characteristic.ml 61.8 KB
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open Misc
open Asttypes
open Types
open Typedtree
open Mytools
open Longident
open Print_tast
open Print_type
open Formula
open Coq
open Path
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open Renaming
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open Printf

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(*#########################################################################*)
(* ** Error messages *)

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exception Not_in_normal_form of Location.t * string
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let not_in_normal_form loc s =
   raise (Not_in_normal_form (loc, s))
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(*#########################################################################*)
(* ** List of external modules that need to be required *)

let external_modules = ref []

let external_modules_add name =
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   if not (List.mem name !external_modules) 
     then external_modules := name::!external_modules
   (* TODO: use a structure more efficient than lists *)
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let external_modules_get_coqtop () = 
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   List.map (fun name -> Coqtop_require [name]) !external_modules
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let external_modules_reset () = 
   external_modules := []


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(*#########################################################################*)
(* ** Lifting of paths *)

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(* Take a module name and add "_ml" suffix to it;
   Moreover, insert a "Require" directive in case the module 
   corresponds to a file (i.e. a compilation unit. *)
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let lift_module_name id =
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   let name = Ident.name id in
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   let coqname = module_name name in
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   if Ident.persistent id then external_modules_add coqname;
   coqname
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   (* -- old:
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     if Ident.persistent id  
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      then (let result = name ^ "_ml" in external_modules_add result; result)
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      else "ML" ^ name
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   *)
   (* -- old: if name = "OkaStream" then "CFPrim" else  *)
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(* Function for adding "_ml" to the modules in a path, 
   including the last constant which is assumed to a module name *)
   (* TODO: rename this function *)

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let rec lift_full_path = function
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  | Pident id -> Pident (Ident.create (lift_module_name id))
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  | Pdot(p, s, pos) -> Pdot(lift_full_path p, (module_name s), pos) 
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  | Papply(p1, p2) -> assert false 

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(* Function for adding "_ml" to the modules in a path, 
   but not changing the last constant in the path *)

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let lift_path = function
  | Pident id -> Pident id
  | Pdot(p, s, pos) -> Pdot(lift_full_path p, s, pos) 
  | Papply(p1, p2) -> assert false 

(** Translates a path into a string. A module called "Test" 
    becomes "Test_ml" if it refers to a file, and it becomes
    "MLTest" if it refers to a functor argument. 
    --todo: call them all "Test_ml"? *)

let lift_full_path_name p =
  Path.name (lift_full_path p)

(** Translates a path into a string --todo: why not full? *)

let lift_path_name p =
  Path.name (lift_path p)


(*#########################################################################*)
(* ** Lifting of types *)

(** Computes the free variables of a [btyp] *)

let rec fv_btyp ?(through_arrow = true) t =
   let aux = fv_btyp in
   match t with
   | Btyp_val -> []
   | Btyp_arrow (t1,t2) -> if through_arrow then aux t1 @ aux t2 else []
   | Btyp_constr (id,ts) -> list_concat_map aux ts
   | Btyp_tuple ts -> list_concat_map aux ts
   | Btyp_var (b,s) -> [s]
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   | Btyp_poly (ss,t) -> unsupported_noloc "poly-types"
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   | Btyp_alias (t,s) -> s :: aux t 

(** Translates a [btyp] into a Coq type *)

let rec lift_btyp t =
   let aux = lift_btyp in
   match t with
   | Btyp_val -> 
      val_type
   | Btyp_arrow (t1,t2) -> 
      val_type
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   | Btyp_constr (id,[t]) when Path.name id = "array" -> 
      (* || Path.name id = "Pervasives.array" *)
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      loc_type
   | Btyp_constr (id,ts) -> 
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      coq_apps (Coq_var (type_constr_name (lift_path_name id))) (List.map aux ts)
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   | Btyp_tuple ts -> 
      coq_prod (List.map aux ts)
   | Btyp_var (b,s) -> 
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      if b then unsupported_noloc "non-generalizable free type variables (of the form '_a); please add a type annotation";
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      Coq_var s
   | Btyp_poly (ss,t) -> 
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      unsupported_noloc "poly-types"
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   | Btyp_alias (t1,s) -> 
      let occ = fv_btyp ~through_arrow:false t1 in
      if List.mem s occ 
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        then unsupported_noloc ("found a recursive type that is not erased by an arrow:" ^ (print_out_type t));
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      aux t1 

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(* TEMPORARILY DEPRECATED

   | Btyp_constr (id,[t]) when Path.name id = "ref" || Path.name id = "Pervasives.ref" ->
      loc_type

   | Btyp_constr (id,[t]) when Path.name id = "heap" || Path.name id = "Heap.heap" ->
      loc_type

   | Btyp_constr (id,[t]) when Path.same id Predef.path_lazy_t || Path.name id = "Lazy.t" -> 
      aux t  
   | Btyp_constr (id,[t]) when Path.name id = "Stream.stream" || Path.name id = "stream" -> 
      Coq_app (Coq_var "list", aux t)
   | Btyp_constr (id,[t]) when Path.name id = "Stream.stream_cell" || Path.name id = "stream_cell" -> 
      Coq_app (Coq_var "list", aux t)
*)
(* REMARK: les Lazy provenant des patterns ne sont pas identique Predef.path_lazy_t *)


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(** Translates a Caml type into a Coq type *)

let lift_typ_exp ty =
  lift_btyp (btyp_of_typ_exp ty)  

(** Translates a Caml type scheme into a Coq type *)

let lift_typ_sch ty =
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   let t = btyp_of_typ_sch_simple ty in
   let fv = fv_btyp ~through_arrow:false t in
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   fv, lift_btyp t

(** Translates the type of a Caml expression into a Coq type *)

let coq_typ e =
   lift_typ_exp (e.exp_type)

(** Translates the type of a Caml pattern into a Coq type *)

let coq_typ_pat p =
   lift_typ_exp (p.pat_type)

(** Decompose "A.B.s" as ("A.B","s") *)

let rec path_decompose = function
    Pident id -> ("", Ident.name id)
  | Pdot(p, s, pos) -> 
      let (f,r) = path_decompose p in
      (f ^ r ^ ".", s)
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  | Papply(p1, p2) -> unsupported_noloc "application in paths"
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(** Extracts a record path_name / path from a type *)

let get_record_decomposed_name_for_exp e = 
   let b = btyp_of_typ_exp (e.exp_type) in   
   match b with 
   | Btyp_constr (p,_) -> path_decompose (lift_path p)
   | _ -> failwith "illegal argument for get_record_decomposed_name_for_exp"



(*#########################################################################*)
(* ** Type arity functions *)

(** Get the number of type arguments of a (polymorphic) free variable *)

let typ_arity_var env x =
   match x with
   | Path.Pident id -> 
      begin try Ident.find_same id env
      with Not_found -> 0 end
   | _ -> 0

(** Get the number of type arguments of a (polymorphic) data constructor *)

let typ_arity_constr c =
   match (c.cstr_res).desc with
   | Tconstr (_,ts,_) -> List.length ts
   | _ -> failwith "typ_arity_constr: result type of constructor is not a type constructor"

(** Translate a Caml data constructor into a Coq expression *)

let coq_of_constructor p c =
   let x = string_of_path p in
   match find_builtin_constructor x with
   | None -> coq_app_var_wilds x (typ_arity_constr c) 
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   | Some (y,arity) -> coq_app_var_wilds y arity
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(*#########################################################################*)
(* ** Lifting of patterns *)

(** Compute the free variables of a pattern *)

let rec pattern_variables p : typed_vars = (* ignores aliases *)
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   let loc = p.pat_loc in
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   let aux = pattern_variables in
   match p.pat_desc with
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   | Tpat_any -> not_in_normal_form loc "wildcard patterns remain after normalization"
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   | Tpat_var s -> [Ident.name s, coq_typ_pat p]
   | Tpat_alias (p, s) -> aux p
   | Tpat_constant c -> []
   | Tpat_tuple l -> list_concat_map aux l
   | Tpat_construct (p, c, ps) -> list_concat_map aux ps
   | Tpat_lazy p1 -> aux p1
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   | Tpat_variant (_,_,_) -> unsupported loc "variant patterns"
   | Tpat_record _ -> unsupported loc "record patterns"
   | Tpat_array pats -> unsupported loc "array patterns"
   | Tpat_or (_,p1,p2) -> unsupported loc "or patterns"
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(** Translate a Caml pattern into a Coq expression, and
    ignores the aliases found in the pattern *)

let rec lift_pat ?(through_aliases=true) p : coq = 
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   let loc = p.pat_loc in
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   let aux = lift_pat ~through_aliases:through_aliases in
   match p.pat_desc with
   | Tpat_var s -> 
      Coq_var (Ident.name s)
   | Tpat_constant (Const_int n) -> 
      Coq_int n
   | Tpat_tuple l -> 
      Coq_tuple (List.map aux l)
   | Tpat_construct (p, c, ps) -> 
      coq_apps (coq_of_constructor p c) (List.map aux ps)
   | Tpat_alias (p, ak) -> 
      begin match ak with
      | TPat_alias id -> 
          if through_aliases then aux p else Coq_var (Ident.name id)
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      | TPat_constraint ty -> 
          let typ = lift_typ_exp ty.ctyp_type in
          Coq_annot (aux p, typ)
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      | TPat_type pp -> aux p 
      end
   | Tpat_lazy p1 ->
      aux p1
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   | Tpat_record _ -> unsupported loc "record patterns" (* todo! *)
   | Tpat_array pats -> unsupported loc "array patterns" (* todo! *)
   | Tpat_constant _ -> unsupported loc "only integer constant are supported"
   | Tpat_any -> not_in_normal_form loc "wildcard patterns remain after normalization"
   | Tpat_variant (_,_,_) -> unsupported loc "variant patterns"
   | Tpat_or (_,p1,p2) -> unsupported loc "or patterns in depth"
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(** Extracts the aliases from a Caml pattern, in the form of an
    association list mapping variables to Coq expressions *)

let pattern_aliases p : (typed_var*coq) list = 
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   let loc = p.pat_loc in
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   let rec aux p =
      match p.pat_desc with
      | Tpat_var s -> []
      | Tpat_constant (Const_int n) -> []
      | Tpat_tuple l -> list_concat_map aux l
      | Tpat_construct (p, c, ps) -> list_concat_map aux ps
      | Tpat_alias (p1, ak) -> 
          begin match ak with
          | TPat_alias id ->
             ((Ident.name id, coq_typ_pat p), lift_pat ~through_aliases:false p1) :: (aux p1)
          | TPat_constraint _ -> aux p1
          | TPat_type pp -> aux p1
         end
      | Tpat_lazy p1 ->  aux p1
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      | Tpat_record _ -> unsupported loc "record patterns" (* todo! *)
      | Tpat_array pats -> unsupported loc "array patterns" (* todo! *)
      | Tpat_constant _ -> unsupported loc "only integer constant are supported"
      | Tpat_any -> not_in_normal_form loc "wildcard patterns remain after normalization"
      | Tpat_variant (_,_,_) -> unsupported loc "variant patterns"
      | Tpat_or (_,p1,p2) -> unsupported loc "or patterns"   
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      in
   List.rev (aux p)


(*#########################################################################*)
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(* ** Helper functions for various things *)
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let register_cf x =
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   Coqtop_register ("database_cf", x, cf_axiom_name x)
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let register_spec x v =
   Coqtop_register ("database_spec", x, v)

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(* TODO: rewrite this function by using a normalization function that returns p *)
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let rec prefix_for_label typ = 
  match typ.desc with  
  | Tconstr (p, _, _) -> lift_path_name p 
  | Tlink t -> prefix_for_label t
  | _ -> failwith "string_of_label: type of a record should be a Tconstr or Tlink"
  (*
  | Tvar -> failwith "x1"
  | Tarrow _ -> failwith "x2"
  | Ttuple  _ -> failwith "x3"
  | Tconstr _ -> failwith "x4"
  | Tobject  _ -> failwith "x5"
  | Tfield _ -> failwith "x6"
  | Tnil _ -> failwith "x7"
  | Tsubst  _ -> failwith "x9"
  | Tvariant  _ -> failwith "x10"
  | Tunivar -> failwith "x11"
  | Tpoly  _ -> failwith "x12"
  *)

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(* DEPRECATED 
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let string_of_label_with prefix lbl =
  prefix ^ "_" ^ lbl.lbl_name

let string_of_label typ lbl =
  string_of_label_with (prefix_for_label typ) lbl
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*)
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(*#########################################################################*)
(* ** Helper functions for primitive functions *)

let simplify_apply_args loc oargs =
  List.map (function (lab, Some e, Required) -> e | _ -> unsupported loc "optional arguments") oargs 

let get_qualified_pervasives_name f = 
   let name = Path.name f in
   if !Clflags.nopervasives 
      then "Pervasives." ^ name  (* unqualified name when from inside Pervasives *)
      else name  (* qualified name otherwise *)
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let exp_find_inlined_primitive e oargs =
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   let loc = e.exp_loc in
   let args = simplify_apply_args loc oargs in
   match e.exp_desc with
   | Texp_ident (f,d) ->
      let name = get_qualified_pervasives_name f in
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      let _debug() =
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         Printf.printf "exp_find_inlined_primitive: %s\n arity: %d\n name: %s\n" (Path.name f) (List.length args) name
         in
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      (* _debug(); *)
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      begin match args with 
      | [n; {exp_desc = Texp_constant (Const_int m)}] 
           when m <> 0  
             && List.mem name ["Pervasives.mod"; "Pervasives./"] -> 
           begin match find_inlined_primitive name with
           | Some (Primitive_binary_div_or_mod, coq_name) -> Some coq_name
           | _ -> None
           end
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       | [e1; e2] 
           when List.mem name ["Pervasives.&&"; "Pervasives.||"] -> 
           begin match find_inlined_primitive (Path.name f) with
           | Some (Primitive_binary_lazy, coq_name) -> Some coq_name
           | _ -> None
           end
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       | [e1; e2] 
           when List.mem name ["Pervasives.="; "Pervasives.<>"; "Pervasives.<="; 
                               "Pervasives.>="; "Pervasives.<"; "Pervasives.>";
                               "Pervasives.min"; "Pervasives.max"; ] -> 
           let is_number = 
              begin match btyp_of_typ_exp e1.exp_type with
              | Btyp_constr (id,[]) when Path.name id = "int" -> true
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              | _ -> false
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              end in
             (* Remark: by typing, [e2] has the same type as [e1] *)
           if not is_number then 
             unsupported loc (Printf.sprintf "comparison operators on non integer arguments (here, %s)" (string_of_type_exp e1.exp_type));
           begin match find_inlined_primitive name with
           | Some (Primitive_binary_only_numbers, coq_name) -> Some coq_name
           | _ -> failwith ("in exp_find_inlined_primitive, could not find the coq translation of the function: " ^ name)
           end

       | _ -> 
           let arity = List.length args in
           begin match find_inlined_primitive name with
           | Some (Primitive_unary, coq_name) when arity = 1 -> Some coq_name
           | Some (Primitive_binary, coq_name) when arity = 2 -> Some coq_name
           | _ -> None
           end
           (* debug: Printf.printf "exp_find_inlined_primitive: %s %d\n"  (Path.name f)  (List.length args);
           if r = None then Printf.printf "failed\n"; *)

       end

    | _ -> None


let exp_is_inlined_primitive e oargs = 
  exp_find_inlined_primitive e oargs <> None
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(*#########################################################################*)
(* ** Lifting of values *)

(** Translate a Caml identifier into a Coq identifier, possibly 
    applied to wildcards for taking type applications into account *)

let lift_exp_path env p =
   match find_primitive (Path.name p) with
   | None -> 
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      let x = lift_path_name (protect_infix_path p) in
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      coq_app_var_wilds x (typ_arity_var env p)
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   | Some y -> 
      Coq_var y 
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(** Translate a Caml value into a Coq value. Fails if the Coq 
    expression provided is not a value. *)

let rec lift_val env e = 
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   let loc = e.exp_loc in
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   let aux = lift_val env in
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   let fail () =
     not_in_normal_form loc ("in liftval: " ^ Print_tast.string_of_expression false e) in
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   match e.exp_desc with
   | Texp_ident (p,d) -> 
     lift_exp_path env p 
   | Texp_open (p, _) -> 
     assert false
   | Texp_constant (Const_int n) ->
      Coq_int n
   | Texp_constant _ -> 
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      unsupported loc "only integer constant are supported"
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   | Texp_tuple el -> 
      Coq_tuple (List.map aux el)
   | Texp_construct (p, c, es) ->
      coq_apps (coq_of_constructor p c) (List.map aux es)
   | Texp_record (l, opt_init_expr) ->  
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       if opt_init_expr <> None then unsupported loc "record-with expression"; (* todo *)
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       if List.length l < 1 then failwith "record should have at least one field";
       let labels = ((fun (p,li,ei) -> li) (List.hd l)).lbl_all in
       let args = Array.make (Array.length labels) (Coq_var "dummy") in
       let register_arg lbl v =
          Array.iteri (fun i lbli -> if lbl.lbl_name = lbli.lbl_name then args.(i) <- v) labels in
       List.iter (fun (p,lbl,v) -> register_arg lbl (aux v)) l;
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       let constr = record_constructor_name_from_type (prefix_for_label (e.exp_type)) in
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       let typ_args = 
          match btyp_of_typ_exp e.exp_type with
          | Btyp_constr (id,ts) -> List.map lift_btyp ts
          | _ -> failwith "record should have a type-constructor as type"
          in
       coq_apps (coq_var_at constr) (typ_args @ Array.to_list args)
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   | Texp_apply (funct, oargs) ->
      let fo = exp_find_inlined_primitive funct oargs in
      let f = match fo with
         | Some f -> f
         | _ -> fail()
         in
      let args = simplify_apply_args loc oargs in
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      coq_apps (Coq_var f) (List.map aux args)
   | Texp_lazy e -> 
      aux e
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   | Texp_constraint (e, Some ty, None) -> 
      let typ = lift_typ_exp ty.ctyp_type in
      Coq_annot (aux e, typ)
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   (* --uncomment for debugging 
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   | Texp_function _ -> not_in_normal_form loc "function"
   | Texp_apply _ -> not_in_normal_form loc "apply"
   | Texp_assertfalse -> not_in_normal_form loc "assert false"
   | Texp_try(body, pat_expr_list) -> not_in_normal_form loc "try expression"
   | Texp_variant(l, arg) ->  not_in_normal_form loc "variant expression"
   | Texp_setfield(arg, p, lbl, newval) -> not_in_normal_form loc "set-field expression"
   | Texp_array expr_list -> not_in_normal_form loc "array expressions"
   | Texp_ifthenelse(cond, ifso, None) -> not_in_normal_form loc "if-then-without-else expressions"
   | Texp_sequence(expr1, expr2) -> not_in_normal_form loc "sequence expressions"
   | Texp_while(cond, body) -> not_in_normal_form loc "while expressions"
   | Texp_for(param, low, high, dir, body) -> not_in_normal_form loc "for expressions"
   | Texp_when(cond, body) -> not_in_normal_form loc "when expressions"
   | Texp_send(_ , _, _) -> not_in_normal_form loc "send expressions"
   | Texp_new (cl, _) -> not_in_normal_form loc "new expressions"
   | Texp_instvar(path_self, path) -> not_in_normal_form loc "inst-var expressions"
   | Texp_setinstvar(path_self, path, expr) -> not_in_normal_form loc "set-inst-var expressions"
   | Texp_override(path_self, modifs) -> not_in_normal_form loc "override expressions"
   | Texp_letmodule(id, modl, body) -> not_in_normal_form loc "let-module expressions"
   | Texp_assert (cond) -> not_in_normal_form loc "assert expressions"
   | Texp_object (_, _) -> not_in_normal_form loc "object expressions"
   | Texp_poly _  -> not_in_normal_form loc "object expressions"
   | Texp_newtype _  -> not_in_normal_form loc "object expressions"
   | Texp_pack _  -> not_in_normal_form loc "object expressions"
   | Texp_let _ -> not_in_normal_form loc "let"
   | Texp_match _ -> not_in_normal_form loc "match"
   | Texp_field _ -> not_in_normal_form loc "field"
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   *)
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   | _ -> fail()
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   (* --todo: could be a value in a purely-functional setting
   | Texp_field (e, lbl) ->
       let typ = e.exp_type in
       Coq_app (Coq_var (string_of_label typ lbl), aux e) *)


(*#########################################################################*)
(* ** Helper functions for producing label names *)

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(* FOR FUTURE USE *)

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let counter_local_label = 
   ref 0
let get_next_local_label () = 
   incr counter_local_label;
   "_m" ^ (string_of_int !counter_local_label)
let reset_local_labels() = 
   counter_local_label := 0

let used_labels : (var list) ref = 
   ref []
let reset_used_labels () =
   used_labels := []
let add_used_label x =
   if not (List.mem x !used_labels)
      then used_labels := x :: !used_labels

let cfg_extract_labels () =
   let labs = List.rev !used_labels in
   let cft = [ Cftop_coqs (list_mapi (fun i x -> Coqtop_label (x,i+1)) labs) ] in
   reset_used_labels();
   cft


(*#########################################################################*)
(* ** Helper functions for names *)

(** Takes a pattern that is expected to be reduced simply to an identifier, 
    and returns this identifier *)

let rec pattern_ident p =
   match p.pat_desc with
   | Tpat_var s -> s
   | Tpat_alias (p1,_) -> pattern_ident p1
   | _ -> failwith ("pattern_ident: the pattern is not a name: " ^ (Print_tast.string_of_pattern false p))

(** Takes a pattern that is expected to be reduced simply to an identifier, 
    and returns the name of this identifier *)

let pattern_name p =
   Ident.name (pattern_ident p)

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(** Takes a function name and encodes its name in case of an infix operator *)

let pattern_name_protect_infix p =
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   protect_infix (pattern_name p)
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(** An alternative version of function extract_label_names, for obtaining record labels *)

let rec extract_label_names_simple env ty =
  let ty = Ctype.repr ty in
  match ty.desc with
  | Tconstr (path, _, _) ->
      let td = Env.find_type path env in
      begin match td.type_kind with
      | Type_record (fields, _) ->
          List.map (fun (name, _, _) -> name) fields
      | Type_abstract when td.type_manifest <> None ->
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          unsupported_noloc "building of a record with abstract type"
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      | _ -> assert false
      end
  | _ -> assert false


(*#########################################################################*)
(* ** Characteristic formulae for expressions *)

(** Translate a Caml expression into its Coq characteristic formula *)

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let rec cfg_exp env e = 
   let loc = e.exp_loc in
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   let aux = cfg_exp env in
   let lift e = lift_val env e in
   let ret e = Cf_ret (lift e) in
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   let not_normal ?s:(s="") () =
      not_in_normal_form loc (s ^ Print_tast.string_of_expression false e) in
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   match e.exp_desc with
   | Texp_ident (x,d) -> ret e
   | Texp_open (p, {exp_desc = Texp_ident _}) -> assert false
   | Texp_constant cst -> ret e
   | Texp_tuple el -> ret e
   | Texp_construct(p, cstr, args) -> ret e
   (* TODO: only in purely function setting:   | Texp_record (lbl_expr_list, opt_init_expr) -> ret e*)

   | Texp_record (lbl_expr_list, opt_init_expr) ->
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      if opt_init_expr <> None then unsupported loc "record-with"; 
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      let named_args = List.map (fun (p,li,ei) -> (li.lbl_name,ei)) lbl_expr_list in
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      let build_arg (name, arg) =
        let value = coq_apps coq_dyn_at [coq_typ arg; lift arg] in
        Coq_tuple [Coq_var (record_field_name name); value]
        in
      let arg = coq_list (List.map build_arg named_args) in
      Cf_record_new (arg)

      (* DEPRECATED
      let (pathfront,pathend) = get_record_decomposed_name_for_exp e in
      let func = Coq_var (pathfront ^ (record_make_name pathend)) in 
      let fields_names = extract_label_names_scimple e.exp_env e.exp_type in
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      let args = 
         try List.map (fun name -> List.assoc name named_args) fields_names
         with Not_found -> failwith "some fields are missing in a record construction" 
         in
      let tprod = coq_prod (List.map coq_typ args) in
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      Cf_app ([tprod], loc_type, func, [Coq_tuple (List.map lift args)]) 
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      *)
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   | Texp_apply (funct, oargs) when exp_is_inlined_primitive funct oargs -> ret e

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   | Texp_function (_, pat_expr_list, partial) -> not_normal ~s:"The function involved has not been lifted properly during normalization;\n check the normalized file in _output folder.\n" ()
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   | Texp_let(rf, fvs, pat_expr_list, body) ->
      
      let is_let_fun = 
         match (snd (List.hd pat_expr_list)).exp_desc with
         | Texp_function (_,_,_) -> true
         | Texp_constraint ({exp_desc = Texp_function (_,_,_)},_,_) -> true (* todo: generalize *)
         | _ -> false in

      (* binding of functions, possibly mutually-recursive *)
      if is_let_fun then begin
        let env' = match rf with 
           | Nonrecursive -> env
           | Recursive -> env
              (* --todo: add better support for local polymorphic recursion
              List.fold_left (fun (pat,bod) acc -> Ident.add (pattern_ident pat) 0 acc) env pat_expr_list *)
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           | Default -> unsupported loc "Default recursion mode"
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           in
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        let ncs = List.map (fun (pat,bod) -> (pattern_name_protect_infix pat, cfg_func env' fvs pat bod)) pat_expr_list in
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        let cf_body = cfg_exp env' body in 
        add_used_label (fst (List.hd ncs));
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        Cf_fun (ncs, cf_body)
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        (* --todo: check what happens with recursive types *)

      (* let-binding of a single value *)
      end else begin 
        if (List.length pat_expr_list <> 1) then not_normal();
        let (pat,bod) = List.hd pat_expr_list in
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        let x = pattern_name_protect_infix pat in
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        let fvs_typ, typ = lift_typ_sch pat.pat_type in
        let fvs = List.map name_of_type fvs in
        let fvs_strict = list_intersect fvs fvs_typ in
        let fvs_others = list_minus fvs fvs_strict in
            
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        (* deprecated: pure-mode let-binding
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        if !pure_mode then begin 
       
           let cf1 = cfg_exp env bod in
           let env' = Ident.add (pattern_ident pat) (List.length fvs_strict) env in
           let cf2 = cfg_exp env' body in
           add_used_label x;
           Cf_letpure (x, fvs_strict, fvs_others, typ, cf1, cf2)
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         end else *)
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        (* value let-binding *)
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        if Typecore.is_nonexpansive bod then begin 
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           let v = 
             try lift_val env bod  
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             with Not_in_normal_form (loc2, s) -> 
                raise (Not_in_normal_form (loc2, s ^ " (only value can satisfy the value restriction)"))
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             in
           let env' = Ident.add (pattern_ident pat) (List.length fvs_strict) env in
           let cf = cfg_exp env' body in
           add_used_label x;
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           Cf_val (x, fvs_strict, fvs_others, typ, v, cf)
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        (* term let-binding *)
        end else begin
            
           if fvs_strict <> [] || fvs_others <> [] 
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               then unsupported loc "relaxed value restriction";
               (* not_in_normal_form loc ("(un value restriction) "
                                        ^ (Print_tast.string_of_expression false e));*)
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           let cf1 = cfg_exp env bod in
           let env' = Ident.add (pattern_ident pat) (List.length fvs_strict) env in
           let cf2 = cfg_exp env' body in
           add_used_label x;
           Cf_let ((x,typ), cf1, cf2)

        end
      end

   | Texp_ifthenelse (cond, ifso, Some ifnot) ->
      (* old: Cf_caseif (aux cond, aux ifso, aux ifnot) *)
      Cf_caseif (lift cond, aux ifso, aux ifnot) 

   | Texp_apply (funct, oargs) ->
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      let args = simplify_apply_args loc oargs in
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      let tr = coq_typ e in
      let ts = List.map coq_typ args in
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      Cf_app (ts, tr, lift funct, List.map lift args) 
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   | Texp_match (arg, pat_expr_list, partial) ->
      let tested = lift arg in
      let conclu = match partial with Partial -> Cf_fail | Total -> Cf_done in
      let cfg_case (pat,body) acc =
         let whenopt, cfbody =  
            match body.exp_desc with 
            | Texp_when (econd, ebody) ->
                let w = 
                   try lift_val env econd  
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                   with Not_in_normal_form (loc2, s) -> 
                      raise (Not_in_normal_form (loc2, s ^ " (Only total expressions are allowed in when clauses)"))
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                   in
                Some w, aux ebody
            | _ -> None, aux body
            in
         Cf_case (tested, pattern_variables pat, lift_pat pat, whenopt, pattern_aliases pat, cfbody, acc) in
      let label = get_next_local_label() in
      add_used_label label;
      Cf_match (label, List.length pat_expr_list, List.fold_right cfg_case pat_expr_list conclu)

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   | Texp_assert e -> 
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      Cf_assert (aux e)

   | Texp_assertfalse -> 
      Cf_fail

   | Texp_lazy e -> 
      aux e

   | Texp_sequence(expr1, expr2) -> 
      Cf_seq (aux expr1, aux expr2)

   | Texp_while(cond, body) -> 
      Cf_while (aux cond, aux body)

   | Texp_for(param, low, high, dir, body) -> 
      begin match dir with 
        | Upto -> Cf_for (Ident.name param, lift low, lift high, aux body)
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        | Downto -> unsupported loc "for-downto expressions" (* later *)
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      end

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   | Texp_array args -> 
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      let arg = coq_list (List.map lift args) in
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      let targ = (* ['a], obtained by extraction from ['a array]. *) 
         match btyp_of_typ_exp e.exp_type with
         | Btyp_constr (id,[t]) when Path.name id = "array" -> lift_btyp t
         | _ -> failwith "Texp_array should always have type ['a array]"
         in
      let ts = coq_apps (Coq_var "Coq.Init.Datatypes.list") [targ] in
      let tr = coq_typ e in (* 'a array *)
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      let func = Coq_var "STDLIB.Array_ml.make_empty" in 
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      Cf_app ([ts], tr, func, [arg])
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   | Texp_field (arg, p, lbl) -> 
      let tr = coq_typ e in 
      let ts = coq_typ arg in (* todo: check it is always 'loc' *)
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      let func = Coq_var "CFML.CFApp.record_get" in
      let field = Coq_var (record_field_name lbl.lbl_name) in
      Cf_app ([ts; coq_nat], tr, func, [lift arg; field]) 
      (* DEPRECATED
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      let func = Coq_var (record_field_get_name lbl.lbl_name) in
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      Cf_app ([ts], tr, func, [lift arg]) 
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      *)
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   | Texp_setfield(arg, p, lbl, newval) -> 
      let ts1 = coq_typ arg in (* todo: check it is always 'loc' *)
      let ts2 = coq_typ newval in 
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      let func = Coq_var "CFML.CFApp.record_set" in
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      let field = Coq_var (record_field_name lbl.lbl_name) in
      Cf_app ([ts1; coq_nat; ts2], coq_unit, func, [lift arg; field; lift newval]) 
      (* DEPRECATED
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      let func = Coq_var (record_field_set_name lbl.lbl_name) in
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      Cf_app ([ts1;ts2], coq_unit, func, [lift arg; lift newval])
      *)
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   | Texp_try(body, pat_expr_list) -> unsupported loc "try expression"
   | Texp_variant(l, arg) ->  unsupported loc "variant expression"
   | Texp_ifthenelse(cond, ifso, None) -> unsupported loc "if-then-without-else expressions should have been normalized"
   | Texp_when(cond, body) -> unsupported loc "when expressions outside of pattern matching"
   | Texp_send(_, _, _) -> unsupported loc "send expressions"
   | Texp_new (cl, _) -> unsupported loc "new expressions"
   | Texp_instvar(path_self, path) -> unsupported loc "inst-var expressions"
   | Texp_setinstvar(path_self, path, expr) -> unsupported loc "set-inst-var expressions"
   | Texp_override(path_self, modifs) -> unsupported loc "override expressions"
   | Texp_letmodule(id, modl, body) -> unsupported loc "let-module expressions"
   | Texp_object _ -> unsupported loc "object expressions"
   | Texp_poly (_,_) -> unsupported loc "poly"
   | Texp_newtype (_,_) -> unsupported loc "newtype"
   | Texp_pack _ -> unsupported loc "pack"
   | Texp_open (_,_) -> unsupported loc "open in term"
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   | Texp_constraint (e, Some ty, None) -> aux e
      (* LATER: see if it is needed
      let typ = lift_typ_exp ty.ctyp_type in
      CF_annot (aux e, typ)
      *)
   | Texp_constraint (e, _, _) -> unsupported loc "advanced type constraint"

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and cfg_func env fvs pat bod =
   let rec get_typed_args acc e =
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      let loc = e.exp_loc in
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      match e.exp_desc with
      | Texp_function (_,[p1,e1],partial) 
      | Texp_constraint ({exp_desc = Texp_function (_,[p1,e1],partial)},_,_) ->
         if partial <> Total 
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            then not_in_normal_form loc (Print_tast.string_of_expression false e);
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         get_typed_args ((pattern_name p1, coq_typ_pat p1)::acc) e1
      | _ -> List.rev acc, e
      in  
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   let f = pattern_name_protect_infix pat in
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   let targs, body = get_typed_args [] bod in
   let typ = coq_typ body in
   let cf_body = cfg_exp env body in
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   let cf_body = if !Mytools.use_credits then Cf_pay cf_body else cf_body in
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   let fvs = List.map name_of_type fvs in
   Cf_body (f, fvs, targs, typ, cf_body) 
   (* --todo: check if the set of type variables quantified is not too
      conservative. Indeed, some type variables may no longer occur. *)


(*#########################################################################*)
(* ** Characteristic formulae for modules *)

(** Helper functions to find out the kind of a type declaration *)

let is_algebraic (name,dec) =
   match dec.typ_type.type_kind with Type_variant _ -> true | _ -> false 

let is_type_abbrev (name,dec) =
   match dec.typ_type.type_kind with Type_abstract -> true | _ -> false 

let is_type_record (name,dec) =
   match dec.typ_type.type_kind with Type_record _ -> true | _ -> false 

(** Generate the top-level Coq declarations associated with 
    a top-level declaration from a module. *)

let rec cfg_structure_item s : cftops = 
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  let loc = s.str_loc in
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  match s.str_desc with
  | Tstr_value(rf, fvs, pat_expr_list) ->
      reset_local_labels();

      (* --todo: improve code sharing between local bindings and top-level bindings *)
      let is_let_fun (pat,exp) = 
         match exp.exp_desc with 
         | Texp_function (_,_,_) -> true
         | Texp_constraint({exp_desc = Texp_function (_,_,_)},_,_) -> true
         | _ -> false in

      if List.for_all is_let_fun pat_expr_list then begin
        let env' = match rf with 
           | Nonrecursive -> Ident.empty
           | Recursive -> Ident.empty
               (* --todo: better support for polymorphic recursion
              List.fold_left (fun (pat,bod) acc -> Ident.add (pattern_ident pat) 0 acc) env pat_expr_list *)
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           | Default -> unsupported loc "Default recursion mode"
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           in
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        let ncs = List.map (fun (pat,bod) -> (pattern_name_protect_infix pat, cfg_func env' fvs pat bod)) pat_expr_list in
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          (List.map (fun (name,_) -> Cftop_val (name, val_type)) ncs)
        @ (List.map (fun (name,cf_body) -> Cftop_fun_cf (name, cf_body)) ncs)
        @ [Cftop_coqs (List.map (fun (name,_) -> register_cf name) ncs)]
   
      (* let-binding of a single value *)
      end else if (List.length pat_expr_list = 1) then begin (* later: check it is not a function *)
        let (pat,bod) = List.hd pat_expr_list in
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        let x = pattern_name_protect_infix pat in
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        (* DEPRECATED if (hack_recognize_okasaki_lazy x) then [] else *)
        begin
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        let fvs_typ, typ = lift_typ_sch pat.pat_type in
        let fvs = List.map name_of_type fvs in
        let fvs_strict = list_intersect fvs fvs_typ in
        let fvs_others = list_minus fvs fvs_strict in
        
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        (* deprecated: pure-mode let-binding 
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        if !pure_mode then begin 

           let cf_body = cfg_exp (Ident.empty) bod in
           let implicits = 
              match fvs_strict with
              | [] -> []
              | _ ->  [ Coqtop_implicit (x, List.map (fun t -> (t,Coqi_maximal)) fvs_strict) ]
              in
           [ Cftop_val (x, coq_forall_types fvs_strict typ);
             Cftop_coqs implicits;
             Cftop_pure_cf (x, fvs_strict, fvs_others, cf_body); 
             Cftop_coqs [register_cf x]; ] 
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        end else*)
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        (* value let-binding *)
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        if Typecore.is_nonexpansive bod then begin 
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           let v = 
             try lift_val (Ident.empty) bod  
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             with Not_in_normal_form (loc2, s) -> 
                (* TODO: here and elsewhere, use a wrapper for extending the errors *)
                raise (Not_in_normal_form (loc2, s ^ " (only value can satisfy the value restriction)"))
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            in
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           let v_typed = coq_annot v typ in
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           let implicits = 
              match fvs_strict with
              | [] -> []
              | _ ->  [ Coqtop_implicit (x, List.map (fun t -> (t,Coqi_maximal)) fvs_strict) ]
              in
           [ Cftop_val (x, coq_forall_types fvs_strict typ);
             Cftop_coqs implicits;
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             Cftop_val_cf (x, fvs_strict, fvs_others, v_typed); 
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             Cftop_coqs [register_cf x]; ] 

        (* term let-binding -- later *)
        end else begin
            
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           unsupported loc "top-level binding of terms that are not values";
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           (* if fvs_strict <> [] || fvs_others <> [] 
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               then not_in_normal_form loc ("(unsatisfied value restriction) "
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                                        ^ (Print_tast.string_of_expression false e));
           let cf1 = cfg_exp env bod in
           let env' = Ident.add (pattern_ident pat) (List.length fvs_strict) env in
           let cf2 = cfg_exp env' body in
           add_used_label x;
           Cf_let ((x,typ), cf1, cf2) *)

        end

      end (* for skip_cf *)

     end else
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        unsupported loc ("mutually-recursive values that are not all functions");
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  | Tstr_type(decls) -> [ Cftop_coqs (cfg_type_decls decls) ]

  | Tstr_module(id, modl) -> cfg_module id modl 

  | Tstr_modtype(id, decl) -> cfg_modtype id decl

  | Tstr_open path -> 
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      (* TEMPORARILY DEPRECATED if is_primitive_module (Path.name path) then [] else *)
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      [ Cftop_coqs [ Coqtop_require_import [ lift_full_path_name path ] ] ]
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  | Tstr_primitive(id, descr) ->
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      let id = protect_infix (Ident.name id) in
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      let fvs, typ = lift_typ_sch descr.val_desc.ctyp_type in
      let typ = coq_fun_types fvs typ in
      [ Cftop_val (id, typ) ]

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  | Tstr_exception(id, decl) ->
      [] (* unsupported "exceptions" *)
  | Tstr_exn_rebind(id, path) -> 
      [] (* unsupported "exceptions" *)

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  | Tstr_recmodule bindings -> unsupported loc "recursive modules"
  | Tstr_class _ -> unsupported loc "objects"
  | Tstr_class_type _ -> unsupported loc "objects"
  | Tstr_include (m,ids) -> unsupported loc "module-include"
  | Tstr_eval expr -> unsupported loc "top level eval expression (let _)"
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(** Generate the top-level Coq declarations associated with 
    a type abbreviation. *)

and cfg_type_abbrev (name,dec) =
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   let x = type_constr_name (Ident.name name) in
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   let args = List.map name_of_type dec.typ_type.type_params in
   let sort = coq_impl_types (List.length args) in
   let coqs = match dec.typ_type.type_manifest with
      | None -> [Coqtop_param (x, sort)]
      | Some t -> [Coqtop_def ((x, sort), coq_fun_types args (lift_typ_exp t));
                   Coqtop_hint_unfold ([x],"typeclass_instances") ] in
   coqs, [] 

(** Generate the top-level Coq declarations associated with 
    a record definition. *)

and cfg_type_record (name,dec) =
   let x = Ident.name name in
   let name_of_field lbl = 
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      record_field_name lbl in
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   let fields = match dec.typ_type.type_kind with Type_record (l,_) -> l | _ -> assert false in
   (* let fields_base_names = List.map (fun (lbl,_,_) -> lbl) fields in *)
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