Add circuits

ocaml/Circuits.ml

@@ -0,0 +1,98 @@
+(* ============================================
+               Boolean circuits
+   ============================================ *)
+
+(* _________ Types _________ *)
+
+type var = string
+type id = int 
+
+type op =
+  | CIn of int | COut | CShare
+  | CAnd | COr | CNeg
+
+type input = id
+type gate = input list * op * id
+type circuit = gate list
+
+(* _________ Getters _________ *)
+
+let get_node_info circ node =
+    let (ins, op, i) =
+      List.hd (List.filter (fun (_, _, i) -> i = node) circ)
+  in (ins, op)
+
+let get_inputs circ node =
+  let (ins, _) = get_node_info circ node in ins
+
+let get_op circ node =
+  let (_, op) = get_node_info circ node in op
+
+let extract_bin_ins = function
+  | [] -> failwith "Error extract_bin_ins: no input."
+  | h1::h2::t -> (h1, h2)
+  | _ -> failwith "Error extract_bin_ins: inputs does not match."
+
+(* _________ Evaluation _________ *)
+
+(* provides the boolean value of the node 'concl' in a circuit 'circ' *)
+let rec value circ concl =
+  match get_op circ concl with
+  | CIn i -> i
+  | CShare | COut ->
+    let x = List.hd (get_inputs circ concl) in
+    value circ x
+  | CAnd ->
+    let (x, y) = extract_bin_ins (get_inputs circ concl) in
+    let vx = value circ x in
+    let vy = value circ y in
+    min vx vy
+  | COr ->
+    let (x, y) = extract_bin_ins (get_inputs circ concl) in
+    let vx = value circ x in
+    let vy = value circ y in
+    max vx vy
+  | CNeg ->
+    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) =
+    List.hd (List.filter (fun (_, o, _) -> o = COut) circ) in
+  value circ concl
+
+(* _________ Examples _________ *)
+
+let make_gate ins op id = (ins, op, id)
+let make_input value id = ([], CIn value, id)
+
+let make_and_circ x y = [
+  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 = [
+  make_input x 0;
+  make_input y 1;
+  make_gate [0;1] COr 2;
+  make_gate [2] COut 3
+]
+
+let make_neg_circ x = [
+  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 = [
+  make_input x 0;
+  make_gate [0] CShare 1;
+  make_gate [1] CNeg 2;
+  make_gate [1;2] COr 3;
+  make_gate [3] COut 4
+]