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# 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()
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