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177
Task/Universal-Turing-machine/Go/universal-turing-machine-1.go
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177
Task/Universal-Turing-machine/Go/universal-turing-machine-1.go
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package turing
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type Symbol byte
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type Motion byte
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const (
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Left Motion = 'L'
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Right Motion = 'R'
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Stay Motion = 'N'
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)
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type Tape struct {
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data []Symbol
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pos, left int
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blank Symbol
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}
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// NewTape returns a new tape filled with 'data' and position set to 'start'.
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// 'start' does not need to be range, the tape will be extended if required.
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func NewTape(blank Symbol, start int, data []Symbol) *Tape {
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t := &Tape{
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data: data,
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blank: blank,
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}
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if start < 0 {
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t.Left(-start)
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}
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t.Right(start)
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return t
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}
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func (t *Tape) Stay() {}
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func (t *Tape) Data() []Symbol { return t.data[t.left:] }
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func (t *Tape) Read() Symbol { return t.data[t.pos] }
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func (t *Tape) Write(s Symbol) { t.data[t.pos] = s }
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func (t *Tape) Dup() *Tape {
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t2 := &Tape{
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data: make([]Symbol, len(t.Data())),
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blank: t.blank,
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}
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copy(t2.data, t.Data())
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t2.pos = t.pos - t.left
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return t2
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}
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func (t *Tape) String() string {
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s := ""
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for i := t.left; i < len(t.data); i++ {
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b := t.data[i]
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if i == t.pos {
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s += "[" + string(b) + "]"
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} else {
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s += " " + string(b) + " "
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}
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}
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return s
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}
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func (t *Tape) Move(a Motion) {
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switch a {
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case Left:
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t.Left(1)
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case Right:
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t.Right(1)
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case Stay:
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t.Stay()
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}
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}
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const minSz = 16
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func (t *Tape) Left(n int) {
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t.pos -= n
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if t.pos < 0 {
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// Extend left
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var sz int
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for sz = minSz; cap(t.data[t.left:])-t.pos >= sz; sz <<= 1 {
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}
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newd := make([]Symbol, sz)
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newl := len(newd) - cap(t.data[t.left:])
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n := copy(newd[newl:], t.data[t.left:])
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t.data = newd[:newl+n]
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t.pos += newl - t.left
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t.left = newl
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}
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if t.pos < t.left {
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if t.blank != 0 {
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for i := t.pos; i < t.left; i++ {
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t.data[i] = t.blank
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}
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}
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t.left = t.pos
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}
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}
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func (t *Tape) Right(n int) {
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t.pos += n
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if t.pos >= cap(t.data) {
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// Extend right
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var sz int
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for sz = minSz; t.pos >= sz; sz <<= 1 {
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}
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newd := make([]Symbol, sz)
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n := copy(newd[t.left:], t.data[t.left:])
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t.data = newd[:t.left+n]
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}
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if i := len(t.data); t.pos >= i {
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t.data = t.data[:t.pos+1]
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if t.blank != 0 {
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for ; i < len(t.data); i++ {
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t.data[i] = t.blank
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}
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}
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}
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}
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type State string
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type Rule struct {
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State
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Symbol
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Write Symbol
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Motion
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Next State
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}
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func (i *Rule) key() key { return key{i.State, i.Symbol} }
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func (i *Rule) action() action { return action{i.Write, i.Motion, i.Next} }
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type key struct {
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State
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Symbol
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}
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type action struct {
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write Symbol
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Motion
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next State
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}
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type Machine struct {
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tape *Tape
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start, state State
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transition map[key]action
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l func(string, ...interface{}) // XXX
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}
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func NewMachine(rules []Rule) *Machine {
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m := &Machine{transition: make(map[key]action, len(rules))}
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if len(rules) > 0 {
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m.start = rules[0].State
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}
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for _, r := range rules {
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m.transition[r.key()] = r.action()
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}
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return m
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}
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func (m *Machine) Run(input *Tape) (int, *Tape) {
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m.tape = input.Dup()
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m.state = m.start
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for cnt := 0; ; cnt++ {
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if m.l != nil {
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m.l("%3d %4s: %v\n", cnt, m.state, m.tape)
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}
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sym := m.tape.Read()
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act, ok := m.transition[key{m.state, sym}]
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if !ok {
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return cnt, m.tape
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}
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m.tape.Write(act.write)
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m.tape.Move(act.Motion)
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m.state = act.next
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}
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}
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@ -0,0 +1,71 @@
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package main
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import (
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".." // XXX path to above turing package
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"fmt"
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)
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func main() {
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var incrementer = turing.NewMachine([]turing.Rule{
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{"q0", '1', '1', turing.Right, "q0"},
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{"q0", 'B', '1', turing.Stay, "qf"},
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})
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input := turing.NewTape('B', 0, []turing.Symbol{'1', '1', '1'})
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cnt, output := incrementer.Run(input)
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fmt.Println("Turing machine halts after", cnt, "operations")
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fmt.Println("Resulting tape:", output)
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var beaver = turing.NewMachine([]turing.Rule{
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{"a", '0', '1', turing.Right, "b"},
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{"a", '1', '1', turing.Left, "c"},
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{"b", '0', '1', turing.Left, "a"},
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{"b", '1', '1', turing.Right, "b"},
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{"c", '0', '1', turing.Left, "b"},
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{"c", '1', '1', turing.Stay, "halt"},
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})
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cnt, output = beaver.Run(turing.NewTape('0', 0, nil))
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fmt.Println("Turing machine halts after", cnt, "operations")
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fmt.Println("Resulting tape:", output)
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beaver = turing.NewMachine([]turing.Rule{
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{"A", '0', '1', turing.Right, "B"},
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{"A", '1', '1', turing.Left, "C"},
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{"B", '0', '1', turing.Right, "C"},
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{"B", '1', '1', turing.Right, "B"},
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{"C", '0', '1', turing.Right, "D"},
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{"C", '1', '0', turing.Left, "E"},
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{"D", '0', '1', turing.Left, "A"},
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{"D", '1', '1', turing.Left, "D"},
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{"E", '0', '1', turing.Stay, "H"},
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{"E", '1', '0', turing.Left, "A"},
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})
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cnt, output = beaver.Run(turing.NewTape('0', 0, nil))
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fmt.Println("Turing machine halts after", cnt, "operations")
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fmt.Println("Resulting tape has", len(output.Data()), "cells")
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var sort = turing.NewMachine([]turing.Rule{
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// Moving right, first b→B;s1
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{"s0", 'a', 'a', turing.Right, "s0"},
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{"s0", 'b', 'B', turing.Right, "s1"},
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{"s0", ' ', ' ', turing.Left, "se"},
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// Conintue right to end of tape → s2
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{"s1", 'a', 'a', turing.Right, "s1"},
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{"s1", 'b', 'b', turing.Right, "s1"},
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{"s1", ' ', ' ', turing.Left, "s2"},
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// Continue left over b. a→b;s3, B→b;se
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{"s2", 'a', 'b', turing.Left, "s3"},
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{"s2", 'b', 'b', turing.Left, "s2"},
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{"s2", 'B', 'b', turing.Left, "se"},
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// Continue left until B→a;s0
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{"s3", 'a', 'a', turing.Left, "s3"},
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{"s3", 'b', 'b', turing.Left, "s3"},
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{"s3", 'B', 'a', turing.Right, "s0"},
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// Move to tape start → halt
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{"se", 'a', 'a', turing.Left, "se"},
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{"se", ' ', ' ', turing.Right, "see"},
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})
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input = turing.NewTape(' ', 0, []turing.Symbol("abbabbabababab"))
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cnt, output = sort.Run(input)
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fmt.Println("Turing machine halts after", cnt, "operations")
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fmt.Println("Resulting tape:", output)
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}
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