Source file Lang.ml
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open Cil_types
open Cil_datatype
open Ctypes
open Qed
open Qed.Logic
let dkey_pretty = Wp_parameters.register_category "pretty"
let basename def name =
let rec lookup def s k n =
if k < n then
let c = s.[k] in
if ('a' <= c && c <= 'z') || ('A' <= c && c <= 'Z')
then String.sub s k 1
else lookup def s (succ k) n
else def
in lookup def name 0 (String.length name)
let avoid_leading_backlash s =
if s.[0]='\\' then
let s = Bytes.of_string s in
Bytes.set s 0 '_'; Bytes.to_string s
else s
let comp_id c =
let prefix = if c.cstruct then 'S' else 'U' in
if c.corig_name = "" then
Printf.sprintf "%c%d" prefix c.ckey
else
Printf.sprintf "%c%d_%s" prefix c.ckey c.corig_name
let field_id f =
let c = f.fcomp in
if c.corig_name = "" then
Printf.sprintf "F%d_%s" c.ckey f.fname
else
Printf.sprintf "F%d_%s_%s" c.ckey c.corig_name f.fname
let init_id (f: 'a -> string) (x: 'a) = "Init_" ^ (f x)
let comp_init_id = init_id comp_id
let field_init_id = init_id field_id
let type_id l =
Printf.sprintf "A_%s" l.lt_name
let logic_id f =
let name = avoid_leading_backlash (LogicUsage.get_name f) in
if f.l_type = None
then Printf.sprintf "P_%s" name
else Printf.sprintf "L_%s" name
let ctor_id c = Printf.sprintf "C_%s" (avoid_leading_backlash c.ctor_name)
let lemma_id l = Printf.sprintf "Q_%s" (avoid_leading_backlash l)
type library = string
type datakind = KValue | KInit
type adt =
| Mtype of mdt
| Mrecord of mdt * fields
| Atype of logic_type_info
| Comp of compinfo * datakind
| Wtype of string list * string * string list (** Why3 imported type *)
(** name to print to the provers *)
and mdt = string extern
and 'a extern = {
ext_id : int;
ext_link : 'a ;
ext_library : library; (** a library which it depends on *)
ext_debug : string; (** just for printing during debugging *)
}
and fields = { mutable fields : field list }
and field =
| Mfield of mdt * fields * string * tau
| Cfield of fieldinfo * datakind
and tau = (field,adt) Logic.datatype
let pointer = Context.create "Lang.pointer"
let floats = Context.create "Lang.floats"
let new_extern_id = ref (-1)
let new_extern ~debug ~library ~link =
incr new_extern_id;
{ext_id = !new_extern_id;
ext_library = library;
ext_debug = debug;
ext_link = link}
let ext_compare a b = Datatype.Int.compare a.ext_id b.ext_id
let sort_of_object = function
| C_int _ -> Logic.Sint
| C_pointer _ | C_comp _ | C_array _ -> Logic.Sdata
| C_float f -> Qed.Kind.of_tau (Context.get floats f)
let init_sort_of_object = function
| C_int _ | C_float _ | C_pointer _ -> Logic.Sbool
| C_comp _ | C_array _ -> Logic.Sdata
let sort_of_ctype t = sort_of_object (Ctypes.object_of t)
let sort_of_ltype t = match Ast_types.unroll_logic ~unroll_typedef:false t with
| Ctype typ -> sort_of_ctype typ
| Ltype _ | Lvar _ | Larrow _ -> Logic.Sdata
| Lboolean -> Logic.Sbool
| Linteger -> Logic.Sint
| Lreal -> Logic.Sreal
let t_int = Logic.Int
let t_bool = Logic.Bool
let t_real = Logic.Real
let t_prop = Logic.Prop
let t_addr () = Context.get pointer
let t_float f = Context.get floats f
let t_comp c = Logic.Data(Comp (c, KValue),[])
let t_init c = Logic.Data(Comp (c, KInit), [])
let t_array a = Logic.Array(Logic.Int,a)
let t_farray a b = Logic.Array(a,b)
let t_datatype adt ts = Logic.Data(adt,ts)
let rec t_matrix a n = if n > 0 then t_matrix (t_array a) (pred n) else a
let rec tau_of_object = function
| C_int _ -> Logic.Int
| C_float f -> t_float f
| C_pointer _ -> Context.get pointer
| C_comp c -> t_comp c
| C_array { arr_element = typ } -> t_array (tau_of_ctype typ)
and tau_of_ctype typ = tau_of_object (Ctypes.object_of typ)
let poly = Context.create "Wp.Lang.poly"
let rec init_of_object = function
| C_int _ | C_float _ | C_pointer _ -> Logic.Bool
| C_comp c -> t_init c
| C_array { arr_element = typ } -> t_array (init_of_ctype typ)
and init_of_ctype typ = init_of_object (Ctypes.object_of typ)
let rec varpoly k x = function
| [] -> Warning.error "Unbound type parameter <%s>" x
| y::ys -> if x = y then k else varpoly (succ k) x ys
type t_builtin =
| E_mdt of mdt
| E_why3 of string list * string * string list
| E_poly of (tau list -> tau)
let builtin_types = Context.create "Wp.Lang.builtin_types"
let find_builtin name = Context.get builtin_types name
let adt lt =
try match find_builtin lt.lt_name with
| E_mdt m -> Mtype m
| E_why3(p,m,s) -> Wtype(p,m,s)
| E_poly _ -> assert false
with Not_found -> Atype lt
let atype lt ts =
try match find_builtin lt.lt_name with
| E_mdt m -> Logic.Data(Mtype m,ts)
| E_why3(p,m,s) -> Logic.Data(Wtype(p,m,s),ts)
| E_poly ftau -> ftau ts
with Not_found -> Logic.Data(Atype lt,ts)
let rec tau_of_ltype t =
match Ast_types.unroll_logic ~unroll_typedef:false t with
| Lboolean -> Logic.Bool
| Linteger -> Logic.Int
| Lreal -> Logic.Real
| Ctype typ -> tau_of_ctype typ
| Lvar x -> Logic.Tvar (varpoly 1 x (Context.get poly))
| Ltype(lt,lts) -> atype lt (List.map tau_of_ltype lts)
| Larrow(ts,tr) ->
List.fold_left
(fun r k -> Logic.Array(tau_of_ltype k,r))
(tau_of_ltype tr) ts
let tau_of_return = function None -> Logic.Prop | Some t -> tau_of_ltype t
module ADT =
struct
type t = adt
let basename = function
| Mtype a -> basename "M" a.ext_link
| Mrecord(r,_) -> basename "R" r.ext_link
| Comp (c,KValue) -> basename (if c.cstruct then "S" else "U") c.corig_name
| Comp (c,KInit) -> basename (if c.cstruct then "IS" else "IU") c.corig_name
| Atype lt -> basename "A" lt.lt_name
| Wtype(_,_,s) ->
let rec base def = function [] -> def | w::ws -> base w ws in base "w" s
let debug = function
| Mtype a -> a.ext_debug
| Mrecord(a,_) -> a.ext_debug
| Comp (c, KValue) -> comp_id c
| Comp (c, KInit) -> comp_init_id c
| Atype lt -> type_id lt
| Wtype(p,m,s) -> String.concat "." (p @ m :: s)
let hash = function
| Mtype a | Mrecord(a,_) -> FCHashtbl.hash a
| Comp (c, KValue) -> Compinfo.hash c
| Comp (c, KInit) -> 13 * Compinfo.hash c
| Atype lt -> Logic_type_info.hash lt
| Wtype(p,m,s) -> Hashtbl.hash @@ (p @ m :: s)
let compare a b =
if a==b then 0 else
match a,b with
| Mtype a , Mtype b -> ext_compare a b
| Mtype _ , _ -> (-1)
| _ , Mtype _ -> (+1)
| Mrecord(a,_) , Mrecord(b,_) -> ext_compare a b
| Mrecord _ , _ -> (-1)
| _ , Mrecord _ -> (+1)
| Comp (a, KValue) , Comp (b, KValue)
| Comp (a, KInit) , Comp (b, KInit) -> Compinfo.compare a b
| Comp (_, KValue) , Comp (_, KInit) -> (-1)
| Comp (_, KInit) , Comp (_, KValue) -> (+1)
| Comp _ , _ -> (-1)
| _ , Comp _ -> (+1)
| Atype a , Atype b -> Logic_type_info.compare a b
| Atype _ , _ -> (-1)
| _ , Atype _ -> (+1)
| Wtype(p,m,s), Wtype(p',m',s') -> Stdlib.compare (p,m,s) (p',m',s')
let equal a b = (compare a b = 0)
let pretty fmt a = Format.pp_print_string fmt (debug a)
end
let get_builtin_type ~name =
match find_builtin name with
| E_mdt m -> Mtype m
| E_why3(p,m,s) -> Wtype(p,m,s)
| E_poly _ -> assert false
let mem_builtin_type ~name =
try ignore (find_builtin name) ; true
with Not_found -> false
let is_builtin lt = mem_builtin_type ~name:lt.lt_name
let is_builtin_type ~name = function
| Data(Mtype m,_) ->
begin
try match find_builtin name with
| E_mdt m0 -> m == m0
| _ -> false
with Not_found -> false
end
| Data(Wtype(p,m,s),_) ->
begin
try match find_builtin name with
| E_why3(p0,m0,s0) -> (p,m,s) = (p0,m0,s0)
| _ -> false
with Not_found -> false
end
| _ -> false
let datatype ~library name =
let m = new_extern ~link:name ~library ~debug:name in
Mtype m
let field_observers = ref []
let field_observe fd = List.iter (fun k -> k fd) !field_observers ; fd
let on_field f = field_observers := f :: !field_observers
let cfield ?(kind=KValue) fd = field_observe @@ Cfield(fd,kind)
let record ~link ~library fts =
let m = new_extern ~link ~library ~debug:link in
let r = { fields = [] } in
let fs = List.map (fun (f,t) -> field_observe @@ Mfield(m,r,f,t)) fts in
r.fields <- fs ; Mrecord(m,r)
let field t f =
match t with
| Mrecord(_,r) ->
begin
try List.find (function Mfield(_,_,g,_) -> f = g | _ -> false) r.fields
with Not_found -> Wp_parameters.fatal "No field <%s> in record" f
end
| _ -> Wp_parameters.fatal "No field <%s> in type '%a'" f ADT.pretty t
let comp c = Comp (c, KValue)
let comp_init c = Comp (c, KInit)
let fields_of_adt = function
| Mrecord(_,r) -> r.fields
| Comp (c, k) ->
List.map (fun f -> Cfield (f, k)) (Option.value ~default:[] c.cfields)
| _ -> []
let fields_of_tau = function
| Record fts -> List.map fst fts
| Data(adt,_) -> fields_of_adt adt
| _ -> []
let fields_of_field = function
| Mfield(_,r,_,_) -> r.fields
| Cfield(f, k) ->
List.map (fun f -> Cfield (f, k)) (Option.value ~default:[] f.fcomp.cfields)
let tau_of_field = function
| Mfield(_,_,_,t) -> t
| Cfield(f, KValue) -> tau_of_ctype f.ftype
| Cfield(f, KInit) -> init_of_ctype f.ftype
let tau_of_record = function
| Mfield(mdt,fs,_,_) -> Logic.Data(Mrecord(mdt,fs),[])
| Cfield(f, KValue) -> t_comp f.fcomp
| Cfield(f, KInit) -> t_init f.fcomp
module Field =
struct
type t = field
let debug = function
| Mfield(_,_,f,_) -> f
| Cfield(f, KValue) -> field_id f
| Cfield(f, KInit) -> field_init_id f
let hash = function
| Mfield(_,_,f,_) -> FCHashtbl.hash f
| Cfield(f, KValue) -> Fieldinfo.hash f
| Cfield(f, KInit) -> 13 * Fieldinfo.hash f
let compare f g =
if f==g then 0 else
match f , g with
| Mfield(_,_,f,_) , Mfield(_,_,g,_) -> String.compare f g
| Mfield _ , Cfield _ -> (-1)
| Cfield _ , Mfield _ -> (+1)
| Cfield(f, KValue) , Cfield(g, KValue)
| Cfield(f, KInit) , Cfield(g, KInit) ->
Fieldinfo.compare f g
| Cfield(_, KInit), Cfield(_, KValue) -> (-1)
| Cfield(_, KValue), Cfield(_, KInit) -> (+1)
let equal f g = (compare f g = 0)
let pretty fmt f = Format.pp_print_string fmt (debug f)
let sort = function
| Mfield(_,_,_,s) -> Qed.Kind.of_tau s
| Cfield(f, KValue) -> sort_of_object (Ctypes.object_of f.ftype)
| Cfield(f, KInit) -> init_sort_of_object (Ctypes.object_of f.ftype)
end
type lfun =
| ACSL of Cil_types.logic_info
(** Registered in Definition.t, only *)
| CTOR of Cil_types.logic_ctor_info
(** Not registered in Definition.t, directly converted/printed *)
| FUN of lsymbol
(** Generated or External function *)
and lsymbol = {
m_category : lfun category ;
m_params : sort list ;
m_result : sort ;
m_typeof : tau option list -> tau ;
m_source : source ;
m_coloring : bool ;
}
and source =
| Generated of WpContext.context option * string
| Extern of Engine.link extern
| Wsymbol of string list * string * string list
let lfun_observers = ref []
let lfun_observe lf = List.iter (fun k -> k lf) !lfun_observers ; lf
let on_lfun f = lfun_observers := f :: !lfun_observers
let acsl lf = lfun_observe (ACSL lf)
let ctor cf = lfun_observe (CTOR cf)
let lsymbol m = lfun_observe (FUN m)
let tau_of_lfun phi ts =
match phi with
| ACSL f -> tau_of_return f.l_type
| CTOR c ->
if c.ctor_type.lt_params = [] then Logic.Data(Atype c.ctor_type,[])
else raise Not_found
| FUN m -> match m.m_result with
| Sint -> Int
| Sreal -> Real
| Sbool -> Bool
| _ -> m.m_typeof ts
let is_coloring_lfun = function
| ACSL _ | CTOR _ -> false
| FUN { m_coloring } -> m_coloring
type balance = Nary | Left | Right
let not_found _ = raise Not_found
let generated ?(context=false) name =
let ctxt = if context
then Some (WpContext.get_context ())
else None in
Generated(ctxt,name)
let symbolf
?library
?context
?link
?(balance=Nary)
?(category=Logic.Function)
?(params=[])
?(sort=Logic.Sdata)
?(result:tau option)
?(coloring=false)
?(typecheck:(tau option list -> tau) option)
name =
let buffer = Buffer.create 80 in
Format.kfprintf
(fun fmt ->
Format.pp_print_flush fmt () ;
let name = Buffer.contents buffer in
let source = match library with
| None ->
assert (link = None);
generated ?context name
| Some th ->
let conv n = function
| Nary -> Engine.F_call n
| Left -> Engine.F_left n
| Right -> Engine.F_right n
in
let link = match link with
| None -> conv name balance
| Some info -> info
in
Extern (new_extern ~library:th ~link ~debug:name) in
let typeof =
match typecheck with Some phi -> phi | None ->
match result with Some t -> fun _ -> t | None -> not_found in
let result =
match result with Some t -> Kind.of_tau t | None -> sort in
lsymbol {
m_category = category ;
m_params = params ;
m_result = result ;
m_typeof = typeof ;
m_source = source ;
m_coloring = coloring ;
}
) (Format.formatter_of_buffer buffer) name
let extern_s
~library ?link ?category ?params ?sort ?result ?coloring ?typecheck name =
symbolf
~library ?category ?params ?sort ?result ?coloring ?typecheck ?link "%s" name
let extern_f
~library ?link ?balance ?category ?params ?sort ?result ?coloring ?typecheck name =
symbolf
~library ?category ?params ?link ?balance ?sort ?result ?coloring ?typecheck name
let extern_p ~library ?bool ?prop ?link ?(params=[]) ?(coloring=false) () =
let link =
match bool,prop,link with
| Some b , Some p , None -> Engine.F_bool_prop(b,p)
| _ , _ , Some info -> info
| _ , _ , _ -> assert false
in
let debug = Export.debug link in
lsymbol {
m_category = Logic.Function;
m_params = params ;
m_result = Logic.Sprop;
m_typeof = not_found;
m_source = Extern (new_extern ~library ~link ~debug) ;
m_coloring = coloring ;
}
let extern_fp ~library ?(params=[]) ?link ?(coloring=false) phi =
let link = match link with
| None -> Engine.F_call phi
| Some link -> Engine.F_call link in
lsymbol {
m_category = Logic.Function ;
m_params = params ;
m_result = Logic.Sprop;
m_typeof = not_found;
m_source = Extern (new_extern
~library
~link
~debug:phi) ;
m_coloring = coloring ;
}
let generated_f ?context ?category ?params ?sort ?result ?coloring name =
symbolf ?context ?category ?params ?sort ?result ?coloring name
let generated_p ?context ?(coloring=false) name =
lsymbol {
m_category = Logic.Function ;
m_params = [] ;
m_result = Logic.Sprop;
m_typeof = not_found;
m_source = generated ?context name ;
m_coloring = coloring ;
}
let extern_t name ~link ~library =
new_extern ~link ~library ~debug:name
let imported_t ~package ~theory ~name =
Wtype(package,theory,name)
let imported_f ~package ~theory ~name
?(params=[]) ?(result=Logic.Sprop) ?(typecheck=not_found) () =
lsymbol {
m_category = Logic.Function ;
m_params = params ;
m_result = result ;
m_typeof = typecheck ;
m_source = Wsymbol(package,theory,name) ;
m_coloring = false ;
}
module Fun =
struct
type t = lfun
let debug = function
| ACSL f -> logic_id f
| CTOR c -> ctor_id c
| FUN({m_source=Generated(_,n)}) -> n
| FUN({m_source=Extern e}) -> e.ext_debug
| FUN({m_source=Wsymbol(p,m,s)}) -> String.concat "." (p @ m :: s)
let hash = function
| ACSL f -> Logic_info.hash f
| CTOR c -> Logic_ctor_info.hash c
| FUN({m_source=Generated(_,n)}) -> Datatype.String.hash n
| FUN({m_source=Extern e}) -> e.ext_id
| FUN({m_source=Wsymbol(p,m,s)}) ->
Datatype.String.hash @@ String.concat "." (p @ m :: s)
let compare_context c1 c2 =
match c1 , c2 with
| None , None -> 0
| None , _ -> (-1)
| _ , None -> (+1)
| Some c1 , Some c2 -> WpContext.S.compare c1 c2
let compare_source s1 s2 =
match s1 , s2 with
| Generated(m1,f1), Generated(m2,f2) ->
let cmp = String.compare f1 f2 in
if cmp<>0 then cmp else compare_context m1 m2
| Generated _, _ -> (-1)
| _, Generated _ -> (+1)
| Extern f , Extern g ->
ext_compare f g
| Extern _ , _ -> (-1)
| _ , Extern _ -> (+1)
| Wsymbol(p,m,s) , Wsymbol(p',m',s') ->
Stdlib.compare (p,m,s) (p',m',s')
let compare f g =
if f==g then 0 else
match f , g with
| FUN {m_source=mf} , FUN {m_source=mg} -> compare_source mf mg
| FUN _ , _ -> (-1)
| _ , FUN _ -> (+1)
| ACSL f , ACSL g -> Logic_info.compare f g
| ACSL _ , _ -> (-1)
| _ , ACSL _ -> (+1)
| CTOR c , CTOR d -> Logic_ctor_info.compare c d
let equal f g = (compare f g = 0)
let pretty fmt f = Format.pp_print_string fmt (debug f)
let category = function
| FUN m -> m.m_category
| ACSL _ -> Logic.Function
| CTOR _ -> Logic.Constructor
let sort = function
| FUN m -> m.m_result
| ACSL { l_type=None } -> Logic.Sprop
| ACSL { l_type=Some t } -> sort_of_ltype t
| CTOR _ -> Logic.Sdata
let parameters = ref (fun _ -> [])
let params = function
| FUN m -> m.m_params
| CTOR ct -> List.map sort_of_ltype ct.ctor_params
| (ACSL _) as f -> !parameters f
end
let parameters phi = Fun.parameters := phi
class virtual idprinting =
object(self)
method virtual sanitize : string -> string
method sanitize_type = self#sanitize
method sanitize_field = self#sanitize
method sanitize_fun = self#sanitize
method datatype = function
| Mtype a -> a.ext_link
| Mrecord(a,_) -> a.ext_link
| Comp(c, KValue) -> self#sanitize_type (comp_id c)
| Comp(c, KInit) -> self#sanitize_type (comp_init_id c)
| Atype lt -> self#sanitize_type (type_id lt)
| Wtype(p,m,s) -> String.concat "." (p @ m :: s)
method field = function
| Mfield(_,_,f,_) -> self#sanitize_field f
| Cfield(f, KValue) -> self#sanitize_field (field_id f)
| Cfield(f, KInit) -> self#sanitize_field (field_init_id f)
method link = function
| ACSL f -> Engine.F_call (self#sanitize_fun (logic_id f))
| CTOR c -> Engine.F_call (self#sanitize_fun (ctor_id c))
| FUN({m_source=Generated(_,n)}) -> Engine.F_call (self#sanitize_fun n)
| FUN({m_source=Extern e}) -> e.ext_link
| FUN({m_source=Wsymbol(p,m,s)}) ->
Engine.F_call (String.concat "." (p @ m :: s))
end
let name_of_lfun = function
| ACSL f -> logic_id f
| CTOR c -> ctor_id c
| FUN({m_source=Generated(_,f)}) -> f
| FUN({m_source=Extern e}) -> e.ext_debug
| FUN({m_source=Wsymbol(p,m,s)}) -> String.concat "." (p @ m :: s)
let context_of_lfun = function
| ACSL _ | CTOR _
| FUN({m_source=(Extern _|Wsymbol _)}) -> None
| FUN({m_source=Generated(ctxt,_)}) -> ctxt
let name_of_field = function
| Mfield(_,_,f,_) -> f
| Cfield(f, KValue) -> field_id f
| Cfield(f, KInit) -> field_init_id f
module F =
struct
module QZERO = Qed.Term.Make(ADT)(Field)(Fun)
module DATA =
Datatype.Make
(struct
type t = QZERO.state
let name = "Wp.Qed"
let rehash = Datatype.identity
let structural_descr = Structural_descr.t_unknown
let reprs = [QZERO.get_state ()]
let equal = Datatype.undefined
let compare = Datatype.undefined
let hash = Datatype.undefined
let copy _old = QZERO.create ()
let pretty = Datatype.undefined
let mem_project _ _ = false
end)
module STATE = State_builder.Register(DATA)
(struct
type t = QZERO.state
let create = QZERO.create
let clear = QZERO.clr_state
let get = QZERO.get_state
let set = QZERO.set_state
let clear_some_projects _ _ = false
end)
(struct
let name = "Wp.Qed"
let dependencies = [Ast.self]
let unique_name = name
end)
include (STATE : sig end)
module Pretty = Qed.Pretty.Make(QZERO)
module QED =
struct
include QZERO
let typeof ?(field=tau_of_field) ?(record=tau_of_record) ?(call=tau_of_lfun) e =
QZERO.typeof ~field ~record ~call e
end
include QED
let set_builtin f = QZERO.set_builtin f
let set_builtin' f = QZERO.set_builtin' f
let set_builtin_eq f = QZERO.set_builtin_eq f
let set_builtin_leq f = QZERO.set_builtin_leq f
let set_builtin_get f = QZERO.set_builtin_get f
let set_builtin_field f = QZERO.set_builtin_field f
type unop = term -> term
type binop = term -> term -> term
let e_zero = QED.constant (e_zint Z.zero)
let e_one = QED.constant (e_zint Z.one)
let e_minus_one = QED.constant (e_zint Z.minus_one)
let e_minus_one_real = QED.constant (e_real Q.minus_one)
let e_one_real = QED.constant (e_real Q.one)
let e_zero_real = QED.constant (e_real Q.zero)
let e_int64 z = e_zint (Z.of_string (Int64.to_string z))
let e_fact k e = e_times (Z.of_int k) e
let e_bigint z = e_zint (Z.of_string (Integer.to_string z))
let e_range a b = e_sum [b;e_one;e_opp a]
let e_setfield r f v =
let r = List.map
(fun g -> g,if Field.equal f g then v else e_getfield r g)
(fields_of_field f)
in e_record r
type pred = term
type cmp = term -> term -> pred
type operator = pred -> pred -> pred
let p_bool t = t
let e_prop t = t
let p_bools xs = xs
let e_props xs = xs
let e_lift f = f
let p_lift f = f
let is_zero e = match QED.repr e with
| Kint z -> Integer.equal z Integer.zero
| _ -> false
let eqp = equal
let comparep = compare
let is_ptrue = is_true
let is_pfalse = is_false
let is_equal a b = is_true (e_eq a b)
let is_int e =
try typeof e = Qed.Logic.Int with Not_found -> false
let is_real e =
try typeof e = Qed.Logic.Real with Not_found -> false
let is_prop e =
try match typeof e with Qed.Logic.Prop | Qed.Logic.Bool -> true | _ -> false
with Not_found -> false
let is_arith e =
try match typeof e with Qed.Logic.Int | Qed.Logic.Real -> true | _ -> false
with Not_found -> false
let p_equal = e_eq
let p_equals = List.map (fun (x,y) -> p_equal x y)
let p_neq = e_neq
let p_leq = e_leq
let p_lt = e_lt
let p_positive e = e_leq e_zero e
let p_true = e_true
let p_false = e_false
let p_not = e_not
let p_bind = e_bind
let p_forall = e_forall
let p_exists = e_exists
let p_subst = e_subst
let p_subst_var = e_subst_var
let p_and p q = e_and [p;q]
let p_or p q = e_or [p;q]
let p_imply h p = e_imply [h] p
let p_hyps hs p = e_imply hs p
let p_equiv = e_equiv
let p_if = e_if
let p_conj = e_and
let p_disj = e_or
let p_all f xs = e_and (List.map f xs)
let p_any f xs = e_or (List.map f xs)
let e_vars e = List.sort Var.compare (Vars.elements (vars e))
let p_vars = e_vars
let p_call = e_fun ~result:Prop
let p_close = e_close_forall
let occurs x t = Vars.mem x (vars t)
let intersect a b = Vars.intersect (vars a) (vars b)
let occursp = occurs
let intersectp = intersect
let varsp = vars
let p_expr = repr
let e_expr = repr
let pp_tau = Pretty.pp_tau
let context_pp = Context.create "Lang.F.pp"
let pp_term fmt e =
if Wp_parameters.has_dkey dkey_pretty
then QED.debug fmt e
else
match Context.get_opt context_pp with
| Some env -> Pretty.pp_term_env env fmt e
| None ->
let env = Pretty.known Pretty.empty (QED.vars e) in
Pretty.pp_term env fmt e
let pp_pred = pp_term
let pp_var fmt x = pp_term fmt (e_var x)
let pp_vars fmt xs =
begin
Format.fprintf fmt "@[<hov 2>{" ;
Vars.iter (fun x -> Format.fprintf fmt "@ %a" pp_var x) xs ;
Format.fprintf fmt " }@]" ;
end
let debugp = QED.debug
type env = Pretty.env
let env xs = Pretty.known Pretty.empty xs
let marker = Pretty.marks
let mark_e = QED.mark
let mark_p = QED.mark
let define f env m =
List.fold_left
(fun env t ->
let x,env_x = Pretty.fresh env t in
f env x t ; env_x)
env (QED.defs m)
let pp_eterm = Pretty.pp_term
let pp_epred = Pretty.pp_term
module Pmap = Tmap
module Pset = Tset
let set_builtin_1 f r =
set_builtin f (function [e] -> r e | _ -> raise Not_found)
let set_builtin_2 f r =
set_builtin f (function [a;b] -> r a b | _ -> raise Not_found)
let set_builtin_2' f r =
set_builtin' f (function [a;b] -> r a b | _ -> raise Not_found)
let set_builtin_eqp = set_builtin_eq
end
open F
module N = struct
let ( + ) = e_add
let ( ~-: ) x = e_sub e_zero x
let ( - ) = e_sub
let ( * ) = e_mul
let ( / ) = e_div
let ( mod ) = e_mod
let ( = ) = p_equal
let ( < ) = p_lt
let ( > ) x y = p_lt y x
let ( <= ) = p_leq
let ( >= ) x y = p_leq y x
let ( <> ) = p_neq
let ( ==> ) = p_imply
let ( &&: ) = p_and
let ( ||: ) = p_or
let not = p_not
let ( $ ) = e_fun
let ( $$ ) = p_call
end
type gamma = {
mutable hyps : pred list ;
}
let cpool = Context.create "Lang.pool"
let cgamma = Context.create "Lang.gamma"
let add_vars pool = function
| None -> ()
| Some xs -> F.add_vars pool xs
let new_pool ?copy ?(vars = Vars.empty) () =
let pool = F.pool ?copy () in
F.add_vars pool vars ; pool
let new_gamma ?copy () =
match copy with
| None -> { hyps=[] }
| Some g -> { hyps = g.hyps }
let get_pool () = Context.get cpool
let get_gamma () = Context.get cgamma
let has_gamma () = Context.defined cgamma
let freshvar ?basename tau = F.fresh (Context.get cpool) ?basename tau
let freshen x = F.alpha (Context.get cpool) x
let local ?pool ?vars ?gamma f =
let pool = match pool with None -> F.pool () | Some p -> p in
add_vars pool vars ;
let gamma = match gamma with None -> { hyps=[] } | Some g -> g in
Context.bind cpool pool (Context.bind cgamma gamma f)
let sigma () = F.sigma ~pool:(Context.get cpool) ()
let alpha () =
let sigma = sigma () in
let alpha = ref Tmap.empty in
let lookup e x =
try Tmap.find e !alpha with Not_found ->
let y = F.Subst.fresh sigma (F.tau_of_var x) in
let ey = e_var y in alpha := Tmap.add e ey !alpha; ey in
let compute e =
match F.repr e with
| Fvar x -> lookup e x
| _ -> raise Not_found in
F.Subst.add_fun sigma compute ; sigma
let subst xs vs =
let sigma = sigma () in
begin
try List.iter2 (fun x v -> F.Subst.add sigma (e_var x) v) xs vs
with Invalid_argument _ -> raise (Invalid_argument "Wp.Lang.Subst.sigma")
end ; sigma
let e_subst f =
let sigma = sigma () in
F.Subst.add_fun sigma f ; F.e_subst sigma
let p_subst f =
let sigma = sigma () in
F.Subst.add_fun sigma f ; F.p_subst sigma
let masked = ref false
let without_assume job x =
if !masked
then job x
else
try masked := true ; let y = job x in masked := false ; y
with err -> masked := false ; raise err
let assume p =
if p != p_true && not !masked then
let d = Context.get cgamma in
d.hyps <- p :: d.hyps
let hypotheses g = g.hyps
let get_hypotheses () = (Context.get cgamma).hyps
let filter_hypotheses xs =
let d = Context.get cgamma in
let vars = List.fold_right Vars.add xs Vars.empty in
let matches p = Vars.intersect vars (varsp p) in
let hs_with_vars , hs_without_vars = List.partition matches d.hyps in
d.hyps <- hs_without_vars ; hs_with_vars
(** For why3_api but circular dependency *)
module For_export = struct
type specific_equality = {
for_tau:(tau -> bool);
mk_new_eq:F.binop;
}
(** delay the create at most as possible (due to constants handling in qed) *)
let state = ref None
let init = ref (fun () -> ())
let add_init f =
let old = !init in
init := (fun () -> old (); f ())
let get_state () =
match !state with
| None ->
let st = QZERO.create () in
QZERO.in_state st !init ();
state := Some st;
st
| Some st -> st
let rebuild ?cache t = QZERO.rebuild_in_state (get_state ()) ?cache t
let set_builtin f c =
add_init (fun () -> QZERO.set_builtin ~force:true f c)
let set_builtin' f c =
add_init (fun () -> QZERO.set_builtin' ~force:true f c)
let set_builtin_eq f c =
add_init (fun () -> QZERO.set_builtin_eq ~force:true f c)
let set_builtin_leq f c =
add_init (fun () -> QZERO.set_builtin_leq ~force:true f c)
let in_state f v = QZERO.in_state (get_state ()) f v
end
exception Contradiction
class type simplifier =
object
method name : string
method copy : simplifier
method assume : F.pred -> unit
method target : F.pred -> unit
method fixpoint : unit
method infer : F.pred list
method equivalent_exp : F.term -> F.term
method weaker_hyp : F.pred -> F.pred
method equivalent_branch : F.pred -> F.pred
method stronger_goal : F.pred -> F.pred
end
let is_atomic_pred = function
| Neq _ | Eq _ | Leq _ | Lt _ | Fun _ -> true
| _ -> false
let is_literal p = match repr p with
| Not p -> is_atomic_pred (repr p)
| _ -> is_atomic_pred (repr p)
let iter_consequence_literals f_literal p =
let f_literal = (fun p -> if QED.lc_closed p then f_literal p else ()) in
let rec aux_pos p = match repr p with
| And ps -> List.iter aux_pos ps
| Not p -> aux_neg p
| Bind((Forall|Exists),_,a) -> aux_pos (QED.lc_repr a)
| rep when is_atomic_pred rep -> f_literal p
| _ -> ()
and aux_neg p = match repr p with
| Imply (hs,p) -> List.iter aux_pos hs ; aux_neg p
| Or ps -> List.iter aux_neg ps
| Not p -> aux_pos p
| Bind((Forall|Exists),_,a) -> aux_neg (QED.lc_repr a)
| rep when is_atomic_pred rep -> f_literal (e_not p)
| _ -> ()
in aux_pos p