 insertions, 0 deletions
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()