Separated Turing machine implementation into components

* i.e. separate namespaces and headers for _Tape_ and _State_ functions
* `void` is now used as the `BLANK` field value

3 files changed, 208 insertions, 0 deletions

diff --git a/example/turing/src/machine.h b/example/turing/src/machine.h
new file mode 100644
index 0000000..2404d9a
--- /dev/null
+++ b/example/turing/src/machine.h
@@ -0,0 +1,98 @@
+#ifndef TYPEASVALUE_EXAMPLE_TURING_MACHINE_H_
+#define TYPEASVALUE_EXAMPLE_TURING_MACHINE_H_
+
+#include "conditional/cond.h"
+
+#include "state.h"
+#include "tape.h"
+
+namespace machine {
+
+// (define (simulate transition tape state position)
+//   (if (= state FINAL)
+//     tape
+//     (let* ((current_symbol (readSymbol 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))))
+//       (simulate transition
+//                 (writeSymbol position next_symbol tape)
+//                 next_state,
+//                 next_position)))
+template <
+	template<typename, typename> class Transition,
+	typename                           State,
+	typename                           Tape,
+	typename                           Position
+>
+class simulate {
+	private:
+		using current_symbol = tape::readSymbol<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<
+				tav::IsEqualValue<direction, tav::Char<'R'>>,
+				tav::Add<Position, tav::Size<1>>
+			>,
+			tav::Branch<
+				tav::IsEqualValue<direction, tav::Char<'L'>>,
+				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<simulate<
+			Transition,
+			next_state,
+			tape::writeSymbol<Position, next_symbol, Tape>,
+			next_position
+		>>;
+};
+
+template <
+	template<typename, typename> class Transition,
+	typename                           Tape,
+	typename                           Position
+>
+struct simulate<Transition, void, Tape, Position> {
+	typedef Tape type;
+};
+
+// (define (run program state tape position)
+//   (simulate (transition program)
+//             tape
+//             state
+//             position))
+template <
+	typename Program,
+	typename State,
+	typename Tape,
+	typename Position
+>
+using run = tav::Eval<simulate<
+	state::transition<Program>::template state,
+	State,
+	Tape,
+	Position
+>>;
+
+}
+
+#endif // TYPEASVALUE_EXAMPLE_TURING_MACHINE_H_
diff --git a/example/turing/src/state.h b/example/turing/src/state.h
new file mode 100644
index 0000000..f5bd7f2
--- /dev/null
+++ b/example/turing/src/state.h
@@ -0,0 +1,64 @@
+#ifndef TYPEASVALUE_EXAMPLE_TURING_SRC_STATE_H_
+#define TYPEASVALUE_EXAMPLE_TURING_SRC_STATE_H_
+
+#include "type.h"
+#include "list/list.h"
+#include "list/operation/higher/find.h"
+
+namespace machine {
+
+namespace state {
+
+struct 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<field::ID,   State>>,
+		tav::IsEqualValue<Read, tav::Nth<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 (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>;
+};
+
+}
+
+}
+
+#endif // TYPEASVALUE_EXAMPLE_TURING_SRC_STATE_H_
diff --git a/example/turing/src/tape.h b/example/turing/src/tape.h
new file mode 100644
index 0000000..39814d8
--- /dev/null
+++ b/example/turing/src/tape.h
@@ -0,0 +1,46 @@
+#ifndef TYPEASVALUE_EXAMPLE_TURING_SRC_TAPE_H_
+#define TYPEASVALUE_EXAMPLE_TURING_SRC_TAPE_H_
+
+#include "type.h"
+#include "list/list.h"
+#include "list/operation/replace_nth.h"
+#include "conditional/if.h"
+
+namespace machine {
+
+namespace tape {
+
+// (define (readSymbol position tape)
+//   (if (= (length tape) position)
+//       '()
+//       (nth position tape)))
+template <
+	typename Position,
+	typename Tape
+>
+using readSymbol = tav::If<
+	tav::IsEqualValue<tav::Length<Tape>, Position>,
+	void,
+	tav::Nth<Position, Tape>
+>;
+
+// (define (writeSymbol position symbol tape)
+//   (if (= (length tape) position)
+//       (append tape (list symbol))
+//       (replace-nth position symbol tape)))
+template <
+	typename Position,
+	typename Symbol,
+	typename Tape
+>
+using writeSymbol = tav::If<
+	tav::IsEqualValue<tav::Length<Tape>, Position>,
+	tav::Append<Tape, tav::List<Symbol>>,
+	tav::ReplaceNth<Position, Symbol, Tape>
+>;
+
+}
+
+}
+
+#endif // TYPEASVALUE_EXAMPLE_TURING_SRC_TAPE_H_