(** {2 Auxiliary functions} *)

let uri = UriManager.uri_of_string

let const ?(subst = []) uri = Cic.Const (uri, subst)
let var ?(subst = []) uri = Cic.Var (uri, subst)
let mutconstruct ?(subst = []) uri typeno consno =
  Cic.MutConstruct (uri, typeno, consno, subst)
let mutind ?(subst = []) uri typeno = Cic.MutInd (uri, typeno, subst)

let indtyuri_of_uri uri =
  let index_sharp =  String.index uri '#' in
  let index_num = index_sharp + 3 in
  (UriManager.uri_of_string (String.sub uri 0 index_sharp),
   int_of_string(String.sub uri index_num (String.length uri - index_num)) - 1)

let indconuri_of_uri uri =
  let index_sharp =  String.index uri '#' in
  let index_div = String.rindex uri '/' in
  let index_con = index_div + 1 in
    (UriManager.uri_of_string (String.sub uri 0 index_sharp),
    int_of_string
      (String.sub uri (index_sharp + 3) (index_div - index_sharp - 3)) - 1,
    int_of_string
      (String.sub uri index_con (String.length uri - index_con)))

let term_of_uri ?(subst = []) uri =
  let s = UriManager.string_of_uri uri in
  try
  (* Constant *)
  (* TODO explicit substitutions? *)
  let len = String.length s in
  let sub = String.sub s (len -4) 4 in
  if sub = ".con" then
    const ~subst uri
  else if sub = ".var" then
    var ~subst uri
  else
    (try
      (* Inductive Type *)
      let (uri, typeno) = indtyuri_of_uri s in
      mutind ~subst uri typeno
     with
      | UriManager.IllFormedUri _ | Failure _ | Invalid_argument _ ->
          (* Constructor of an Inductive Type *)
          let (uri, typeno, consno) = indconuri_of_uri s in
          mutconstruct ~subst uri typeno consno)
 with
 | Invalid_argument _ | Not_found -> raise (UriManager.IllFormedUri s)

(** {2 Helm's objects shorthands} *)

module Logic =
  struct
    let eq_URI = uri "cic:/Coq/Init/Logic/eq.ind"
    let true_URI = uri "cic:/Coq/Init/Logic/True.ind"
    let false_URI = uri "cic:/Coq/Init/Logic/False.ind"
  end

module Logic_Type =
  struct
    let eqt_URI = uri "cic:/Coq/Init/Logic_Type/eqT.ind"
    let sym_eqt_URI = uri "cic:/Coq/Init/Logic_Type/sym_eqT.con"

    let refl_eqt = mutconstruct eqt_URI 0 1
    let sym_eqt = const sym_eqt_URI
  end

module Datatypes =
  struct
    let bool_URI = uri "cic:/Coq/Init/Datatypes/bool.ind"
    let nat_URI = uri "cic:/Coq/Init/Datatypes/nat.ind"

    let trueb = mutconstruct bool_URI 0 1
    let falseb = mutconstruct bool_URI 0 2
    let zero = mutconstruct nat_URI 0 1
    let succ = mutconstruct nat_URI 0 2
  end

module Reals =
  struct
    let r_URI = uri "cic:/Coq/Reals/Rdefinitions/R.con"
    let rplus_URI = uri "cic:/Coq/Reals/Rdefinitions/Rplus.con"
    let rmult_URI = uri "cic:/Coq/Reals/Rdefinitions/Rmult.con"
    let ropp_URI = uri "cic:/Coq/Reals/Rdefinitions/Ropp.con"
    let r0_URI = uri "cic:/Coq/Reals/Rdefinitions/R0.con"
    let r1_URI = uri "cic:/Coq/Reals/Rdefinitions/R1.con"
    let rtheory_URI = uri "cic:/Coq/Reals/Rbase/RTheory.con"

    let r = const r_URI
    let rplus = const rplus_URI
    let rmult = const rmult_URI
    let ropp = const ropp_URI
    let r0 = const r0_URI
    let r1 = const r1_URI
    let rtheory = const rtheory_URI
  end

module Peano =
  struct
    let plus_URI = uri "cic:/Coq/Init/Peano/plus.con"
    let mult_URI = uri "cic:/Coq/Init/Peano/mult.con"
    let pred_URI = uri "cic:/Coq/Init/Peano/pred.con"

    let plus = const plus_URI
    let mult = const mult_URI
    let pred = const pred_URI
  end

(** {2 Helpers for creating common terms}
 *  (e.g. numbers)} *)

exception NegativeInteger

let build_nat n =
  if n < 0 then raise NegativeInteger;
  let rec aux = function
    | 0 -> Datatypes.zero
    | n -> Cic.Appl [ Datatypes.succ; (aux (n - 1)) ]
  in
  aux n

let build_real n =
  if n < 0 then raise NegativeInteger;
  let rec aux = function
    | 0 -> Reals.r0
    | 1 -> Reals.r1 (* to avoid trailing "+ 0" *)
    | n -> Cic.Appl [ Reals.rplus; Reals.r1; (aux (n - 1)) ]
  in
  aux n