lustrec / src / tools / zustre / zustre_common.ml @ 58301109
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open Lustre_types 

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open Machine_code_types 
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open Machine_code_common 
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open Format 
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(* open Horn_backend_common 
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* open Horn_backend *) 
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open Zustre_data 
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module HBC = Horn_backend_common 
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let node_name = HBC.node_name 
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let concat = HBC.concat 
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let rename_machine = HBC.rename_machine 
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let rename_machine_list = HBC.rename_machine_list 
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let rename_next = HBC.rename_next 
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let rename_mid = HBC.rename_mid 
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let rename_current = HBC.rename_current 
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let rename_current_list = HBC.rename_current_list 
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let rename_mid_list = HBC.rename_mid_list 
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let rename_next_list = HBC.rename_next_list 
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let full_memory_vars = HBC.full_memory_vars 
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let inout_vars = HBC.inout_vars 
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let reset_vars = HBC.reset_vars 
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let step_vars = HBC.step_vars 
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let local_memory_vars = HBC.local_memory_vars 
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let step_vars_m_x = HBC.step_vars_m_x 
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let step_vars_c_m_x = HBC.step_vars_c_m_x 
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let machine_reset_name = HBC.machine_reset_name 
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let machine_step_name = HBC.machine_step_name 
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let machine_stateless_name = HBC.machine_stateless_name 
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let preprocess = Horn_backend.preprocess 
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exception UnknownFunction of (string * (Format.formatter > unit)) 
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(** Sorts 
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A sort is introduced for each basic type and each enumerated type. 
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A hashtbl records these and allow easy access to sort values, when 
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provided with a enumerated type name. 
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*) 
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let bool_sort = Z3.Boolean.mk_sort !ctx 
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let int_sort = Z3.Arithmetic.Integer.mk_sort !ctx 
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let real_sort = Z3.Arithmetic.Real.mk_sort !ctx 
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let get_const_sort = Hashtbl.find const_sorts 
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let get_sort_elems = Hashtbl.find sort_elems 
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let get_tag_sort = Hashtbl.find const_tags 
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let decl_sorts () = 
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Hashtbl.iter (fun typ decl > 
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match typ with 
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 Tydec_const var > 
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(match decl.top_decl_desc with 
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 TypeDef tdef > ( 
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match tdef.tydef_desc with 
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 Tydec_enum tl > 
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let new_sort = Z3.Enumeration.mk_sort_s !ctx var tl in 
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Hashtbl.add const_sorts var new_sort; 
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Hashtbl.add sort_elems new_sort tl; 
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List.iter (fun t > Hashtbl.add const_tags t new_sort) tl 
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 _ > Format.eprintf "Unknown type : %a@.@?" Printers.pp_var_type_dec_desc typ; assert false 
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) 
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 _ > assert false 
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) 
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 _ > ()) Corelang.type_table 
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let rec type_to_sort t = 
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if Types.is_bool_type t then bool_sort else 
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if Types.is_int_type t then int_sort else 
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if Types.is_real_type t then real_sort else 
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match (Types.repr t).Types.tdesc with 
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 Types.Tconst ty > get_const_sort ty 
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 Types.Tclock t > type_to_sort t 
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 Types.Tarray(dim,ty) > Z3.Z3Array.mk_sort !ctx int_sort (type_to_sort ty) 
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 Types.Tstatic(d, ty)> type_to_sort ty 
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 Types.Tarrow _ 
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 _ > Format.eprintf "internal error: pp_type %a@." 
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Types.print_ty t; assert false 
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(* let idx_var = *) 
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(* Z3.FuncDecl.mk_func_decl_s !ctx "__idx__" [] idx_sort *) 
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(* let uid_var = *) 
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(* Z3.FuncDecl.mk_func_decl_s !ctx "__uid__" [] uid_sort *) 
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(** Func decls 
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Similarly fun_decls are registerd, by their name, into a hashtbl. The 
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proposed encoding introduces a 0ary fun_decl to model variables and 
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fun_decl with arguments to declare reset and step predicates. 
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*) 
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let register_fdecl id fd = Hashtbl.add decls id fd 
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let get_fdecl id = 
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try 
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Hashtbl.find decls id 
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with Not_found > (Format.eprintf "Unable to find func_decl %s@.@?" id; raise Not_found) 
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let pp_fdecls fmt = 
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Format.fprintf fmt "Registered fdecls: @[%a@]@ " 
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(Utils.fprintf_list ~sep:"@ " Format.pp_print_string) (Hashtbl.fold (fun id _ accu > id::accu) decls []) 
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let decl_var id = 
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(* Format.eprintf "Declaring var %s@." id.var_id; *) 
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let fdecl = Z3.FuncDecl.mk_func_decl_s !ctx id.var_id [] (type_to_sort id.var_type) in 
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register_fdecl id.var_id fdecl; 
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fdecl 
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let idx_sort = int_sort 
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let uid_sort = Z3.Z3List.mk_sort !ctx (Z3.Symbol.mk_string !ctx "uid_list") int_sort 
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let uid_conc = 
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let fd = Z3.Z3List.get_cons_decl uid_sort in 
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fun head tail > Z3.FuncDecl.apply fd [head;tail] 
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let get_instance_uid = 
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let hash : (string, int) Hashtbl.t = Hashtbl.create 13 in 
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let cpt = ref 0 in 
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fun i > 
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let id = 
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if Hashtbl.mem hash i then 
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Hashtbl.find hash i 
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else ( 
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incr cpt; 
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Hashtbl.add hash i !cpt; 
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!cpt 
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) 
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in 
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Z3.Arithmetic.Integer.mk_numeral_i !ctx id 
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let decl_rel ?(no_additional_vars=false) name args_sorts = 
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(* Enriching arg_sorts with two new variables: a counting index and an 
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uid *) 
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let args_sorts = 
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if no_additional_vars then args_sorts else idx_sort::uid_sort::args_sorts in 
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(* let args_sorts = List.map (fun v > type_to_sort v.var_type) args in *) 
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if !debug then 
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Format.eprintf "Registering fdecl %s (%a)@." 
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name 
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(Utils.fprintf_list ~sep:"@ " 
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(fun fmt sort > Format.fprintf fmt "%s" (Z3.Sort.to_string sort))) 
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args_sorts 
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; 
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let fdecl = Z3.FuncDecl.mk_func_decl_s !ctx name args_sorts bool_sort in 
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Z3.Fixedpoint.register_relation !fp fdecl; 
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register_fdecl name fdecl; 
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fdecl 
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(* Shared variables to describe counter and uid *) 
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let idx = Corelang.dummy_var_decl "__idx__" Type_predef.type_int 
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let idx_var = Z3.Expr.mk_const_f !ctx (decl_var idx) 
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let uid = Corelang.dummy_var_decl "__uid__" Type_predef.type_int 
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let uid_fd = Z3.FuncDecl.mk_func_decl_s !ctx "__uid__" [] uid_sort 
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let _ = register_fdecl "__uid__" uid_fd 
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let uid_var = Z3.Expr.mk_const_f !ctx uid_fd 
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(** Conversion functions 
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The following is similar to the Horn backend. Each printing function is 
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rephrased from pp_xx to xx_to_expr and produces a Z3 value. 
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*) 
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(* Returns the f_decl associated to the variable v *) 
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let horn_var_to_expr v = 
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Z3.Expr.mk_const_f !ctx (get_fdecl v.var_id) 
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(* Used to print boolean constants *) 
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let horn_tag_to_expr t = 
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if t = Corelang.tag_true then 
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Z3.Boolean.mk_true !ctx 
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else if t = Corelang.tag_false then 
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Z3.Boolean.mk_false !ctx 
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else 
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(* Finding the associated sort *) 
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let sort = get_tag_sort t in 
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let elems = get_sort_elems sort in 
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let res : Z3.Expr.expr option = 
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List.fold_left2 (fun res cst expr > 
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match res with 
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 Some _ > res 
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 None > if t = cst then Some (expr:Z3.Expr.expr) else None 
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) None elems (Z3.Enumeration.get_consts sort) 
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in 
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match res with None > assert false  Some s > s 
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(* Prints a constant value *) 
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let rec horn_const_to_expr c = 
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match c with 
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 Const_int i > Z3.Arithmetic.Integer.mk_numeral_i !ctx i 
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 Const_real (_,_,s) > Z3.Arithmetic.Real.mk_numeral_s !ctx s 
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 Const_tag t > horn_tag_to_expr t 
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 _ > assert false 
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(* Default value for each type, used when building arrays. Eg integer array 
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[2;7] is defined as (store (store (0) 1 7) 0 2) where 0 is this default value 
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for the type integer (arrays). 
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*) 
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let rec horn_default_val t = 
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let t = Types.dynamic_type t in 
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if Types.is_bool_type t then Z3.Boolean.mk_true !ctx else 
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if Types.is_int_type t then Z3.Arithmetic.Integer.mk_numeral_i !ctx 0 else 
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if Types.is_real_type t then Z3.Arithmetic.Real.mk_numeral_i !ctx 0 else 
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(* match (Types.dynamic_type t).Types.tdesc with 
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*  Types.Tarray(dim, l) > (\* TODO PL: this strange code has to be (heavily) checked *\) 
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* let valt = Types.array_element_type t in 
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* fprintf fmt "((as const (Array Int %a)) %a)" 
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* pp_type valt 
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* pp_default_val valt 
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*  Types.Tstruct(l) > assert false 
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*  Types.Ttuple(l) > assert false 
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* _ > *) assert false 
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(* Conversion of basic library functions *) 
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let horn_basic_app i val_to_expr vl = 
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match i, vl with 
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 "ite", [v1; v2; v3] > 
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Z3.Boolean.mk_ite 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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(val_to_expr v3) 
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 "uminus", [v] > 
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Z3.Arithmetic.mk_unary_minus 
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!ctx 
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(val_to_expr v) 
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 "not", [v] > 
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Z3.Boolean.mk_not 
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!ctx 
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(val_to_expr v) 
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 "=", [v1; v2] > 
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Z3.Boolean.mk_eq 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 "&&", [v1; v2] > 
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Z3.Boolean.mk_and 
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!ctx 
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[val_to_expr v1; 
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val_to_expr v2] 
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 "", [v1; v2] > 
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Z3.Boolean.mk_or 
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!ctx 
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[val_to_expr v1; 
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val_to_expr v2] 
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 "impl", [v1; v2] > 
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Z3.Boolean.mk_implies 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 "mod", [v1; v2] > 
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Z3.Arithmetic.Integer.mk_mod 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 "equi", [v1; v2] > 
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Z3.Boolean.mk_eq 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 "xor", [v1; v2] > 
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Z3.Boolean.mk_xor 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 "!=", [v1; v2] > 
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Z3.Boolean.mk_not 
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!ctx 
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( 
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Z3.Boolean.mk_eq 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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) 
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 "/", [v1; v2] > 
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Z3.Arithmetic.mk_div 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 "+", [v1; v2] > 
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Z3.Arithmetic.mk_add 
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!ctx 
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[val_to_expr v1; val_to_expr v2] 
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 "", [v1; v2] > 
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Z3.Arithmetic.mk_sub 
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!ctx 
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[val_to_expr v1 ; val_to_expr v2] 
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 "*", [v1; v2] > 
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Z3.Arithmetic.mk_mul 
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!ctx 
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[val_to_expr v1; val_to_expr v2] 
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 "<", [v1; v2] > 
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Z3.Arithmetic.mk_lt 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 "<=", [v1; v2] > 
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Z3.Arithmetic.mk_le 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 ">", [v1; v2] > 
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Z3.Arithmetic.mk_gt 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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 ">=", [v1; v2] > 
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Z3.Arithmetic.mk_ge 
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!ctx 
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(val_to_expr v1) 
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(val_to_expr v2) 
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(*  _, [v1; v2] > Z3.Boolean.mk_and 
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* !ctx 
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* (val_to_expr v1) 
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* (val_to_expr v2) 
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* 
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* Format.fprintf fmt "(%s %a %a)" i val_to_exprr v1 val_to_expr v2 *) 
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 _ > ( 
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let msg fmt = Format.fprintf fmt 
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"internal error: zustre unkown function %s (nb args = %i)@." 
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i (List.length vl) 
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in 
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raise (UnknownFunction(i, msg)) 
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) 
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(* Convert a value expression [v], with internal function calls only. [pp_var] 
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is a printer for variables (typically [pp_c_var_read]), but an offset suffix 
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may be added for array variables 
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*) 
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let rec horn_val_to_expr ?(is_lhs=false) m self v = 
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match v.value_desc with 
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 Cst c > horn_const_to_expr c 
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(* Code specific for arrays *) 
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 Array il > 
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(* An array definition: 
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(store ( 
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... 
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(store ( 
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store ( 
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default_val 
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) 
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idx_n val_n 
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) 
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idx_n1 val_n1) 
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... 
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idx_1 val_1 
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) *) 
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let rec build_array (tab, x) = 
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match tab with 
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 [] > horn_default_val v.value_type(* (get_type v) *) 
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 h::t > 
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Z3.Z3Array.mk_store 
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!ctx 
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(build_array (t, (x+1))) 
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(Z3.Arithmetic.Integer.mk_numeral_i !ctx x) 
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(horn_val_to_expr ~is_lhs:is_lhs m self h) 
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in 
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build_array (il, 0) 
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 Access(tab,index) > 
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Z3.Z3Array.mk_select !ctx 
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(horn_val_to_expr ~is_lhs:is_lhs m self tab) 
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(horn_val_to_expr ~is_lhs:is_lhs m self index) 
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(* Code specific for arrays *) 
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 Power (v, n) > assert false 
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 Var v > 
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if is_memory m v then 
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if Types.is_array_type v.var_type 
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then assert false 
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else horn_var_to_expr (rename_machine self ((if is_lhs then rename_next else rename_current) (* self *) v)) 
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else 
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horn_var_to_expr 
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(rename_machine 
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self 
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v) 
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 Fun (n, vl) > horn_basic_app n (horn_val_to_expr m self) vl 
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let no_reset_to_exprs machines m i = 
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let (n,_) = List.assoc i m.minstances in 
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let target_machine = List.find (fun m > m.mname.node_id = (Corelang.node_name n)) machines in 
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let m_list = 
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rename_machine_list 
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(concat m.mname.node_id i) 
433 
(rename_mid_list (full_memory_vars machines target_machine)) 
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in 
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let c_list = 
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rename_machine_list 
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(concat m.mname.node_id i) 
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(rename_current_list (full_memory_vars machines target_machine)) 
439 
in 
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match c_list, m_list with 
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 [chd], [mhd] > 
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let expr = 
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Z3.Boolean.mk_eq !ctx 
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(horn_var_to_expr mhd) 
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(horn_var_to_expr chd) 
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in 
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[expr] 
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 _ > ( 
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let exprs = 
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List.map2 (fun mhd chd > 
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Z3.Boolean.mk_eq !ctx 
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(horn_var_to_expr mhd) 
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(horn_var_to_expr chd) 
454 
) 
455 
m_list 
456 
c_list 
457 
in 
458 
exprs 
459 
) 
460  
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let instance_reset_to_exprs machines m i = 
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let (n,_) = List.assoc i m.minstances in 
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let target_machine = List.find (fun m > m.mname.node_id = (Corelang.node_name n)) machines in 
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let vars = 
465 
(rename_machine_list 
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(concat m.mname.node_id i) 
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(rename_current_list (full_memory_vars machines target_machine))@ (rename_mid_list (full_memory_vars machines target_machine)) 
468 
) 
469 

470 
in 
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let expr = 
472 
Z3.Expr.mk_app 
473 
!ctx 
474 
(get_fdecl (machine_reset_name (Corelang.node_name n))) 
475 
(List.map (horn_var_to_expr) (idx::uid::vars)) 
476 
in 
477 
[expr] 
478  
479 
let instance_call_to_exprs machines reset_instances m i inputs outputs = 
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let self = m.mname.node_id in 
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482 
(* Building call args *) 
483 
let idx_uid_inout = 
484 
(* Additional input to register step counters, and uid *) 
485 
let idx = horn_var_to_expr idx in 
486 
let uid = uid_conc (get_instance_uid i) (horn_var_to_expr uid) in 
487 
let inout = 
488 
List.map (horn_val_to_expr m self) 
489 
(inputs @ (List.map (fun v > mk_val (Var v) v.var_type) outputs)) 
490 
in 
491 
idx::uid::inout 
492 
in 
493 

494 
try (* stateful node instance *) 
495 
begin 
496 
let (n,_) = List.assoc i m.minstances in 
497 
let target_machine = List.find (fun m > m.mname.node_id = Corelang.node_name n) machines in 
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499 
(* Checking whether this specific instances has been reset yet *) 
500 
let reset_exprs = 
501 
if not (List.mem i reset_instances) then 
502 
(* If not, declare mem_m = mem_c *) 
503 
no_reset_to_exprs machines m i 
504 
else 
505 
[] (* Nothing to add yet *) 
506 
in 
507 

508 
let mems = full_memory_vars machines target_machine in 
509 
let rename_mems f = rename_machine_list (concat m.mname.node_id i) (f mems) in 
510 
let mid_mems = rename_mems rename_mid_list in 
511 
let next_mems = rename_mems rename_next_list in 
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513 
let call_expr = 
514 
match Corelang.node_name n, inputs, outputs, mid_mems, next_mems with 
515 
 "_arrow", [i1; i2], [o], [mem_m], [mem_x] > begin 
516 
let stmt1 = (* out = ite mem_m then i1 else i2 *) 
517 
Z3.Boolean.mk_eq !ctx 
518 
( (* output var *) 
519 
horn_val_to_expr 
520 
~is_lhs:true 
521 
m self 
522 
(mk_val (Var o) o.var_type) 
523 
) 
524 
( 
525 
Z3.Boolean.mk_ite !ctx 
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(horn_var_to_expr mem_m) 
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(horn_val_to_expr m self i1) 
528 
(horn_val_to_expr m self i2) 
529 
) 
530 
in 
531 
let stmt2 = (* mem_X = false *) 
532 
Z3.Boolean.mk_eq !ctx 
533 
(horn_var_to_expr mem_x) 
534 
(Z3.Boolean.mk_false !ctx) 
535 
in 
536 
[stmt1; stmt2] 
537 
end 
538  
539 
 node_name_n > 
540 
let expr = 
541 
Z3.Expr.mk_app 
542 
!ctx 
543 
(get_fdecl (machine_step_name (node_name n))) 
544 
( (* Arguments are input, output, mid_mems, next_mems *) 
545 
idx_uid_inout @ List.map (horn_var_to_expr) (mid_mems@next_mems) 
546 

547 
) 
548 
in 
549 
[expr] 
550 
in 
551  
552 
reset_exprs@call_expr 
553 
end 
554 
with Not_found > ( (* stateless node instance *) 
555 
let (n,_) = List.assoc i m.mcalls in 
556 
let expr = 
557 
Z3.Expr.mk_app 
558 
!ctx 
559 
(get_fdecl (machine_stateless_name (node_name n))) 
560 
idx_uid_inout (* Arguments are inputs, outputs *) 
561 
in 
562 
[expr] 
563 
) 
564  
565  
566 

567 
(* (\* Prints a [value] indexed by the suffix list [loop_vars] *\) *) 
568 
(* let rec value_suffix_to_expr self value = *) 
569 
(* match value.value_desc with *) 
570 
(*  Fun (n, vl) > *) 
571 
(* horn_basic_app n (horn_val_to_expr self) (value_suffix_to_expr self vl) *) 
572 

573 
(*  _ > *) 
574 
(* horn_val_to_expr self value *) 
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576  
577 
(* type_directed assignment: array vs. statically sized type 
578 
 [var_type]: type of variable to be assigned 
579 
 [var_name]: name of variable to be assigned 
580 
 [value]: assigned value 
581 
 [pp_var]: printer for variables 
582 
*) 
583 
let assign_to_exprs m var_name value = 
584 
let self = m.mname.node_id in 
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let e = 
586 
Z3.Boolean.mk_eq 
587 
!ctx 
588 
(horn_val_to_expr ~is_lhs:true m self var_name) 
589 
(horn_val_to_expr m self value) 
590 
(* was: TODO deal with array accesses (value_suffix_to_expr self value) *) 
591 
in 
592 
[e] 
593  
594 

595 
(* Convert instruction to Z3.Expr and update the set of reset instances *) 
596 
let rec instr_to_exprs machines reset_instances (m: machine_t) instr : Z3.Expr.expr list * ident list = 
597 
match Corelang.get_instr_desc instr with 
598 
 MComment _ > [], reset_instances 
599 
 MNoReset i > (* we assign middle_mem with mem_m. And declare i as reset *) 
600 
no_reset_to_exprs machines m i, 
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i::reset_instances 
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 MReset i > (* we assign middle_mem with reset: reset(mem_m) *) 
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instance_reset_to_exprs machines m i, 
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i::reset_instances 
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 MLocalAssign (i,v) > 
606 
assign_to_exprs 
607 
m 
608 
(mk_val (Var i) i.var_type) v, 
609 
reset_instances 
610 
 MStateAssign (i,v) > 
611 
assign_to_exprs 
612 
m 
613 
(mk_val (Var i) i.var_type) v, 
614 
reset_instances 
615 
 MStep ([i0], i, vl) when Basic_library.is_internal_fun i (List.map (fun v > v.value_type) vl) > 
616 
assert false (* This should not happen anymore *) 
617 
 MStep (il, i, vl) > 
618 
(* if reset instance, just print the call over mem_m , otherwise declare mem_m = 
619 
mem_c and print the call to mem_m *) 
620 
instance_call_to_exprs machines reset_instances m i vl il, 
621 
reset_instances (* Since this instance call will only happen once, we 
622 
don't have to update reset_instances *) 
623  
624 
 MBranch (g,hl) > (* (g = tag1 => expr1) and (g = tag2 => expr2) ... 
625 
should not be produced yet. Later, we will have to 
626 
compare the reset_instances of each branch and 
627 
introduced the mem_m = mem_c for branches to do not 
628 
address it while other did. Am I clear ? *) 
629 
(* For each branch we obtain the logical encoding, and the information 
630 
whether a sub node has been reset or not. If a node has been reset in one 
631 
of the branch, then all others have to have the mem_m = mem_c 
632 
statement. *) 
633 
let self = m.mname.node_id in 
634 
let branch_to_expr (tag, instrs) = 
635 
let branch_def, branch_resets = instrs_to_expr machines reset_instances m instrs in 
636 
let e = 
637 
Z3.Boolean.mk_implies !ctx 
638 
(Z3.Boolean.mk_eq !ctx 
639 
(horn_val_to_expr m self g) 
640 
(horn_tag_to_expr tag)) 
641 
branch_def in 
642  
643 
[e], branch_resets 
644 

645 
in 
646 
List.fold_left (fun (instrs, resets) b > 
647 
let b_instrs, b_resets = branch_to_expr b in 
648 
instrs@b_instrs, resets@b_resets 
649 
) ([], reset_instances) hl 
650  
651 
and instrs_to_expr machines reset_instances m instrs = 
652 
let instr_to_exprs rs i = instr_to_exprs machines rs m i in 
653 
let e_list, rs = 
654 
match instrs with 
655 
 [x] > instr_to_exprs reset_instances x 
656 
 _::_ > (* TODO: check whether we should compuyte a AND on the exprs (expr list) built here. It was performed in the printer setting but seems to be useless here since the output is a list of exprs *) 
657 

658 
List.fold_left (fun (exprs, rs) i > 
659 
let exprs_i, rs_i = instr_to_exprs rs i in 
660 
exprs@exprs_i, rs@rs_i 
661 
) 
662 
([], reset_instances) instrs 
663 

664 

665 
 [] > [], reset_instances 
666 
in 
667 
let e = 
668 
match e_list with 
669 
 [e] > e 
670 
 [] > Z3.Boolean.mk_true !ctx 
671 
 _ > Z3.Boolean.mk_and !ctx e_list 
672 
in 
673 
e, rs 
674  
675  
676 
(*********************************************************) 
677  
678 
(* Quantifiying universally all occuring variables *) 
679 
let add_rule ?(dont_touch=[]) vars expr = 
680 
(* let fds = Z3.Expr.get_args expr in *) 
681 
(* Format.eprintf "Expr %s: args: [%a]@." *) 
682 
(* (Z3.Expr.to_string expr) *) 
683 
(* (Utils.fprintf_list ~sep:", " (fun fmt e > Format.pp_print_string fmt (Z3.Expr.to_string e))) fds; *) 
684  
685 
(* (\* Old code relying on provided vars *\) *) 
686 
(* let sorts = (List.map (fun id > type_to_sort id.var_type) vars) in *) 
687 
(* let symbols = (List.map (fun id > Z3.FuncDecl.get_name (get_fdecl id.var_id)) vars) in *) 
688 

689 
(* New code: we extract vars from expr *) 
690 
let module FDSet = Set.Make (struct type t = Z3.FuncDecl.func_decl 
691 
let compare = compare 
692 
let hash = Hashtbl.hash 
693 
end) 
694 
in 
695 
let rec get_expr_vars e = 
696 
let open Utils in 
697 
let nb_args = Z3.Expr.get_num_args e in 
698 
if nb_args <= 0 then ( 
699 
let fdecl = Z3.Expr.get_func_decl e in 
700 
(* let params = Z3.FuncDecl.get_parameters fdecl in *) 
701 
(* Format.eprintf "Extracting info about %s: @." (Z3.Expr.to_string e); *) 
702 
let dkind = Z3.FuncDecl.get_decl_kind fdecl in 
703 
match dkind with Z3enums.OP_UNINTERPRETED > ( 
704 
(* Format.eprintf "kind = %s, " (match dkind with Z3enums.OP_TRUE > "true"  Z3enums.OP_UNINTERPRETED > "uninter"); *) 
705 
(* let open Z3.FuncDecl.Parameter in *) 
706 
(* List.iter (fun p > *) 
707 
(* match p with *) 
708 
(* P_Int i > Format.eprintf "int %i" i *) 
709 
(*  P_Dbl f > Format.eprintf "dbl %f" f *) 
710 
(*  P_Sym s > Format.eprintf "symb" *) 
711 
(*  P_Srt s > Format.eprintf "sort" *) 
712 
(*  P_Ast _ >Format.eprintf "ast" *) 
713 
(*  P_Fdl f > Format.eprintf "fundecl" *) 
714 
(*  P_Rat s > Format.eprintf "rat %s" s *) 
715 

716 
(* ) params; *) 
717 
(* Format.eprintf "]@."; *) 
718 
FDSet.singleton fdecl 
719 
) 
720 
 _ > FDSet.empty 
721 
) 
722 
else (*if nb_args > 0 then*) 
723 
List.fold_left 
724 
(fun accu e > FDSet.union accu (get_expr_vars e)) 
725 
FDSet.empty (Z3.Expr.get_args e) 
726 
in 
727 
let extracted_vars = FDSet.elements (FDSet.diff (get_expr_vars expr) (FDSet.of_list dont_touch)) in 
728 
let extracted_sorts = List.map Z3.FuncDecl.get_range extracted_vars in 
729 
let extracted_symbols = List.map Z3.FuncDecl.get_name extracted_vars in 
730  
731 
if !debug then ( 
732 
Format.eprintf "Declaring rule: %s with variables @[<v 0>@ [%a@ ]@]@ @." 
733 
(Z3.Expr.to_string expr) 
734 
(Utils.fprintf_list ~sep:",@ " (fun fmt e > Format.fprintf fmt "%s" (Z3.Expr.to_string e))) (List.map horn_var_to_expr vars) 
735 
) 
736 
; 
737 
let expr = Z3.Quantifier.mk_forall_const 
738 
!ctx (* context *) 
739 
(List.map horn_var_to_expr vars) (* TODO provide bounded variables as expr *) 
740 
(* sorts (\* sort list*\) *) 
741 
(* symbols (\* symbol list *\) *) 
742 
expr (* expression *) 
743 
None (* quantifier weight, None means 1 *) 
744 
[] (* pattern list ? *) 
745 
[] (* ? *) 
746 
None (* ? *) 
747 
None (* ? *) 
748 
in 
749 
(* Format.eprintf "OK@.@?"; *) 
750  
751 
(* 
752 
TODO: bizarre la declaration de INIT tout seul semble poser pb. 
753 
*) 
754 
Z3.Fixedpoint.add_rule !fp 
755 
(Z3.Quantifier.expr_of_quantifier expr) 
756 
None 
757  
758 

759 
(********************************************************) 
760 

761 
let machine_reset machines m = 
762 
let locals = local_memory_vars machines m in 
763 

764 
(* print "x_m = x_c" for each local memory *) 
765 
let mid_mem_def = 
766 
List.map (fun v > 
767 
Z3.Boolean.mk_eq !ctx 
768 
(horn_var_to_expr (rename_mid v)) 
769 
(horn_var_to_expr (rename_current v)) 
770 
) locals 
771 
in 
772  
773 
(* print "child_reset ( associated vars _ {c,m} )" for each subnode. 
774 
Special treatment for _arrow: _first = true 
775 
*) 
776  
777 
let reset_instances = 
778 

779 
List.map (fun (id, (n, _)) > 
780 
let name = node_name n in 
781 
if name = "_arrow" then ( 
782 
Z3.Boolean.mk_eq !ctx 
783 
( 
784 
let vdecl = get_fdecl ((concat m.mname.node_id id) ^ "._arrow._first_m") in 
785 
Z3.Expr.mk_const_f !ctx vdecl 
786 
) 
787 
(Z3.Boolean.mk_true !ctx) 
788 

789 
) else ( 
790 
let machine_n = get_machine machines name in 
791 

792 
Z3.Expr.mk_app 
793 
!ctx 
794 
(get_fdecl (name ^ "_reset")) 
795 
(List.map (horn_var_to_expr) 
796 
(idx::uid:: (* Additional vars: counters, uid *) 
797 
(rename_machine_list (concat m.mname.node_id id) (reset_vars machines machine_n)) 
798 
)) 
799 

800 
) 
801 
) m.minstances 
802 

803 

804 
in 
805 

806 
Z3.Boolean.mk_and !ctx (mid_mem_def @ reset_instances) 
807 

808 

809  
810 
(* TODO: empty list means true statement *) 
811 
let decl_machine machines m = 
812 
if m.mname.node_id = Arrow.arrow_id then 
813 
(* We don't do arrow function *) 
814 
() 
815 
else 
816 
begin 
817 
let _ = 
818 
List.map decl_var 
819 
( 
820 
(inout_vars machines m)@ 
821 
(rename_current_list (full_memory_vars machines m)) @ 
822 
(rename_mid_list (full_memory_vars machines m)) @ 
823 
(rename_next_list (full_memory_vars machines m)) @ 
824 
(rename_machine_list m.mname.node_id m.mstep.step_locals) 
825 
) 
826 
in 
827 
if is_stateless m then 
828 
begin 
829 
if !debug then 
830 
Format.eprintf "Declaring a stateless machine: %s@." m.mname.node_id; 
831  
832 
(* Declaring single predicate *) 
833 
let vars = inout_vars machines m in 
834 
let vars_types = List.map (fun v > type_to_sort v.var_type) vars in 
835 
let _ = decl_rel (machine_stateless_name m.mname.node_id) vars_types in 
836 

837 
let horn_body, _ (* don't care for reset here *) = 
838 
instrs_to_expr 
839 
machines 
840 
([] (* No reset info for stateless nodes *) ) 
841 
m 
842 
m.mstep.step_instrs 
843 
in 
844 
let horn_head = 
845 
Z3.Expr.mk_app 
846 
!ctx 
847 
(get_fdecl (machine_stateless_name m.mname.node_id)) 
848 
( List.map (horn_var_to_expr) (idx::uid:: (* Additional vars: counters, uid *) vars)) 
849 
in 
850 
(* this line seems useless *) 
851 
let vars = idx::uid::vars@(rename_machine_list m.mname.node_id m.mstep.step_locals) in 
852 
(* Format.eprintf "useless Vars: %a@." (Utils.fprintf_list ~sep:"@ " Printers.pp_var) vars; *) 
853 
match m.mstep.step_asserts with 
854 
 [] > 
855 
begin 
856 
(* Rule for single predicate : "; Stateless step rule @." *) 
857 
(*let vars = rename_machine_list m.mname.node_id m.mstep.step_locals in*) 
858 
(* TODO clean code *) 
859 
(* Format.eprintf "used Vars: %a@." (Utils.fprintf_list ~sep:"@ " Printers.pp_var) vars; *) 
860 
add_rule vars (Z3.Boolean.mk_implies !ctx horn_body horn_head) 
861 

862 
end 
863 
 assertsl > 
864 
begin 
865 
(*Rule for step "; Stateless step rule with Assertions @.";*) 
866 
let body_with_asserts = 
867 
Z3.Boolean.mk_and !ctx (horn_body :: List.map (horn_val_to_expr m m.mname.node_id) assertsl) 
868 
in 
869 
let vars = rename_machine_list m.mname.node_id m.mstep.step_locals in 
870 
add_rule vars (Z3.Boolean.mk_implies !ctx body_with_asserts horn_head) 
871 
end 
872 
end 
873 
else 
874 
begin 
875  
876 
(* Rule for reset *) 
877  
878 
let vars = reset_vars machines m in 
879 
let vars_types = List.map (fun v > type_to_sort v.var_type) vars in 
880 
let _ = decl_rel (machine_reset_name m.mname.node_id) vars_types in 
881 
let horn_reset_body = machine_reset machines m in 
882 
let horn_reset_head = 
883 
Z3.Expr.mk_app 
884 
!ctx 
885 
(get_fdecl (machine_reset_name m.mname.node_id)) 
886 
( List.map (horn_var_to_expr) (idx::uid:: (* Additional vars: counters, uid *) vars)) 
887 
in 
888  
889 

890 
let _ = 
891 
add_rule (idx::uid::vars) (Z3.Boolean.mk_implies !ctx horn_reset_body horn_reset_head) 
892 

893 
in 
894  
895 
(* Rule for step*) 
896 
let vars = step_vars machines m in 
897 
let vars_types = List.map (fun v > type_to_sort v.var_type) vars in 
898 
let _ = decl_rel (machine_step_name m.mname.node_id) vars_types in 
899 
let horn_step_body, _ (* don't care for reset here *) = 
900 
instrs_to_expr 
901 
machines 
902 
[] 
903 
m 
904 
m.mstep.step_instrs 
905 
in 
906 
let horn_step_head = 
907 
Z3.Expr.mk_app 
908 
!ctx 
909 
(get_fdecl (machine_step_name m.mname.node_id)) 
910 
( List.map (horn_var_to_expr) (idx::uid:: (* Additional vars: counters, uid *) vars)) 
911 
in 
912 
match m.mstep.step_asserts with 
913 
 [] > 
914 
begin 
915 
(* Rule for single predicate *) 
916 
let vars = (step_vars_c_m_x machines m) @(rename_machine_list m.mname.node_id m.mstep.step_locals) in 
917 
add_rule (idx::uid::vars) (Z3.Boolean.mk_implies !ctx horn_step_body horn_step_head) 
918 

919 
end 
920 
 assertsl > 
921 
begin 
922 
(* Rule for step Assertions @.; *) 
923 
let body_with_asserts = 
924 
Z3.Boolean.mk_and !ctx 
925 
(horn_step_body :: List.map (horn_val_to_expr m m.mname.node_id) assertsl) 
926 
in 
927 
let vars = (step_vars_c_m_x machines m) @(rename_machine_list m.mname.node_id m.mstep.step_locals) in 
928 
add_rule (idx::uid::vars) (Z3.Boolean.mk_implies !ctx body_with_asserts horn_step_head) 
929 

930 
end 
931 

932 
end 
933 
end 
934  
935  
936  
937 
(* Debug functions *) 
938  
939 
let rec extract_expr_fds e = 
940 
(* Format.eprintf "@[<v 2>Extracting fundecls from expr %s@ " *) 
941 
(* (Z3.Expr.to_string e); *) 
942 

943 
(* Removing quantifier is there are some *) 
944 
let e = (* I didn't found a nicer way to do it than with an exception. My 
945 
bad *) 
946 
try 
947 
let eq = Z3.Quantifier.quantifier_of_expr e in 
948 
let e2 = Z3.Quantifier.get_body eq in 
949 
(* Format.eprintf "Extracted quantifier body@ "; *) 
950 
e2 
951 

952 
with _ > Format.eprintf "No quantifier info@ "; e 
953 
in 
954 
let _ = 
955 
try 
956 
( 
957 
let fd = Z3.Expr.get_func_decl e in 
958 
let fd_symbol = Z3.FuncDecl.get_name fd in 
959 
let fd_name = Z3.Symbol.to_string fd_symbol in 
960 
if not (Hashtbl.mem decls fd_name) then 
961 
register_fdecl fd_name fd; 
962 
(* Format.eprintf "fdecls (%s): %s@ " *) 
963 
(* fd_name *) 
964 
(* (Z3.FuncDecl.to_string fd); *) 
965 
try 
966 
( 
967 
let args = Z3.Expr.get_args e in 
968 
(* Format.eprintf "@[<v>@ "; *) 
969 
(* List.iter extract_expr_fds args; *) 
970 
(* Format.eprintf "@]@ "; *) 
971 
() 
972 
) 
973 
with _ > 
974 
Format.eprintf "Impossible to extract fundecl args for expression %s@ " 
975 
(Z3.Expr.to_string e) 
976 
) 
977 
with _ > 
978 
Format.eprintf "Impossible to extract anything from expression %s@ " 
979 
(Z3.Expr.to_string e) 
980 
in 
981 
(* Format.eprintf "@]@ " *) 
982 
() 
983  
984 
(* Local Variables: *) 
985 
(* compilecommand:"make C ../.." *) 
986 
(* End: *) 