aboutsummaryrefslogtreecommitdiff
path: root/entries/omentic/tm/tm.nim
blob: 71debe4606c450f6425cf8a5940c2e9f902eed40 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
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()