open Circuits
open Resolution
(* ============================================
               Stellar Circuits
   ============================================ *)

let port pol i v = Func ("c"^(string_of_int i), pol, v)
let inport i x = port Neg i [Var x]
let outport i x = port Pos i [Var x]

let call_cneg pol arg res = Func ("neg", pol, [arg; res])
let call_cand pol arg1 arg2 res = Func ("and", pol, [arg1; arg2; res])
let call_cor pol arg1 arg2 res = Func ("or", pol, [arg1; arg2; res])

let star_of_gate circ (ins, op, outs) =
  match op with
  | CIn i -> [port Pos (List.hd outs) [make_const (string_of_int i)]]
  | COut -> [inport (List.hd ins) "r"; Var "r"]
  | CShare -> 
      let (o1, o2) = twinhd outs in
      [inport (List.hd ins) "x"; outport o1 "x"; outport o2 "x"] 
  | CNeg -> [
      inport (List.hd ins) "x";
      call_cneg Neg (Var "x") (Var "r");
      outport (List.hd outs) "r" 
    ]
  | CAnd ->
      let (i1, i2) = twinhd ins in [
        inport i1 "x";
        inport i2 "y";
        call_cand Neg (Var "x") (Var "y") (Var "r");
        outport (List.hd outs) "r" 
      ]
  | COr ->
      let (i1, i2) = twinhd ins in [
        inport i1 "x";
        inport i2 "y";
        call_cor Neg (Var "x") (Var "y") (Var "r");
        outport (List.hd outs) "r" 
      ]

let const_of_circuit (circ : circuit) = List.map (star_of_gate circ) circ

let prop_logic : constellation = [
  [call_cneg Pos (make_const "0") (make_const "1")];
  [call_cneg Pos (make_const "1") (make_const "0")];
  [call_cand Pos (make_const "0") (make_const "0") (make_const "0")];
  [call_cand Pos (make_const "0") (make_const "1") (make_const "0")];
  [call_cand Pos (make_const "1") (make_const "0") (make_const "0")];
  [call_cand Pos (make_const "1") (make_const "1") (make_const "1")];
  [call_cor Pos (make_const "0") (make_const "0") (make_const "0")];
  [call_cor Pos (make_const "0") (make_const "1") (make_const "1")];
  [call_cor Pos (make_const "1") (make_const "0") (make_const "1")];
  [call_cor Pos (make_const "1") (make_const "1") (make_const "1")]
]