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#include <iostream>
#include "type.h"
#include "operation/math.h"
#include "function/apply.h"
#include "conditional/if.h"
#include "conditional/cond.h"
#include "list/operation/replace_nth.h"
#include "list/operation/higher/find.h"
#include "list/generator/make_list.h"
#include "runtime/list/for_each.h"
struct symbol {
struct BLANK { };
};
struct movement {
struct RIGHT { };
struct LEFT { };
struct NONE { };
};
// helper for easier state access
struct state_field {
using ID = tav::Size<0>;
using READ = tav::Size<1>;
using WRITE = tav::Size<2>;
using NEXT = tav::Size<3>;
using MOVE = tav::Size<4>;
};
// (define (state_predicate id read)
// (lambda (state)
// (and (= id (nth ID state))
// (= read (nth READ state)))))
template <
typename Id,
typename Read
>
struct state_predicate {
template <typename State>
using function = tav::And<
tav::IsEqualValue<Id, tav::Nth<state_field::ID, State>>,
tav::IsEqualValue<Read, tav::Nth<state_field::READ, State>>
>;
};
// (define (findState id read states)
// (find (state_predicate id read) states))
template <
typename Id,
typename Read,
typename States
>
using findState = tav::Find<
state_predicate<Id, Read>::template function,
States
>;
// (define (readSymbolFromTape position tape)
// (if (= (length tape) position)
// BLANK
// (nth position tape)))
template <
typename Position,
typename Tape
>
using readSymbolFromTape = tav::If<
tav::IsEqualValue<tav::Length<Tape>, Position>,
symbol::BLANK,
tav::Nth<Position, Tape>
>;
// (define (writeSymbolToTape position symbol tape)
// (if (= (length tape) position)
// (append tape (list symbol))
// (replace-nth position symbol tape)))
template <
typename Position,
typename Symbol,
typename Tape
>
using writeSymbolToTape = tav::If<
tav::IsEqualValue<tav::Length<Tape>, Position>,
tav::Append<Tape, tav::List<Symbol>>,
tav::ReplaceNth<Position, Symbol, Tape>
>;
// (define (transition states)
// (lambda (state symbol)
// (findState state symbol states)))
template <typename States>
struct transition {
template <
typename State,
typename Symbol
>
using state = findState<State, Symbol, States>;
};
// (define (simulateTuringMachine transition tape state position)
// (if (= state FINAL)
// tape
// (let* ((current_symbol (readSymbolFromTape position tape))
// (current_state (transition state current_symbol))
// (direction (nth MOVE current_state))
// (next_symbol (nth WRITE current_state))
// (next_state (nth NEXT current_state))
// (next_position (cond ((= direction RIGHT) (+ position 1))
// ((= direction LEFT) (- Position 1))
// (else position))))
// (simulateTuringMachine transition
// (writeSymbolToTape position next_symbol tape)
// next_state,
// next_position)))
template <
template<typename, typename> class Transition,
typename Tape,
typename State,
typename Position
>
class simulateTuringMachine {
private:
using current_symbol = readSymbolFromTape<Position, Tape>;
using current_state = Transition<State, current_symbol>;
using direction = tav::Nth<state_field::MOVE, current_state>;
using next_symbol = tav::Nth<state_field::WRITE, current_state>;
using next_state = tav::Nth<state_field::NEXT, current_state>;
using next_position = tav::Cond<
tav::Branch<
std::is_same<direction, movement::RIGHT>,
tav::Add<Position, tav::Size<1>>
>,
tav::Branch<
std::is_same<direction, movement::LEFT>,
tav::Substract<Position, tav::Size<1>>
>,
tav::Else<
Position
>
>;
static_assert(
tav::Not<tav::LowerThan<next_position, tav::Size<0>>>::value,
"next position out of bounds"
);
public:
using type = tav::Eval<simulateTuringMachine<
Transition,
writeSymbolToTape<Position, next_symbol, Tape>,
next_state,
next_position
>>;
};
template <
template<typename, typename> class Transition,
typename Tape,
typename Position
>
struct simulateTuringMachine<Transition, Tape, void, Position> {
typedef Tape type;
};
// (define mirror (list (list 1 1 0 2 RIGHT) [...]))
using mirror = tav::List<
// [state] [read] [write] [next state] [head movement]
tav::List<tav::Size<1>, tav::Int<1>, tav::Int<0>, tav::Size<2>, movement::RIGHT>,
tav::List<tav::Size<1>, tav::Int<0>, tav::Int<0>, void, movement::NONE >,
tav::List<tav::Size<2>, tav::Int<1>, tav::Int<1>, tav::Size<2>, movement::RIGHT>,
tav::List<tav::Size<2>, tav::Int<0>, tav::Int<0>, tav::Size<3>, movement::RIGHT>,
tav::List<tav::Size<3>, tav::Int<1>, tav::Int<1>, tav::Size<3>, movement::RIGHT>,
tav::List<tav::Size<3>, tav::Int<0>, tav::Int<1>, tav::Size<4>, movement::LEFT >,
tav::List<tav::Size<4>, tav::Int<1>, tav::Int<1>, tav::Size<4>, movement::LEFT >,
tav::List<tav::Size<4>, tav::Int<0>, tav::Int<0>, tav::Size<5>, movement::LEFT >,
tav::List<tav::Size<5>, tav::Int<1>, tav::Int<1>, tav::Size<5>, movement::LEFT >,
tav::List<tav::Size<5>, tav::Int<0>, tav::Int<1>, tav::Size<1>, movement::RIGHT>
>;
// (define mirror_initial_tape (list 1 1 1 0 0 0 0))
using mirror_initial_tape = tav::ListOfType<int, 1, 1, 1, 0, 0, 0, 0>;
// (define mirror_final_tape
// (simulateTuringMachine (transition mirror)
// mirror_initial_tape
// 1
// 0))
using mirror_final_tape = tav::Eval<simulateTuringMachine<
transition<mirror>::template state,
mirror_initial_tape,
tav::Size<1>,
tav::Size<0>
>>;
// (define busy_beaver (list (list 'A' 0 1 'B' RIGHT) [...]))
using busy_beaver = tav::List<
// [state] [read] [write] [next state] [head movement]
tav::List<tav::Char<'A'>, tav::Int<0>, tav::Int<1>, tav::Char<'B'>, movement::RIGHT>,
tav::List<tav::Char<'A'>, tav::Int<1>, tav::Int<1>, tav::Char<'C'>, movement::LEFT >,
tav::List<tav::Char<'B'>, tav::Int<0>, tav::Int<1>, tav::Char<'A'>, movement::LEFT >,
tav::List<tav::Char<'B'>, tav::Int<1>, tav::Int<1>, tav::Char<'B'>, movement::RIGHT>,
tav::List<tav::Char<'C'>, tav::Int<0>, tav::Int<1>, tav::Char<'B'>, movement::LEFT >,
tav::List<tav::Char<'C'>, tav::Int<1>, tav::Int<1>, void, movement::NONE >
>;
// (define busy_beaver_initial_tape (make-list 13 0))
using busy_beaver_initial_tape = tav::MakeList<tav::Size<13>, tav::Int<0>>;
// (define busy_beaver_final_tape
// (simulateTuringMachine (transition busy_beaver)
// busy_beaver_initial_tape
// 'A'
// 6))
using busy_beaver_final_tape = tav::Eval<simulateTuringMachine<
transition<busy_beaver>::template state,
busy_beaver_initial_tape,
tav::Char<'A'>,
tav::Size<6>
>>;
int main(int, char **) {
const auto printField = [](const int x) {
std::cout << x << " ";
};
std::cout << "1. Mirror"
<< std::endl
<<
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