Safe Haskell | Safe |
---|---|

Language | Haskell2010 |

This module defines everything required to simulate a simple deterministic
Turing machine. There are several equivalent but slightly different
definitions of Turing machines in use - ours has the machine write *and*
move in each step of execution. In addition, we allow a special movement
`DontMove`

that results in just a write operation.

You just define a transition function using suitable state and input types and run it:

`>>>`

let f (q, Just 0) = Just (q, Just 0, MoveRight) f ("even", Just 1) = Just ("odd", Just 0, MoveRight) f ("odd", Just 1) = Just ("even", Just 0, MoveRight) f _ = Nothing t = mkTuringMachine f "even" ["even"] -- a machine that decides parity in run t [0, 0, 1, 1, 1] :} Reject`:{`

- data TuringMachine s q
- mkTuringMachine :: TransitionFunction s q -> q -> [q] -> TuringMachine s q
- data Movement
- type TransitionFunction s q = (q, Maybe s) -> Maybe (q, Maybe s, Movement)
- data MachineResult
- run :: Eq q => TuringMachine s q -> [s] -> MachineResult
- runFor :: (Integral i, Eq q) => i -> TuringMachine s q -> [s] -> Maybe MachineResult

# The Turing machine

data TuringMachine s q Source

Abstract type representing a Turing machine. It is parameterized over
the alphabet and state types. A full definition contains the initial state,
a list of accepting states and the transition function. Construct through
`mkTuringMachine`

.

mkTuringMachine :: TransitionFunction s q -> q -> [q] -> TuringMachine s q Source

Construct a Turing machine from the transition function, its initial state and a list of accepting states.

# Associated types

A Turing machine has three options of moving its read head: left, right, or no move at all.

type TransitionFunction s q = (q, Maybe s) -> Maybe (q, Maybe s, Movement) Source

The transition function maps the current state and tape contents
to a triple describing the new state, the value to write to the tape, and
a head movement. If the function is `Nothing`

for the current state
and tape contents, the machine halts.

data MachineResult Source

A machine can either accept or reject the input (for now).

# Running a machine

run :: Eq q => TuringMachine s q -> [s] -> MachineResult Source

Run a machine indefinitely on the given input. If it halts, it either accepts or rejects the input.

runFor :: (Integral i, Eq q) => i -> TuringMachine s q -> [s] -> Maybe MachineResult Source