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Ingy döt Net 2023-07-01 11:58:00 -04:00
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236
Task/Universal-Turing-machine/D/universal-turing-machine-1.d Normal file
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import std.stdio, std.algorithm, std.string, std.conv, std.array,
std.exception, std.traits, std.math, std.range;
struct UTM(State, Symbol, bool doShow=true)
if (is(State == enum) && is(Symbol == enum)) {
static assert(is(typeof({ size_t x = State.init; })),
"State must to be usable as array index.");
static assert([EnumMembers!State].equal(EnumMembers!State.length.iota),
"State must be a plain enum.");
static assert(is(typeof({ size_t x = Symbol.init; })),
"Symbol must to be usable as array index.");
static assert([EnumMembers!Symbol].equal(EnumMembers!Symbol.length.iota),
"Symbol must be a plain enum.");
enum Direction { right, left, stay }
private const TuringMachine tm;
private TapeHead head;
alias SymbolMap = string[EnumMembers!Symbol.length];
// The first index of this 'rules' matrix is a subtype of State
// because it can't contain H, but currently D can't enforce this,
// statically unlike Ada language.
Rule[EnumMembers!Symbol.length][EnumMembers!State.length - 1] mRules;
static struct Rule {
Symbol toWrite;
Direction direction;
State nextState;
this(in Symbol toWrite_, in Direction direction_, in State nextState_)
pure nothrow @safe @nogc {
this.toWrite = toWrite_;
this.direction = direction_;
this.nextState = nextState_;
}
}
// This is kept separated from the rest so it can be inialized
// one field at a time in the main function, yet it will become
// const.
static struct TuringMachine {
Symbol blank;
State initialState;
Rule[Symbol][State] rules;
Symbol[] input;
SymbolMap symbolMap;
}
static struct TapeHead {
immutable Symbol blank;
Symbol[] tapeLeft, tapeRight;
int position;
const SymbolMap sMap;
size_t nSteps;
this(in ref TuringMachine t) pure nothrow @safe {
this.blank = EnumMembers!Symbol[0];
//tapeRight = t.input.empty ? [this.blank] : t.input.dup;
if (t.input.empty)
this.tapeRight = [this.blank];
else
this.tapeRight = t.input.dup;
this.position = 0;
this.sMap = t.symbolMap;
}
pure nothrow @safe @nogc invariant {
assert(this.tapeRight.length > 0);
if (this.position >= 0)
assert(this.position < this.tapeRight.length);
else
assert(this.position.abs <= this.tapeLeft.length);
}
Symbol readSymb() const pure nothrow @safe @nogc {
if (this.position >= 0)
return this.tapeRight[this.position];
else
return this.tapeLeft[this.position.abs - 1];
}
void showSymb() const @safe {
this.write;
}
void writeSymb(in Symbol symbol) @safe {
static if (doShow)
showSymb;
if (this.position >= 0)
this.tapeRight[this.position] = symbol;
else
this.tapeLeft[this.position.abs - 1] = symbol;
}
void goRight() pure nothrow @safe {
this.position++;
if (position > 0 && position == tapeRight.length)
tapeRight ~= blank;
}
void goLeft() pure nothrow @safe {
this.position--;
if (position < 0 && (position.abs - 1) == tapeLeft.length)
tapeLeft ~= blank;
}
void move(in Direction dir) pure nothrow @safe {
nSteps++;
final switch (dir) with (Direction) {
case left: goLeft; break;
case right: goRight; break;
case stay: /*Do nothing*/ break;
}
}
string toString() const @safe {
immutable pos = tapeLeft.length.signed + this.position + 4;
return format("...%-(%)...", tapeLeft.retro.chain(tapeRight)
.map!(s => sMap[s])) ~
'\n' ~
format("%" ~ pos.text ~ "s", "^") ~
'\n';
}
}
void show() const @safe {
head.showSymb;
}
this(in ref TuringMachine tm_) @safe {
static assert(__traits(compiles, State.H), "State needs a 'H' (Halt).");
immutable errMsg = "Invalid input.";
auto runningStates = remove!(s => s == State.H)([EnumMembers!State]);
enforce(!runningStates.empty, errMsg);
enforce(tm_.rules.length == EnumMembers!State.length - 1, errMsg);
enforce(State.H !in tm_.rules, errMsg);
enforce(runningStates.canFind(tm_.initialState), errMsg);
// Create a matrix to reduce running time.
foreach (immutable State st, const rset; tm_.rules)
foreach (immutable Symbol sy, immutable rule; rset)
mRules[st][sy] = rule;
this.tm = tm_;
head = TapeHead(this.tm);
State state = tm.initialState;
while (state != State.H) {
immutable next = mRules[state][head.readSymb];
head.writeSymb(next.toWrite);
head.move(next.direction);
state = next.nextState;
}
static if (doShow)
show;
writeln("Performed ", head.nSteps, " steps.");
}
}
void main() @safe {
"Incrementer:".writeln;
enum States1 : ubyte { A, H }
enum Symbols1 : ubyte { s0, s1 }
alias M1 = UTM!(States1, Symbols1);
M1.TuringMachine tm1;
with (tm1) with (States1) with (Symbols1) with (M1.Direction) {
alias R = M1.Rule;
initialState = A;
rules = [A: [s0: R(s1, stay, H), s1: R(s1, right, A)]];
input = [s1, s1, s1];
symbolMap = ["0", "1"];
}
M1(tm1);
// http://en.wikipedia.org/wiki/Busy_beaver
"\nBusy Beaver machine (3-state, 2-symbol):".writeln;
enum States2 : ubyte { A, B, C, H }
alias Symbols2 = Symbols1;
alias M2 = UTM!(States2, Symbols2);
M2.TuringMachine tm2;
with (tm2) with (States2) with (Symbols2) with (M2.Direction) {
alias R = M2.Rule;
initialState = A;
rules = [A: [s0: R(s1, right, B), s1: R(s1, left, C)],
B: [s0: R(s1, left, A), s1: R(s1, right, B)],
C: [s0: R(s1, left, B), s1: R(s1, stay, H)]];
symbolMap = ["0", "1"];
}
M2(tm2);
"\nSorting stress test (12212212121212):".writeln;
enum States3 : ubyte { A, B, C, D, E, H }
enum Symbols3 : ubyte { s0, s1, s2, s3 }
alias M3 = UTM!(States3, Symbols3, false);
M3.TuringMachine tm3;
with (tm3) with (States3) with (Symbols3) with (M3.Direction) {
alias R = M3.Rule;
initialState = A;
rules = [A: [s1: R(s1, right, A),
s2: R(s3, right, B),
s0: R(s0, left, E)],
B: [s1: R(s1, right, B),
s2: R(s2, right, B),
s0: R(s0, left, C)],
C: [s1: R(s2, left, D),
s2: R(s2, left, C),
s3: R(s2, left, E)],
D: [s1: R(s1, left, D),
s2: R(s2, left, D),
s3: R(s1, right, A)],
E: [s1: R(s1, left, E),
s0: R(s0, stay, H)]];
input = [s1, s2, s2, s1, s2, s2, s1,
s2, s1, s2, s1, s2, s1, s2];
symbolMap = ["0", "1", "2", "3"];
}
M3(tm3).show;
"\nPossible best Busy Beaver machine (5-state, 2-symbol):".writeln;
alias States4 = States3;
alias Symbols4 = Symbols1;
alias M4 = UTM!(States4, Symbols4, false);
M4.TuringMachine tm4;
with (tm4) with (States4) with (Symbols4) with (M4.Direction) {
alias R = M4.Rule;
initialState = A;
rules = [A: [s0: R(s1, right, B), s1: R(s1, left, C)],
B: [s0: R(s1, right, C), s1: R(s1, right, B)],
C: [s0: R(s1, right, D), s1: R(s0, left, E)],
D: [s0: R(s1, left, A), s1: R(s1, left, D)],
E: [s0: R(s1, stay, H), s1: R(s0, left, A)]];
symbolMap = ["0", "1"];
}
M4(tm4);
}

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Task/Universal-Turing-machine/D/universal-turing-machine-2.d Normal file
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import std.stdio, std.typecons, std.algorithm, std.string, std.array;
void turing(Sy, St)(in St state, Sy[int] tape, in int pos,
in Tuple!(Sy, int, St)[Sy][St] rules) {
if (state.empty) return;
const r = rules[state][tape[pos] = tape.get(pos, Sy.init)];
writefln("%-(%s%)", tape.keys.sort()
.map!(i => format(i == pos ? "(%s)" : " %s ", tape[i])));
tape[pos] = r[0];
turing(r[2], tape, pos + r[1], rules);
}
void main() {
turing("a", null, 0,
["a": [0: tuple(1, 1, "b"), 1: tuple(1, -1, "c")],
"b": [0: tuple(1, -1, "a"), 1: tuple(1, 1, "b")],
"c": [0: tuple(1, -1, "b"), 1: tuple(1, 0, "")]]);
}