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diff --git a/frontend/abstract_syntax_printer.ml b/frontend/abstract_syntax_printer.ml
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+(*
+  Cours "Sémantique et Application à la Vérification de programmes"
+  
+  Antoine Miné 2014
+  Ecole normale supérieure, Paris, France / CNRS / INRIA
+*)
+
+(* 
+  Pretty-printer for abstract syntax trees.
+*)
+
+open Abstract_syntax_tree
+open Lexing
+
+
+(* locations *)
+(* ********* *)
+
+let string_of_position p =
+  Printf.sprintf "%s:%i:%i" p.pos_fname p.pos_lnum (p.pos_cnum - p.pos_bol)
+    
+let string_of_extent (p,q) =
+  if p.pos_fname = q.pos_fname then
+    if p.pos_lnum = q.pos_lnum then
+      if p.pos_cnum = q.pos_cnum then
+        Printf.sprintf "%s:%i.%i" p.pos_fname p.pos_lnum (p.pos_cnum - p.pos_bol)
+      else
+        Printf.sprintf "%s:%i.%i-%i" p.pos_fname p.pos_lnum (p.pos_cnum - p.pos_bol) (q.pos_cnum - q.pos_bol)
+    else
+      Printf.sprintf "%s:%i.%i-%i.%i" p.pos_fname p.pos_lnum (p.pos_cnum - p.pos_bol) q.pos_lnum (q.pos_cnum - q.pos_bol)
+  else
+    Printf.sprintf "%s:%i.%i-%s:%i.%i" p.pos_fname p.pos_lnum (p.pos_cnum - p.pos_bol) q.pos_fname q.pos_lnum (q.pos_cnum - q.pos_bol)
+
+
+
+(* operators *)
+(* ********* *)
+
+let string_of_unary_op = function
+  | AST_UNARY_PLUS -> "+"
+  | AST_UNARY_MINUS -> "-"
+  | AST_NOT -> "!"
+
+let string_of_binary_op = function
+  | AST_MULTIPLY -> "*"
+  | AST_DIVIDE -> "/"
+  | AST_MODULO -> "%"
+  | AST_PLUS -> "+"
+  | AST_MINUS -> "-"
+  | AST_EQUAL -> "=="
+  | AST_NOT_EQUAL -> "!="
+  | AST_LESS -> "<"
+  | AST_LESS_EQUAL -> "<="
+  | AST_GREATER -> ">"
+  | AST_GREATER_EQUAL -> ">="
+  | AST_AND -> "&&"
+  | AST_OR -> "||"
+
+
+
+(* higher values mean higher precedence *)
+let binary_precedence = function
+  | AST_MULTIPLY | AST_DIVIDE | AST_MODULO -> 6
+  | AST_PLUS  | AST_MINUS -> 5
+  | AST_EQUAL | AST_NOT_EQUAL -> 4
+  | AST_LESS | AST_LESS_EQUAL | AST_GREATER | AST_GREATER_EQUAL -> 3
+  | AST_AND -> 2
+  | AST_OR -> 1
+
+(* precedence of the operator at the root of the expression;
+   this is used to avoid printing unnecessary parentheses
+ *)
+let expr_precedence = function
+  | AST_unary (op, _) -> 99
+  | AST_binary(op, _, _) -> binary_precedence op
+  | _ -> 100
+
+
+(* utility to print lists *)
+let print_list f sep fmt l =
+  let rec aux = function
+    | [] -> ()
+    | [a] -> f fmt a
+    | a::b -> f fmt a; Format.pp_print_string fmt sep; aux b
+  in
+  aux l
+
+
+(* types *)
+(* ***** *)
+
+let string_of_typ = function
+  | AST_TYP_INT -> "int"
+  | AST_TYP_BOOL -> "bool"
+  | AST_TYP_AUTO -> "auto"
+
+
+(* expressions *)
+(* *********** *)
+
+let print_id fmt v =
+  Format.pp_print_string fmt v
+
+let rec print_expr fmt e = 
+  match e with
+    
+  | AST_unary (op,(e1,_)) ->
+      Format.pp_print_string fmt (string_of_unary_op op);
+      if expr_precedence e1 <= expr_precedence e
+      then Format.fprintf fmt " (%a)" print_expr e1
+      else Format.fprintf fmt " %a" print_expr e1
+
+  | AST_binary (op,(e1,_),(e2,_)) ->
+      if expr_precedence e1 < expr_precedence e
+      then Format.fprintf fmt "(%a) " print_expr e1
+      else Format.fprintf fmt "%a " print_expr e1;
+      Format.pp_print_string fmt (string_of_binary_op op);
+      if expr_precedence e2 <= expr_precedence e
+      then Format.fprintf fmt " (%a)" print_expr e2
+      else Format.fprintf fmt " %a" print_expr e2
+          
+  | AST_int_const (i,_) -> Format.pp_print_string fmt i
+
+  | AST_int_rand ((i1,_),(i2,_)) -> Format.fprintf fmt "rand(%s, %s)" i1 i2
+
+  | AST_bool_const b -> Format.pp_print_bool fmt b
+        
+  | AST_identifier (v,_) -> print_id fmt v
+
+  | AST_expr_call ((i,_),l) ->
+      Format.fprintf fmt "%a(%a)"
+        print_id i (print_list print_expr ",") (List.map fst l)
+
+let print_lvalue fmt v =
+  Format.pp_print_string fmt v
+
+
+
+(* statements *)
+(* ********** *)
+
+let indent ind = ind^"  "
+
+(* ind is a string of spaces (indentation) to put at the begining of each line
+ *)
+let rec print_stat ind fmt = function
+
+  | AST_block b ->
+      print_block ind fmt b
+
+  | AST_assign ((v,_),(e,_)) ->
+      Format.fprintf fmt "%s%a = %a;@\n" 
+        ind print_lvalue v print_expr e
+
+  | AST_if ((e,_), (b1,_), None) ->
+      Format.fprintf fmt "%sif (%a)@\n%a" 
+        ind print_expr e (print_stat (indent ind)) b1
+
+  | AST_if ((e,_), (b1,_), Some (b2,_)) ->
+      Format.fprintf fmt "%sif (%a)@\n%a%selse@\n%a" 
+        ind print_expr e (print_stat (indent ind)) b1
+        ind (print_stat (indent ind)) b2
+
+  | AST_while ((e,_),(b,_)) ->
+      Format.fprintf fmt "%swhile (%a)@\n%a" 
+        ind print_expr e (print_stat (indent ind)) b
+
+  | AST_assert ((e,_)) ->
+      Format.fprintf fmt "%sassert (%a);@\n" 
+        ind print_expr e 
+
+  | AST_print l ->
+      Format.fprintf fmt "%sprint (%a);@\n" 
+        ind (print_list print_id ",") (List.map fst l)
+
+  | AST_local d ->
+      Format.fprintf fmt "%s%a" ind print_var_decl d
+
+  | AST_stat_call ((i,_),l) ->
+      Format.fprintf fmt "%s%a(%a);@\n"
+        ind print_id i (print_list print_expr ",") (List.map fst l)
+ 
+  | AST_return None ->
+      Format.fprintf fmt "%sreturn;@\n" ind
+
+  | AST_return (Some (e,_)) ->
+      Format.fprintf fmt "%sreturn %a;@\n" 
+        ind print_expr e
+
+  | AST_BREAK ->
+      Format.fprintf fmt "%sbreak;@\n" ind
+
+  | AST_HALT ->
+      Format.fprintf fmt "%shalt;@\n" ind
+
+  | AST_label (l,_) ->
+      Format.fprintf fmt "%s%a:@\n" ind print_id l
+
+  | AST_goto (l,_) ->
+      Format.fprintf fmt "%sgoto %a;@\n" ind print_id l
+
+and print_block ind fmt b =
+  Format.fprintf fmt "%s{@\n" ind;
+  List.iter (fun (bb,_) -> print_stat (indent ind) fmt bb) b;
+  Format.fprintf fmt "%s}@\n" ind
+
+
+
+(* declarations *)
+(* ************ *)
+
+and print_var_decl fmt ((t,_),l) =
+  Format.fprintf fmt "%s %a;@\n" 
+    (string_of_typ t) (print_list print_var_init ", ") l
+
+and print_var_init fmt ((i,_),eo) =
+  print_id fmt i;
+  match eo with
+  | None -> ()
+  | Some (e,_) -> Format.fprintf fmt " = %a" print_expr e
+
+let print_arg_decl fmt ((t,_),(i,_)) =
+  Format.fprintf fmt "%s %a"
+    (string_of_typ t) print_id i
+
+let print_fun_decl fmt f =
+  Format.fprintf fmt "%s %a(%a)@\n%a"
+    (match fst (f.fun_typ) with None -> "void" | Some t -> string_of_typ t)
+    print_id (fst f.fun_name)
+    (print_list print_arg_decl  ", ") f.fun_args
+    (print_block "") f.fun_body
+
+let print_toplevel fmt = function
+  | AST_stat (s,_) -> print_stat "" fmt s
+  | AST_fun_decl (f,_) -> print_fun_decl fmt f
+
+
+(* programs *)
+(* ******** *)
+
+let print_prog fmt (p,_) =
+  List.iter (print_toplevel fmt) p