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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()