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Diffstat (limited to 'entries/jj/tm/tm.nim')
-rw-r--r-- | entries/jj/tm/tm.nim | 189 |
1 files changed, 189 insertions, 0 deletions
diff --git a/entries/jj/tm/tm.nim b/entries/jj/tm/tm.nim new file mode 100644 index 0000000..8710acb --- /dev/null +++ b/entries/jj/tm/tm.nim @@ -0,0 +1,189 @@ +# A simple Turing machine simulator implemented in Nim. + +import std/enumerate + +type Symbol = enum + `_`, `$`, `X`, `0`, `1`, `0*`, `1*`, + noop + +type Tape = seq[Symbol] + +type Direction = enum + L, R, S + +type State = enum + ca, cb, cc, cd, ce, cf, cg, ch, ci + sa, sb, sc, sd, + aa, ab, ac, + aaa, aab, aac, aad, aae, aaf, + aba, abb, abc, abd, abe, abf, + ba, bb, bc, + baa, bab, bac, bad, bae, baf, + bba, bbb, bbc, bbd, bbe, bbf, + za, zb, zc, zd + +type Transition = object + current_state: State + read_symbol: seq[Symbol] + next_state: State + write_symbol: Symbol + move_direction: Direction + +# convenience constructor +func δ(a: State, b: seq[Symbol], c: State, d: Symbol, e: Direction): Transition = + return Transition(current_state: a, read_symbol: b, next_state: c, write_symbol: d, move_direction: e) + +# safe get for an infinite tape: pretty, right? +func get(tape: var Tape, i: int): Symbol = + for j in tape.len .. i: + tape.add(`_`) + return tape[i] + +# safe set for an infinite tape +func set(tape: var Tape, i: int, s: Symbol) = + for j in tape.len .. i: + tape.add(`_`) + tape[i] = s + +let turing_machine = @[ + δ(ca, @[`_`], cb, `$`, 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() |