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authorAdrian Kummerlaender2015-02-21 14:56:39 +0100
committerAdrian Kummerlaender2015-02-21 14:56:39 +0100
commiteffddfdd69cf9e5ec700aeda2980c0210575e320 (patch)
tree241f03911920723c38c1d216d56ae7858e2cba24
parentde1f1dc67a1dabcddac2e89a5d703e98a92b7f11 (diff)
Implemented basic Turing machine as an example
* executes and prints the _Busy Beaver_ and _Mirror_ state transitions * this example demonstrates how one may use _TypeAsValue_ to simplify and augment normal statically recursive template metaprograms where it makes sense
-rw-r--r--example/turing/CMakeLists.txt16
-rw-r--r--example/turing/turing.cc257
2 files changed, 273 insertions, 0 deletions
diff --git a/example/turing/CMakeLists.txt b/example/turing/CMakeLists.txt
new file mode 100644
index 0000000..dc08ac9
--- /dev/null
+++ b/example/turing/CMakeLists.txt
@@ -0,0 +1,16 @@
+cmake_minimum_required(VERSION 2.8)
+project(turing)
+
+set(
+ CMAKE_CXX_FLAGS
+ "-std=c++14 -W -Wall -Wextra -Winline -pedantic -ftemplate-depth-1024"
+)
+
+include_directories(
+ ../../src/
+)
+
+add_executable(
+ turing
+ turing.cc
+)
diff --git a/example/turing/turing.cc b/example/turing/turing.cc
new file mode 100644
index 0000000..e1384d8
--- /dev/null
+++ b/example/turing/turing.cc
@@ -0,0 +1,257 @@
+#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
+ << " Initial: ";
+
+ tav::runtime::for_each<mirror_initial_tape>(printField);
+
+ std::cout << std::endl
+ << " Final: ";
+
+ tav::runtime::for_each<mirror_final_tape>(printField);
+
+ std::cout << std::endl
+ << std::endl
+ << "2. Busy Beaver"
+ << std::endl
+ << " Initial: ";
+
+ tav::runtime::for_each<busy_beaver_initial_tape>(printField);
+
+ std::cout << std::endl
+ << " Final: ";
+
+ tav::runtime::for_each<busy_beaver_final_tape>(printField);
+
+ std::cout << std::endl;
+}