Add automata

ocaml/Circuits.ml

@@ -57,7 +57,6 @@ let rec value circ concl =
     let x = List.hd (get_inputs circ concl) in
     let vx = value circ x in
     1 - vx
-  | _ -> -1
 
 let rec eval (circ : circuit) : int =
   let (_, _, concl) =
@@ -66,31 +65,31 @@ let rec eval (circ : circuit) : int =
 
 (* _________ Examples _________ *)
 
-let make_gate ins op id = (ins, op, id)
-let make_input value id = ([], CIn value, id)
+let make_gate ins op id : gate = (ins, op, id)
+let make_input value id : gate = ([], CIn value, id)
 
-let make_and_circ x y = [
+let make_and_circ x y : circuit = [
   make_input x 0;
   make_input y 1;
   make_gate [0;1] CAnd 2;
   make_gate [2] COut 3
 ]
 
-let make_or_circ x y = [
+let make_or_circ x y : circuit = [
   make_input x 0;
   make_input y 1;
   make_gate [0;1] COr 2;
   make_gate [2] COut 3
 ]
 
-let make_neg_circ x = [
+let make_neg_circ x : circuit = [
   make_input x 0;
   make_gate [0] CNeg 1;
   make_gate [1] COut 2
 ]
 
 (* corresponds to the excluded middle x v ~x *)
-let make_em_circ x = [
+let make_em_circ x : circuit = [
   make_input x 0;
   make_gate [0] CShare 1;
   make_gate [1] CNeg 2;

ocaml/FSA.ml

@@ -0,0 +1,32 @@
+(* ============================================
+              Finite State Automata
+   ============================================ *)
+
+type id = int
+
+type state = id
+type initial_state = state
+type final_state = state
+type fa_transition = state * char * state
+type fautomata = initial_state * (fa_transition list) * final_state list
+
+let accepts ((qi, ts, qf) : fautomata) (w : char list) =
+  let rec head q (read : char list) =
+    match read with
+    | [] -> List.mem q qf
+    | c::w ->
+      let (_, _, qnext) =
+        List.hd (List.filter (fun (qs, c', qt) -> qs=q && c=c') ts)
+      in head qnext w
+  in head qi w
+
+(* _________ Examples _________ *)
+
+let even_ones : fautomata = (
+  0,
+  [
+    (0, '1', 1);
+    (1, '1', 0)
+  ],
+  [0]
+)