sig
type library = string
val comp_id : Cil_types.compinfo -> string
val comp_init_id : Cil_types.compinfo -> string
val field_id : Cil_types.fieldinfo -> string
val field_init_id : Cil_types.fieldinfo -> string
val type_id : Cil_types.logic_type_info -> string
val logic_id : Cil_types.logic_info -> string
val ctor_id : Cil_types.logic_ctor_info -> string
val lemma_id : string -> string
type datakind = KValue | KInit
type adt = private
Mtype of Lang.mdt
| Mrecord of Lang.mdt * Lang.fields
| Atype of Cil_types.logic_type_info
| Comp of Cil_types.compinfo * Lang.datakind
and mdt = string Lang.extern
and 'a extern = {
ext_id : int;
ext_link : 'a;
ext_library : Lang.library;
ext_debug : string;
}
and fields = { mutable fields : Lang.field list; }
and field =
Mfield of Lang.mdt * Lang.fields * string * Lang.tau
| Cfield of Cil_types.fieldinfo * Lang.datakind
and tau = (Lang.field, Lang.adt) Qed.Logic.datatype
type t_builtin = E_mdt of Lang.mdt | E_poly of (Lang.tau list -> Lang.tau)
type lfun =
ACSL of Cil_types.logic_info
| CTOR of Cil_types.logic_ctor_info
| Model of Lang.model
and model = {
m_category : Lang.lfun Qed.Logic.category;
m_params : Qed.Logic.sort list;
m_result : Qed.Logic.sort;
m_typeof : Lang.tau option list -> Lang.tau;
m_source : Lang.source;
m_coloring : bool;
}
and source =
Generated of WpContext.context option * string
| Extern of Qed.Engine.link Lang.extern
val mem_builtin_type : name:string -> bool
val is_builtin : Cil_types.logic_type_info -> bool
val is_builtin_type : name:string -> Lang.tau -> bool
val get_builtin_type : name:string -> Lang.adt
val datatype : library:string -> string -> Lang.adt
val record :
link:string -> library:string -> (string * Lang.tau) list -> Lang.adt
val comp : Cil_types.compinfo -> Lang.adt
val comp_init : Cil_types.compinfo -> Lang.adt
val field : Lang.adt -> string -> Lang.field
val fields_of_adt : Lang.adt -> Lang.field list
val fields_of_tau : Lang.tau -> Lang.field list
val fields_of_field : Lang.field -> Lang.field list
val atype : Cil_types.logic_type_info -> Lang.tau list -> Lang.tau
val adt : Cil_types.logic_type_info -> Lang.adt
type balance = Nary | Left | Right
val extern_s :
library:Lang.library ->
?link:Qed.Engine.link ->
?category:Lang.lfun Qed.Logic.category ->
?params:Qed.Logic.sort list ->
?sort:Qed.Logic.sort ->
?result:Lang.tau ->
?coloring:bool ->
?typecheck:(Lang.tau option list -> Lang.tau) -> string -> Lang.lfun
val extern_f :
library:Lang.library ->
?link:Qed.Engine.link ->
?balance:Lang.balance ->
?category:Lang.lfun Qed.Logic.category ->
?params:Qed.Logic.sort list ->
?sort:Qed.Logic.sort ->
?result:Lang.tau ->
?coloring:bool ->
?typecheck:(Lang.tau option list -> Lang.tau) ->
('a, Stdlib.Format.formatter, unit, Lang.lfun) Stdlib.format4 -> 'a
val extern_p :
library:Lang.library ->
?bool:string ->
?prop:string ->
?link:Qed.Engine.link ->
?params:Qed.Logic.sort list -> ?coloring:bool -> unit -> Lang.lfun
val extern_fp :
library:Lang.library ->
?params:Qed.Logic.sort list ->
?link:string -> ?coloring:bool -> string -> Lang.lfun
val generated_f :
?context:bool ->
?category:Lang.lfun Qed.Logic.category ->
?params:Qed.Logic.sort list ->
?sort:Qed.Logic.sort ->
?result:Lang.tau ->
?coloring:bool ->
('a, Stdlib.Format.formatter, unit, Lang.lfun) Stdlib.format4 -> 'a
val generated_p : ?context:bool -> ?coloring:bool -> string -> Lang.lfun
val extern_t : string -> link:string -> library:Lang.library -> Lang.mdt
val tau_of_object : Ctypes.c_object -> Lang.tau
val tau_of_ctype : Cil_types.typ -> Lang.tau
val tau_of_ltype : Cil_types.logic_type -> Lang.tau
val tau_of_return : Cil_types.logic_info -> Lang.tau
val tau_of_lfun : Lang.lfun -> Lang.tau option list -> Lang.tau
val tau_of_field : Lang.field -> Lang.tau
val tau_of_record : Lang.field -> Lang.tau
val init_of_object : Ctypes.c_object -> Lang.tau
val init_of_ctype : Cil_types.typ -> Lang.tau
val t_int : Lang.tau
val t_real : Lang.tau
val t_bool : Lang.tau
val t_prop : Lang.tau
val t_addr : unit -> Lang.tau
val t_comp : Cil_types.compinfo -> Lang.tau
val t_init : Cil_types.compinfo -> Lang.tau
val t_float : Ctypes.c_float -> Lang.tau
val t_array : Lang.tau -> Lang.tau
val t_farray : Lang.tau -> Lang.tau -> Lang.tau
val t_datatype : Lang.adt -> Lang.tau list -> Lang.tau
val t_matrix : Lang.tau -> int -> Lang.tau
val pointer : Lang.tau Context.value
val floats : (Ctypes.c_float -> Lang.tau) Context.value
val poly : string list Context.value
val builtin_types : (string -> Lang.t_builtin) Context.value
val parameters : (Lang.lfun -> Qed.Logic.sort list) -> unit
val name_of_lfun : Lang.lfun -> string
val name_of_field : Lang.field -> string
val is_coloring_lfun : Lang.lfun -> bool
module ADT :
sig
type t = adt
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val debug : t -> string
val basename : t -> string
end
module Field :
sig
type t = field
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val debug : t -> string
val sort : t -> Qed.Logic.sort
end
module Fun :
sig
type t = lfun
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val debug : t -> string
val category : t -> t Qed.Logic.category
val params : t -> Qed.Logic.sort list
val sort : t -> Qed.Logic.sort
end
class virtual idprinting :
object
method datatype : Lang.ADT.t -> string
method field : Lang.Field.t -> string
method link : Lang.Fun.t -> Qed.Engine.link
method virtual sanitize : string -> string
method sanitize_field : string -> string
method sanitize_fun : string -> string
method sanitize_type : string -> string
end
module F :
sig
module QED :
sig
module ADT :
sig
type t = adt
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val debug : t -> string
val basename : t -> string
end
module Field :
sig
type t = field
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val debug : t -> string
val sort : t -> Qed.Logic.sort
end
module Fun :
sig
type t = lfun
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val debug : t -> string
val category : t -> t Qed.Logic.category
val params : t -> Qed.Logic.sort list
val sort : t -> Qed.Logic.sort
end
module Var : Qed.Logic.Variable
type term
type lc_term
module Term :
sig
type t = term
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val debug : t -> string
end
module Tset :
sig
type elt = term
type t
val empty : t
val is_empty : t -> bool
val mem : elt -> t -> bool
val find : elt -> t -> elt
val add : elt -> t -> t
val singleton : elt -> t
val remove : elt -> t -> t
val union : t -> t -> t
val inter : t -> t -> t
val diff : t -> t -> t
val compare : t -> t -> int
val equal : t -> t -> bool
val subset : t -> t -> bool
val iter : (elt -> unit) -> t -> unit
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
val for_all : (elt -> bool) -> t -> bool
val exists : (elt -> bool) -> t -> bool
val filter : (elt -> bool) -> t -> t
val partition : (elt -> bool) -> t -> t * t
val cardinal : t -> int
val elements : t -> elt list
val map : (elt -> elt) -> t -> t
val mapf : (elt -> elt option) -> t -> t
val intersect : t -> t -> bool
end
module Tmap :
sig
type key = term
type 'a t
val is_empty : 'a t -> bool
val empty : 'a t
val add : key -> 'a -> 'a t -> 'a t
val mem : key -> 'a t -> bool
val find : key -> 'a t -> 'a
val remove : key -> 'a t -> 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val iter : (key -> 'a -> unit) -> 'a t -> unit
val map : (key -> 'a -> 'b) -> 'a t -> 'b t
val mapf : (key -> 'a -> 'b option) -> 'a t -> 'b t
val mapq : (key -> 'a -> 'a option) -> 'a t -> 'a t
val filter : (key -> 'a -> bool) -> 'a t -> 'a t
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val union : (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
val inter : (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
val interf :
(key -> 'a -> 'b -> 'c option) -> 'a t -> 'b t -> 'c t
val interq :
(key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val diffq :
(key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val merge :
(key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c t
val iter2 :
(key -> 'a option -> 'b option -> unit) ->
'a t -> 'b t -> unit
val subset : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val insert :
(key -> 'a -> 'a -> 'a) -> key -> 'a -> 'a t -> 'a t
val change :
(key -> 'b -> 'a option -> 'a option) ->
key -> 'b -> 'a t -> 'a t
end
module STset :
sig
type elt = term
type t
val empty : t
val is_empty : t -> bool
val mem : elt -> t -> bool
val add : elt -> t -> t
val singleton : elt -> t
val remove : elt -> t -> t
val union : t -> t -> t
val inter : t -> t -> t
val disjoint : t -> t -> bool
val diff : t -> t -> t
val compare : t -> t -> int
val equal : t -> t -> bool
val subset : t -> t -> bool
val iter : (elt -> unit) -> t -> unit
val map : (elt -> elt) -> t -> t
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
val for_all : (elt -> bool) -> t -> bool
val exists : (elt -> bool) -> t -> bool
val filter : (elt -> bool) -> t -> t
val filter_map : (elt -> elt option) -> t -> t
val partition : (elt -> bool) -> t -> t * t
val cardinal : t -> int
val elements : t -> elt list
val min_elt : t -> elt
val min_elt_opt : t -> elt option
val max_elt : t -> elt
val max_elt_opt : t -> elt option
val choose : t -> elt
val choose_opt : t -> elt option
val split : elt -> t -> t * bool * t
val find : elt -> t -> elt
val find_opt : elt -> t -> elt option
val find_first : (elt -> bool) -> t -> elt
val find_first_opt : (elt -> bool) -> t -> elt option
val find_last : (elt -> bool) -> t -> elt
val find_last_opt : (elt -> bool) -> t -> elt option
val of_list : elt list -> t
val to_seq_from : elt -> t -> elt Seq.t
val to_seq : t -> elt Seq.t
val to_rev_seq : t -> elt Seq.t
val add_seq : elt Seq.t -> t -> t
val of_seq : elt Seq.t -> t
end
module STmap :
sig
type key = term
type +!'a t
val empty : 'a t
val is_empty : 'a t -> bool
val mem : key -> 'a t -> bool
val add : key -> 'a -> 'a t -> 'a t
val update : key -> ('a option -> 'a option) -> 'a t -> 'a t
val singleton : key -> 'a -> 'a t
val remove : key -> 'a t -> 'a t
val merge :
(key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c t
val union :
(key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val iter : (key -> 'a -> unit) -> 'a t -> unit
val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val for_all : (key -> 'a -> bool) -> 'a t -> bool
val exists : (key -> 'a -> bool) -> 'a t -> bool
val filter : (key -> 'a -> bool) -> 'a t -> 'a t
val filter_map : (key -> 'a -> 'b option) -> 'a t -> 'b t
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val cardinal : 'a t -> int
val bindings : 'a t -> (key * 'a) list
val min_binding : 'a t -> key * 'a
val min_binding_opt : 'a t -> (key * 'a) option
val max_binding : 'a t -> key * 'a
val max_binding_opt : 'a t -> (key * 'a) option
val choose : 'a t -> key * 'a
val choose_opt : 'a t -> (key * 'a) option
val split : key -> 'a t -> 'a t * 'a option * 'a t
val find : key -> 'a t -> 'a
val find_opt : key -> 'a t -> 'a option
val find_first : (key -> bool) -> 'a t -> key * 'a
val find_first_opt : (key -> bool) -> 'a t -> (key * 'a) option
val find_last : (key -> bool) -> 'a t -> key * 'a
val find_last_opt : (key -> bool) -> 'a t -> (key * 'a) option
val map : ('a -> 'b) -> 'a t -> 'b t
val mapi : (key -> 'a -> 'b) -> 'a t -> 'b t
val to_seq : 'a t -> (key * 'a) Seq.t
val to_rev_seq : 'a t -> (key * 'a) Seq.t
val to_seq_from : key -> 'a t -> (key * 'a) Seq.t
val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t
val of_seq : (key * 'a) Seq.t -> 'a t
end
type var = Var.t
type tau = (Field.t, ADT.t) Qed.Logic.datatype
module Tau :
sig
type t = tau
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val debug : t -> string
val basename : t -> string
end
module Vars :
sig
type elt = var
type t
val empty : t
val is_empty : t -> bool
val mem : elt -> t -> bool
val find : elt -> t -> elt
val add : elt -> t -> t
val singleton : elt -> t
val remove : elt -> t -> t
val union : t -> t -> t
val inter : t -> t -> t
val diff : t -> t -> t
val compare : t -> t -> int
val equal : t -> t -> bool
val subset : t -> t -> bool
val iter : (elt -> unit) -> t -> unit
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
val for_all : (elt -> bool) -> t -> bool
val exists : (elt -> bool) -> t -> bool
val filter : (elt -> bool) -> t -> t
val partition : (elt -> bool) -> t -> t * t
val cardinal : t -> int
val elements : t -> elt list
val map : (elt -> elt) -> t -> t
val mapf : (elt -> elt option) -> t -> t
val intersect : t -> t -> bool
end
module Vmap :
sig
type key = var
type 'a t
val is_empty : 'a t -> bool
val empty : 'a t
val add : key -> 'a -> 'a t -> 'a t
val mem : key -> 'a t -> bool
val find : key -> 'a t -> 'a
val remove : key -> 'a t -> 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val iter : (key -> 'a -> unit) -> 'a t -> unit
val map : (key -> 'a -> 'b) -> 'a t -> 'b t
val mapf : (key -> 'a -> 'b option) -> 'a t -> 'b t
val mapq : (key -> 'a -> 'a option) -> 'a t -> 'a t
val filter : (key -> 'a -> bool) -> 'a t -> 'a t
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val union : (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
val inter : (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
val interf :
(key -> 'a -> 'b -> 'c option) -> 'a t -> 'b t -> 'c t
val interq :
(key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val diffq :
(key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val merge :
(key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c t
val iter2 :
(key -> 'a option -> 'b option -> unit) ->
'a t -> 'b t -> unit
val subset : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val insert :
(key -> 'a -> 'a -> 'a) -> key -> 'a -> 'a t -> 'a t
val change :
(key -> 'b -> 'a option -> 'a option) ->
key -> 'b -> 'a t -> 'a t
end
type pool
val pool : ?copy:pool -> unit -> pool
val add_var : pool -> var -> unit
val add_vars : pool -> Vars.t -> unit
val add_term : pool -> term -> unit
val fresh : pool -> ?basename:string -> tau -> var
val alpha : pool -> var -> var
val tau_of_var : var -> tau
val sort_of_var : var -> Qed.Logic.sort
val base_of_var : var -> string
type 'a expression =
(Field.t, ADT.t, Fun.t, var, lc_term, 'a) Qed.Logic.term_repr
type repr = term expression
type record = (Field.t * term) list
val decide : term -> bool
val is_true : term -> Qed.Logic.maybe
val is_false : term -> Qed.Logic.maybe
val is_prop : term -> bool
val is_int : term -> bool
val is_real : term -> bool
val is_arith : term -> bool
val are_equal : term -> term -> Qed.Logic.maybe
val eval_eq : term -> term -> bool
val eval_neq : term -> term -> bool
val eval_lt : term -> term -> bool
val eval_leq : term -> term -> bool
val repr : term -> repr
val sort : term -> Qed.Logic.sort
val vars : term -> Vars.t
type path = int list
val subterm : term -> path -> term
val change_subterm : term -> path -> term -> term
val e_true : term
val e_false : term
val e_bool : bool -> term
val e_literal : bool -> term -> term
val e_int : int -> term
val e_float : float -> term
val e_zint : Z.t -> term
val e_real : Q.t -> term
val e_var : var -> term
val e_opp : term -> term
val e_times : Z.t -> term -> term
val e_sum : term list -> term
val e_prod : term list -> term
val e_add : term -> term -> term
val e_sub : term -> term -> term
val e_mul : term -> term -> term
val e_div : term -> term -> term
val e_mod : term -> term -> term
val e_eq : term -> term -> term
val e_neq : term -> term -> term
val e_leq : term -> term -> term
val e_lt : term -> term -> term
val e_imply : term list -> term -> term
val e_equiv : term -> term -> term
val e_and : term list -> term
val e_or : term list -> term
val e_not : term -> term
val e_if : term -> term -> term -> term
val e_const : tau -> term -> term
val e_get : term -> term -> term
val e_set : term -> term -> term -> term
val e_getfield : term -> Field.t -> term
val e_record : record -> term
val e_fun : ?result:tau -> Fun.t -> term list -> term
val e_repr : ?result:tau -> repr -> term
val e_forall : var list -> term -> term
val e_exists : var list -> term -> term
val e_lambda : var list -> term -> term
val e_apply : term -> term list -> term
val e_bind : Qed.Logic.binder -> var -> term -> term
val lc_open : var -> lc_term -> term
val e_unbind : var -> lc_term -> term
val e_open :
pool:pool ->
?forall:bool ->
?exists:bool ->
?lambda:bool -> term -> (Qed.Logic.binder * var) list * term
val e_close : (Qed.Logic.binder * var) list -> term -> term
type sigma
val sigma : ?pool:pool -> unit -> sigma
module Subst :
sig
type t = sigma
val create : ?pool:pool -> unit -> t
val copy : sigma -> sigma
val fresh : t -> tau -> var
val find : t -> term -> term
val filter : t -> term -> bool
val add : t -> term -> term -> unit
val add_fun : t -> (term -> term) -> unit
val add_filter : t -> (term -> bool) -> unit
val add_var : t -> var -> unit
val add_vars : t -> Vars.t -> unit
val add_term : t -> term -> unit
end
val e_subst : sigma -> term -> term
val e_subst_var : var -> term -> term -> term
val lc_vars : term -> Qed.Bvars.t
val lc_closed : term -> bool
val lc_repr : lc_term -> term
val lc_iter : (term -> unit) -> term -> unit
val f_map :
?pool:pool ->
?forall:bool ->
?exists:bool -> ?lambda:bool -> (term -> term) -> term -> term
val f_iter :
?pool:pool ->
?forall:bool ->
?exists:bool -> ?lambda:bool -> (term -> unit) -> term -> unit
val typeof :
?field:(Field.t -> tau) ->
?record:(Field.t -> tau) ->
?call:(Fun.t -> tau option list -> tau) -> term -> tau
val set_builtin :
?force:bool -> Fun.t -> (term list -> term) -> unit
val set_builtin' :
?force:bool -> Fun.t -> (term list -> tau option -> term) -> unit
val set_builtin_map :
?force:bool -> Fun.t -> (term list -> term list) -> unit
val set_builtin_get :
?force:bool ->
Fun.t -> (term list -> tau option -> term -> term) -> unit
val set_builtin_eq :
?force:bool -> Fun.t -> (term -> term -> term) -> unit
val set_builtin_leq :
?force:bool -> Fun.t -> (term -> term -> term) -> unit
val consequence : term -> term -> term
val literal : term -> bool * term
val affine : term -> term Qed.Logic.affine
val record_with : record -> (term * record) option
type t = term
val id : t -> int
val hash : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val pretty : Format.formatter -> t -> unit
val weigth : t -> int
val is_closed : t -> bool
val is_simple : t -> bool
val is_atomic : t -> bool
val is_primitive : t -> bool
val is_neutral : Fun.t -> t -> bool
val is_absorbant : Fun.t -> t -> bool
val size : t -> int
val basename : t -> string
val debug : Format.formatter -> t -> unit
val pp_id : Format.formatter -> t -> unit
val pp_rid : Format.formatter -> t -> unit
val pp_repr : Format.formatter -> repr -> unit
val is_subterm : term -> term -> bool
val shared :
?shared:(term -> bool) ->
?shareable:(term -> bool) ->
?subterms:((term -> unit) -> term -> unit) ->
term list -> term list
type marks
val marks :
?shared:(term -> bool) ->
?shareable:(term -> bool) ->
?subterms:((term -> unit) -> term -> unit) -> unit -> marks
val mark : marks -> term -> unit
val share : marks -> term -> unit
val defs : marks -> term list
end
type var = Lang.F.QED.var
type tau = Lang.F.QED.tau
type pool = Lang.F.QED.pool
module Tau = QED.Tau
module Var = QED.Var
module Vars :
sig
type elt = var
type t
val empty : t
val is_empty : t -> bool
val mem : elt -> t -> bool
val find : elt -> t -> elt
val add : elt -> t -> t
val singleton : elt -> t
val remove : elt -> t -> t
val union : t -> t -> t
val inter : t -> t -> t
val diff : t -> t -> t
val compare : t -> t -> int
val equal : t -> t -> bool
val subset : t -> t -> bool
val iter : (elt -> unit) -> t -> unit
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
val for_all : (elt -> bool) -> t -> bool
val exists : (elt -> bool) -> t -> bool
val filter : (elt -> bool) -> t -> t
val partition : (elt -> bool) -> t -> t * t
val cardinal : t -> int
val elements : t -> elt list
val map : (elt -> elt) -> t -> t
val mapf : (elt -> elt option) -> t -> t
val intersect : t -> t -> bool
end
module Vmap :
sig
type key = var
type 'a t
val is_empty : 'a t -> bool
val empty : 'a t
val add : key -> 'a -> 'a t -> 'a t
val mem : key -> 'a t -> bool
val find : key -> 'a t -> 'a
val remove : key -> 'a t -> 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val iter : (key -> 'a -> unit) -> 'a t -> unit
val map : (key -> 'a -> 'b) -> 'a t -> 'b t
val mapf : (key -> 'a -> 'b option) -> 'a t -> 'b t
val mapq : (key -> 'a -> 'a option) -> 'a t -> 'a t
val filter : (key -> 'a -> bool) -> 'a t -> 'a t
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val union : (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
val inter : (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
val interf : (key -> 'a -> 'b -> 'c option) -> 'a t -> 'b t -> 'c t
val interq : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val diffq : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val merge :
(key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c t
val iter2 :
(key -> 'a option -> 'b option -> unit) -> 'a t -> 'b t -> unit
val subset : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val insert : (key -> 'a -> 'a -> 'a) -> key -> 'a -> 'a t -> 'a t
val change :
(key -> 'b -> 'a option -> 'a option) ->
key -> 'b -> 'a t -> 'a t
end
val pool : ?copy:Lang.F.pool -> unit -> Lang.F.pool
val fresh : Lang.F.pool -> ?basename:string -> Lang.F.tau -> Lang.F.var
val alpha : Lang.F.pool -> Lang.F.var -> Lang.F.var
val add_var : Lang.F.pool -> Lang.F.var -> unit
val add_vars : Lang.F.pool -> Lang.F.Vars.t -> unit
val tau_of_var : Lang.F.var -> Lang.F.tau
type term = Lang.F.QED.term
type record = (Lang.field * Lang.F.term) list
val hash : Lang.F.term -> int
val equal : Lang.F.term -> Lang.F.term -> bool
val compare : Lang.F.term -> Lang.F.term -> int
module Tset :
sig
type elt = term
type t
val empty : t
val is_empty : t -> bool
val mem : elt -> t -> bool
val find : elt -> t -> elt
val add : elt -> t -> t
val singleton : elt -> t
val remove : elt -> t -> t
val union : t -> t -> t
val inter : t -> t -> t
val diff : t -> t -> t
val compare : t -> t -> int
val equal : t -> t -> bool
val subset : t -> t -> bool
val iter : (elt -> unit) -> t -> unit
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
val for_all : (elt -> bool) -> t -> bool
val exists : (elt -> bool) -> t -> bool
val filter : (elt -> bool) -> t -> t
val partition : (elt -> bool) -> t -> t * t
val cardinal : t -> int
val elements : t -> elt list
val map : (elt -> elt) -> t -> t
val mapf : (elt -> elt option) -> t -> t
val intersect : t -> t -> bool
end
module Tmap :
sig
type key = term
type 'a t
val is_empty : 'a t -> bool
val empty : 'a t
val add : key -> 'a -> 'a t -> 'a t
val mem : key -> 'a t -> bool
val find : key -> 'a t -> 'a
val remove : key -> 'a t -> 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val iter : (key -> 'a -> unit) -> 'a t -> unit
val map : (key -> 'a -> 'b) -> 'a t -> 'b t
val mapf : (key -> 'a -> 'b option) -> 'a t -> 'b t
val mapq : (key -> 'a -> 'a option) -> 'a t -> 'a t
val filter : (key -> 'a -> bool) -> 'a t -> 'a t
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val union : (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
val inter : (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
val interf : (key -> 'a -> 'b -> 'c option) -> 'a t -> 'b t -> 'c t
val interq : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val diffq : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val merge :
(key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c t
val iter2 :
(key -> 'a option -> 'b option -> unit) -> 'a t -> 'b t -> unit
val subset : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val insert : (key -> 'a -> 'a -> 'a) -> key -> 'a -> 'a t -> 'a t
val change :
(key -> 'b -> 'a option -> 'a option) ->
key -> 'b -> 'a t -> 'a t
end
type unop = Lang.F.term -> Lang.F.term
type binop = Lang.F.term -> Lang.F.term -> Lang.F.term
val e_zero : Lang.F.term
val e_one : Lang.F.term
val e_minus_one : Lang.F.term
val e_minus_one_real : Lang.F.term
val e_one_real : Lang.F.term
val e_zero_real : Lang.F.term
val constant : Lang.F.term -> Lang.F.term
val e_fact : int -> Lang.F.term -> Lang.F.term
val e_int64 : int64 -> Lang.F.term
val e_bigint : Integer.t -> Lang.F.term
val e_float : float -> Lang.F.term
val e_setfield :
Lang.F.term -> Lang.field -> Lang.F.term -> Lang.F.term
val e_range : Lang.F.term -> Lang.F.term -> Lang.F.term
val is_zero : Lang.F.term -> bool
val e_true : Lang.F.term
val e_false : Lang.F.term
val e_bool : bool -> Lang.F.term
val e_literal : bool -> Lang.F.term -> Lang.F.term
val e_int : int -> Lang.F.term
val e_zint : Z.t -> Lang.F.term
val e_real : Q.t -> Lang.F.term
val e_var : Lang.F.var -> Lang.F.term
val e_opp : Lang.F.term -> Lang.F.term
val e_times : Z.t -> Lang.F.term -> Lang.F.term
val e_sum : Lang.F.term list -> Lang.F.term
val e_prod : Lang.F.term list -> Lang.F.term
val e_add : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_sub : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_mul : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_div : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_mod : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_eq : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_neq : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_leq : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_lt : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_imply : Lang.F.term list -> Lang.F.term -> Lang.F.term
val e_equiv : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_and : Lang.F.term list -> Lang.F.term
val e_or : Lang.F.term list -> Lang.F.term
val e_not : Lang.F.term -> Lang.F.term
val e_if : Lang.F.term -> Lang.F.term -> Lang.F.term -> Lang.F.term
val e_const : Lang.F.tau -> Lang.F.term -> Lang.F.term
val e_get : Lang.F.term -> Lang.F.term -> Lang.F.term
val e_set : Lang.F.term -> Lang.F.term -> Lang.F.term -> Lang.F.term
val e_getfield : Lang.F.term -> Lang.Field.t -> Lang.F.term
val e_record : Lang.F.record -> Lang.F.term
val e_fun :
?result:Lang.F.tau -> Lang.Fun.t -> Lang.F.term list -> Lang.F.term
val e_bind :
Qed.Logic.binder -> Lang.F.var -> Lang.F.term -> Lang.F.term
val e_open :
pool:Lang.F.pool ->
?forall:bool ->
?exists:bool ->
?lambda:bool ->
Lang.F.term -> (Qed.Logic.binder * Lang.F.var) list * Lang.F.term
val e_close :
(Qed.Logic.binder * Lang.F.var) list -> Lang.F.term -> Lang.F.term
type pred
type cmp = Lang.F.term -> Lang.F.term -> Lang.F.pred
type operator = Lang.F.pred -> Lang.F.pred -> Lang.F.pred
module Pmap :
sig
type key = pred
type 'a t
val is_empty : 'a t -> bool
val empty : 'a t
val add : key -> 'a -> 'a t -> 'a t
val mem : key -> 'a t -> bool
val find : key -> 'a t -> 'a
val remove : key -> 'a t -> 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val iter : (key -> 'a -> unit) -> 'a t -> unit
val map : (key -> 'a -> 'b) -> 'a t -> 'b t
val mapf : (key -> 'a -> 'b option) -> 'a t -> 'b t
val mapq : (key -> 'a -> 'a option) -> 'a t -> 'a t
val filter : (key -> 'a -> bool) -> 'a t -> 'a t
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val union : (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
val inter : (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
val interf : (key -> 'a -> 'b -> 'c option) -> 'a t -> 'b t -> 'c t
val interq : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val diffq : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val merge :
(key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c t
val iter2 :
(key -> 'a option -> 'b option -> unit) -> 'a t -> 'b t -> unit
val subset : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val insert : (key -> 'a -> 'a -> 'a) -> key -> 'a -> 'a t -> 'a t
val change :
(key -> 'b -> 'a option -> 'a option) ->
key -> 'b -> 'a t -> 'a t
end
module Pset :
sig
type elt = pred
type t
val empty : t
val is_empty : t -> bool
val mem : elt -> t -> bool
val find : elt -> t -> elt
val add : elt -> t -> t
val singleton : elt -> t
val remove : elt -> t -> t
val union : t -> t -> t
val inter : t -> t -> t
val diff : t -> t -> t
val compare : t -> t -> int
val equal : t -> t -> bool
val subset : t -> t -> bool
val iter : (elt -> unit) -> t -> unit
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
val for_all : (elt -> bool) -> t -> bool
val exists : (elt -> bool) -> t -> bool
val filter : (elt -> bool) -> t -> t
val partition : (elt -> bool) -> t -> t * t
val cardinal : t -> int
val elements : t -> elt list
val map : (elt -> elt) -> t -> t
val mapf : (elt -> elt option) -> t -> t
val intersect : t -> t -> bool
end
val p_true : Lang.F.pred
val p_false : Lang.F.pred
val p_equal : Lang.F.term -> Lang.F.term -> Lang.F.pred
val p_equals : (Lang.F.term * Lang.F.term) list -> Lang.F.pred list
val p_neq : Lang.F.term -> Lang.F.term -> Lang.F.pred
val p_leq : Lang.F.term -> Lang.F.term -> Lang.F.pred
val p_lt : Lang.F.term -> Lang.F.term -> Lang.F.pred
val p_positive : Lang.F.term -> Lang.F.pred
val is_ptrue : Lang.F.pred -> Qed.Logic.maybe
val is_pfalse : Lang.F.pred -> Qed.Logic.maybe
val is_equal : Lang.F.term -> Lang.F.term -> Qed.Logic.maybe
val eqp : Lang.F.pred -> Lang.F.pred -> bool
val comparep : Lang.F.pred -> Lang.F.pred -> int
val p_bool : Lang.F.term -> Lang.F.pred
val e_prop : Lang.F.pred -> Lang.F.term
val p_bools : Lang.F.term list -> Lang.F.pred list
val e_props : Lang.F.pred list -> Lang.F.term list
val e_lift : (Lang.F.term -> Lang.F.term) -> Lang.F.pred -> Lang.F.pred
val p_lift : (Lang.F.pred -> Lang.F.pred) -> Lang.F.term -> Lang.F.term
val p_not : Lang.F.pred -> Lang.F.pred
val p_and : Lang.F.pred -> Lang.F.pred -> Lang.F.pred
val p_or : Lang.F.pred -> Lang.F.pred -> Lang.F.pred
val p_imply : Lang.F.pred -> Lang.F.pred -> Lang.F.pred
val p_equiv : Lang.F.pred -> Lang.F.pred -> Lang.F.pred
val p_hyps : Lang.F.pred list -> Lang.F.pred -> Lang.F.pred
val p_if : Lang.F.pred -> Lang.F.pred -> Lang.F.pred -> Lang.F.pred
val p_conj : Lang.F.pred list -> Lang.F.pred
val p_disj : Lang.F.pred list -> Lang.F.pred
val p_any : ('a -> Lang.F.pred) -> 'a list -> Lang.F.pred
val p_all : ('a -> Lang.F.pred) -> 'a list -> Lang.F.pred
val p_call : Lang.lfun -> Lang.F.term list -> Lang.F.pred
val p_forall : Lang.F.var list -> Lang.F.pred -> Lang.F.pred
val p_exists : Lang.F.var list -> Lang.F.pred -> Lang.F.pred
val p_bind :
Qed.Logic.binder -> Lang.F.var -> Lang.F.pred -> Lang.F.pred
type sigma
module Subst :
sig
val copy : Lang.F.sigma -> Lang.F.sigma
val find : Lang.F.sigma -> Lang.F.term -> Lang.F.term
val add : Lang.F.sigma -> Lang.F.term -> Lang.F.term -> unit
val add_fun : Lang.F.sigma -> (Lang.F.term -> Lang.F.term) -> unit
val add_filter : Lang.F.sigma -> (Lang.F.term -> bool) -> unit
end
val e_subst : Lang.F.sigma -> Lang.F.term -> Lang.F.term
val p_subst : Lang.F.sigma -> Lang.F.pred -> Lang.F.pred
val p_subst_var :
Lang.F.var -> Lang.F.term -> Lang.F.pred -> Lang.F.pred
val e_vars : Lang.F.term -> Lang.F.var list
val p_vars : Lang.F.pred -> Lang.F.var list
val p_close : Lang.F.pred -> Lang.F.pred
val pp_tau : Stdlib.Format.formatter -> Lang.F.tau -> unit
val pp_var : Stdlib.Format.formatter -> Lang.F.var -> unit
val pp_vars : Stdlib.Format.formatter -> Lang.F.Vars.t -> unit
val pp_term : Stdlib.Format.formatter -> Lang.F.term -> unit
val pp_pred : Stdlib.Format.formatter -> Lang.F.pred -> unit
val debugp : Stdlib.Format.formatter -> Lang.F.pred -> unit
type env
val context_pp : Lang.F.env Context.value
type marks = Lang.F.QED.marks
val env : Lang.F.Vars.t -> Lang.F.env
val marker : Lang.F.env -> Lang.F.marks
val mark_e : Lang.F.marks -> Lang.F.term -> unit
val mark_p : Lang.F.marks -> Lang.F.pred -> unit
val defs : Lang.F.marks -> Lang.F.term list
val define :
(Lang.F.env -> string -> Lang.F.term -> unit) ->
Lang.F.env -> Lang.F.marks -> Lang.F.env
val pp_eterm :
Lang.F.env -> Stdlib.Format.formatter -> Lang.F.term -> unit
val pp_epred :
Lang.F.env -> Stdlib.Format.formatter -> Lang.F.pred -> unit
val p_expr : Lang.F.pred -> Lang.F.pred Lang.F.QED.expression
val e_expr : Lang.F.pred -> Lang.F.term Lang.F.QED.expression
val lc_closed : Lang.F.term -> bool
val lc_iter : (Lang.F.term -> unit) -> Lang.F.term -> unit
val decide : Lang.F.term -> bool
val basename : Lang.F.term -> string
val is_true : Lang.F.term -> Qed.Logic.maybe
val is_false : Lang.F.term -> Qed.Logic.maybe
val is_prop : Lang.F.term -> bool
val is_int : Lang.F.term -> bool
val is_real : Lang.F.term -> bool
val is_arith : Lang.F.term -> bool
val is_closed : Lang.F.term -> bool
val is_simple : Lang.F.term -> bool
val is_atomic : Lang.F.term -> bool
val is_primitive : Lang.F.term -> bool
val is_neutral : Lang.Fun.t -> Lang.F.term -> bool
val is_absorbant : Lang.Fun.t -> Lang.F.term -> bool
val record_with : Lang.F.record -> (Lang.F.term * Lang.F.record) option
val are_equal : Lang.F.term -> Lang.F.term -> Qed.Logic.maybe
val eval_eq : Lang.F.term -> Lang.F.term -> bool
val eval_neq : Lang.F.term -> Lang.F.term -> bool
val eval_lt : Lang.F.term -> Lang.F.term -> bool
val eval_leq : Lang.F.term -> Lang.F.term -> bool
val repr : Lang.F.term -> Lang.F.QED.repr
val sort : Lang.F.term -> Qed.Logic.sort
val vars : Lang.F.term -> Lang.F.Vars.t
val varsp : Lang.F.pred -> Lang.F.Vars.t
val occurs : Lang.F.var -> Lang.F.term -> bool
val occursp : Lang.F.var -> Lang.F.pred -> bool
val intersect : Lang.F.term -> Lang.F.term -> bool
val intersectp : Lang.F.pred -> Lang.F.pred -> bool
val is_subterm : Lang.F.term -> Lang.F.term -> bool
val typeof :
?field:(Lang.Field.t -> Lang.F.tau) ->
?record:(Lang.Field.t -> Lang.F.tau) ->
?call:(Lang.Fun.t -> Lang.F.tau option list -> Lang.F.tau) ->
Lang.F.term -> Lang.F.tau
val set_builtin :
Lang.lfun -> (Lang.F.term list -> Lang.F.term) -> unit
val set_builtin_get :
Lang.lfun ->
(Lang.F.term list -> Lang.F.tau option -> Lang.F.term -> Lang.F.term) ->
unit
val set_builtin_1 : Lang.lfun -> Lang.F.unop -> unit
val set_builtin_2 : Lang.lfun -> Lang.F.binop -> unit
val set_builtin_2' :
Lang.lfun ->
(Lang.F.term -> Lang.F.term -> Lang.F.tau option -> Lang.F.term) ->
unit
val set_builtin_eq : Lang.lfun -> Lang.F.binop -> unit
val set_builtin_leq : Lang.lfun -> Lang.F.binop -> unit
val set_builtin_eqp : Lang.lfun -> Lang.F.cmp -> unit
val release : unit -> unit
end
module N :
sig
val ( + ) : Lang.F.binop
val ( - ) : Lang.F.binop
val ( ~- ) : Lang.F.unop
val ( * ) : Lang.F.binop
val ( / ) : Lang.F.binop
val ( mod ) : Lang.F.binop
val ( = ) : Lang.F.cmp
val ( < ) : Lang.F.cmp
val ( > ) : Lang.F.cmp
val ( <= ) : Lang.F.cmp
val ( >= ) : Lang.F.cmp
val ( <> ) : Lang.F.cmp
val ( ==> ) : Lang.F.operator
val ( && ) : Lang.F.operator
val ( || ) : Lang.F.operator
val not : Lang.F.pred -> Lang.F.pred
val ( $ ) :
?result:Lang.tau -> Lang.lfun -> Lang.F.term list -> Lang.F.term
val ( $$ ) : Lang.lfun -> Lang.F.term list -> Lang.F.pred
end
type gamma
val new_pool :
?copy:Lang.F.pool -> ?vars:Lang.F.Vars.t -> unit -> Lang.F.pool
val new_gamma : ?copy:Lang.gamma -> unit -> Lang.gamma
val local :
?pool:Lang.F.pool ->
?vars:Lang.F.Vars.t -> ?gamma:Lang.gamma -> ('a -> 'b) -> 'a -> 'b
val freshvar : ?basename:string -> Lang.F.tau -> Lang.F.var
val freshen : Lang.F.var -> Lang.F.var
val assume : Lang.F.pred -> unit
val without_assume : ('a -> 'b) -> 'a -> 'b
val hypotheses : Lang.gamma -> Lang.F.pred list
val get_pool : unit -> Lang.F.pool
val get_gamma : unit -> Lang.gamma
val has_gamma : unit -> bool
val get_hypotheses : unit -> Lang.F.pred list
val filter_hypotheses : Lang.F.var list -> Lang.F.pred list
val sigma : unit -> Lang.F.sigma
val alpha : unit -> Lang.F.sigma
val subst : Lang.F.var list -> Lang.F.term list -> Lang.F.sigma
val e_subst : (Lang.F.term -> Lang.F.term) -> Lang.F.term -> Lang.F.term
val p_subst : (Lang.F.term -> Lang.F.term) -> Lang.F.pred -> Lang.F.pred
exception Contradiction
val is_literal : Lang.F.term -> bool
val iter_consequence_literals :
(Lang.F.term -> unit) -> Lang.F.term -> unit
class type simplifier =
object
method assume : Lang.F.pred -> unit
method copy : Lang.simplifier
method equivalent_branch : Lang.F.pred -> Lang.F.pred
method equivalent_exp : Lang.F.term -> Lang.F.term
method fixpoint : unit
method infer : Lang.F.pred list
method name : string
method stronger_goal : Lang.F.pred -> Lang.F.pred
method target : Lang.F.pred -> unit
method weaker_hyp : Lang.F.pred -> Lang.F.pred
end
module For_export :
sig
type specific_equality = {
for_tau : Lang.F.tau -> bool;
mk_new_eq : Lang.F.binop;
}
val rebuild :
?cache:Lang.F.term Lang.F.Tmap.t ->
Lang.F.term -> Lang.F.term * Lang.F.term Lang.F.Tmap.t
val set_builtin :
Lang.Fun.t -> (Lang.F.term list -> Lang.F.term) -> unit
val set_builtin' :
Lang.Fun.t ->
(Lang.F.term list -> Lang.F.tau option -> Lang.F.term) -> unit
val set_builtin_eq :
Lang.Fun.t -> (Lang.F.term -> Lang.F.term -> Lang.F.term) -> unit
val set_builtin_leq :
Lang.Fun.t -> (Lang.F.term -> Lang.F.term -> Lang.F.term) -> unit
val in_state : ('a -> 'b) -> 'a -> 'b
end
end