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 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 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 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_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 fresh : t -> tau -> var
val get : t -> term -> term
val filter : t -> term -> bool
val add : t -> term -> term -> unit
val add_map : t -> term Tmap.t -> 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 = Wp.Lang.F.QED.var
type tau = Wp.Lang.F.QED.tau
type pool = Wp.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:Wp.Lang.F.pool -> unit -> Wp.Lang.F.pool
val fresh :
Wp.Lang.F.pool -> ?basename:string -> Wp.Lang.F.tau -> Wp.Lang.F.var
val alpha : Wp.Lang.F.pool -> Wp.Lang.F.var -> Wp.Lang.F.var
val add_var : Wp.Lang.F.pool -> Wp.Lang.F.var -> unit
val add_vars : Wp.Lang.F.pool -> Wp.Lang.F.Vars.t -> unit
val tau_of_var : Wp.Lang.F.var -> Wp.Lang.F.tau
type term = Wp.Lang.F.QED.term
type record = (Wp.Lang.field * Wp.Lang.F.term) list
val hash : Wp.Lang.F.term -> int
val equal : Wp.Lang.F.term -> Wp.Lang.F.term -> bool
val compare : Wp.Lang.F.term -> Wp.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 = Wp.Lang.F.term -> Wp.Lang.F.term
type binop = Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_zero : Wp.Lang.F.term
val e_one : Wp.Lang.F.term
val e_minus_one : Wp.Lang.F.term
val e_minus_one_real : Wp.Lang.F.term
val e_one_real : Wp.Lang.F.term
val e_zero_real : Wp.Lang.F.term
val constant : Wp.Lang.F.term -> Wp.Lang.F.term
val e_fact : int -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_int64 : int64 -> Wp.Lang.F.term
val e_bigint : Integer.t -> Wp.Lang.F.term
val e_float : float -> Wp.Lang.F.term
val e_setfield :
Wp.Lang.F.term -> Wp.Lang.field -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_range : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val is_zero : Wp.Lang.F.term -> bool
val e_true : Wp.Lang.F.term
val e_false : Wp.Lang.F.term
val e_bool : bool -> Wp.Lang.F.term
val e_literal : bool -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_int : int -> Wp.Lang.F.term
val e_zint : Z.t -> Wp.Lang.F.term
val e_real : Q.t -> Wp.Lang.F.term
val e_var : Wp.Lang.F.var -> Wp.Lang.F.term
val e_opp : Wp.Lang.F.term -> Wp.Lang.F.term
val e_times : Z.t -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_sum : Wp.Lang.F.term list -> Wp.Lang.F.term
val e_prod : Wp.Lang.F.term list -> Wp.Lang.F.term
val e_add : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_sub : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_mul : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_div : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_mod : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_eq : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_neq : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_leq : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_lt : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_imply : Wp.Lang.F.term list -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_equiv : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_and : Wp.Lang.F.term list -> Wp.Lang.F.term
val e_or : Wp.Lang.F.term list -> Wp.Lang.F.term
val e_not : Wp.Lang.F.term -> Wp.Lang.F.term
val e_if :
Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_const : Wp.Lang.F.tau -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_get : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_set :
Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_getfield : Wp.Lang.F.term -> Wp.Lang.Field.t -> Wp.Lang.F.term
val e_record : Wp.Lang.F.record -> Wp.Lang.F.term
val e_fun :
?result:Wp.Lang.F.tau ->
Wp.Lang.Fun.t -> Wp.Lang.F.term list -> Wp.Lang.F.term
val e_bind :
Qed.Logic.binder -> Wp.Lang.F.var -> Wp.Lang.F.term -> Wp.Lang.F.term
val e_open :
pool:Wp.Lang.F.pool ->
?forall:bool ->
?exists:bool ->
?lambda:bool ->
Wp.Lang.F.term ->
(Qed.Logic.binder * Wp.Lang.F.var) list * Wp.Lang.F.term
val e_close :
(Qed.Logic.binder * Wp.Lang.F.var) list ->
Wp.Lang.F.term -> Wp.Lang.F.term
type pred
type cmp = Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.pred
type operator = Wp.Lang.F.pred -> Wp.Lang.F.pred -> Wp.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 : Wp.Lang.F.pred
val p_false : Wp.Lang.F.pred
val p_equal : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.pred
val p_equals :
(Wp.Lang.F.term * Wp.Lang.F.term) list -> Wp.Lang.F.pred list
val p_neq : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.pred
val p_leq : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.pred
val p_lt : Wp.Lang.F.term -> Wp.Lang.F.term -> Wp.Lang.F.pred
val p_positive : Wp.Lang.F.term -> Wp.Lang.F.pred
val is_ptrue : Wp.Lang.F.pred -> Qed.Logic.maybe
val is_pfalse : Wp.Lang.F.pred -> Qed.Logic.maybe
val is_equal : Wp.Lang.F.term -> Wp.Lang.F.term -> Qed.Logic.maybe
val eqp : Wp.Lang.F.pred -> Wp.Lang.F.pred -> bool
val comparep : Wp.Lang.F.pred -> Wp.Lang.F.pred -> int
val p_bool : Wp.Lang.F.term -> Wp.Lang.F.pred
val e_prop : Wp.Lang.F.pred -> Wp.Lang.F.term
val p_bools : Wp.Lang.F.term list -> Wp.Lang.F.pred list
val e_props : Wp.Lang.F.pred list -> Wp.Lang.F.term list
val lift :
(Wp.Lang.F.term -> Wp.Lang.F.term) -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_not : Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_and : Wp.Lang.F.pred -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_or : Wp.Lang.F.pred -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_imply : Wp.Lang.F.pred -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_equiv : Wp.Lang.F.pred -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_hyps : Wp.Lang.F.pred list -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_if :
Wp.Lang.F.pred -> Wp.Lang.F.pred -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_conj : Wp.Lang.F.pred list -> Wp.Lang.F.pred
val p_disj : Wp.Lang.F.pred list -> Wp.Lang.F.pred
val p_any : ('a -> Wp.Lang.F.pred) -> 'a list -> Wp.Lang.F.pred
val p_all : ('a -> Wp.Lang.F.pred) -> 'a list -> Wp.Lang.F.pred
val p_call : Wp.Lang.lfun -> Wp.Lang.F.term list -> Wp.Lang.F.pred
val p_forall : Wp.Lang.F.var list -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_exists : Wp.Lang.F.var list -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_bind :
Qed.Logic.binder -> Wp.Lang.F.var -> Wp.Lang.F.pred -> Wp.Lang.F.pred
type sigma
module Subst :
sig
val get : Wp.Lang.F.sigma -> Wp.Lang.F.term -> Wp.Lang.F.term
val add : Wp.Lang.F.sigma -> Wp.Lang.F.term -> Wp.Lang.F.term -> unit
val add_map :
Wp.Lang.F.sigma -> Wp.Lang.F.term Wp.Lang.F.Tmap.t -> unit
val add_fun :
Wp.Lang.F.sigma -> (Wp.Lang.F.term -> Wp.Lang.F.term) -> unit
val add_filter : Wp.Lang.F.sigma -> (Wp.Lang.F.term -> bool) -> unit
end
val e_subst : Wp.Lang.F.sigma -> Wp.Lang.F.term -> Wp.Lang.F.term
val p_subst : Wp.Lang.F.sigma -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val p_subst_var :
Wp.Lang.F.var -> Wp.Lang.F.term -> Wp.Lang.F.pred -> Wp.Lang.F.pred
val e_vars : Wp.Lang.F.term -> Wp.Lang.F.var list
val p_vars : Wp.Lang.F.pred -> Wp.Lang.F.var list
val p_close : Wp.Lang.F.pred -> Wp.Lang.F.pred
val pp_tau : Stdlib.Format.formatter -> Wp.Lang.F.tau -> unit
val pp_var : Stdlib.Format.formatter -> Wp.Lang.F.var -> unit
val pp_vars : Stdlib.Format.formatter -> Wp.Lang.F.Vars.t -> unit
val pp_term : Stdlib.Format.formatter -> Wp.Lang.F.term -> unit
val pp_pred : Stdlib.Format.formatter -> Wp.Lang.F.pred -> unit
val debugp : Stdlib.Format.formatter -> Wp.Lang.F.pred -> unit
type env
val context_pp : Wp.Lang.F.env Wp.Context.value
type marks = Wp.Lang.F.QED.marks
val env : Wp.Lang.F.Vars.t -> Wp.Lang.F.env
val marker : Wp.Lang.F.env -> Wp.Lang.F.marks
val mark_e : Wp.Lang.F.marks -> Wp.Lang.F.term -> unit
val mark_p : Wp.Lang.F.marks -> Wp.Lang.F.pred -> unit
val defs : Wp.Lang.F.marks -> Wp.Lang.F.term list
val define :
(Wp.Lang.F.env -> string -> Wp.Lang.F.term -> unit) ->
Wp.Lang.F.env -> Wp.Lang.F.marks -> Wp.Lang.F.env
val pp_eterm :
Wp.Lang.F.env -> Stdlib.Format.formatter -> Wp.Lang.F.term -> unit
val pp_epred :
Wp.Lang.F.env -> Stdlib.Format.formatter -> Wp.Lang.F.pred -> unit
val p_expr : Wp.Lang.F.pred -> Wp.Lang.F.pred Wp.Lang.F.QED.expression
val e_expr : Wp.Lang.F.pred -> Wp.Lang.F.term Wp.Lang.F.QED.expression
val lc_closed : Wp.Lang.F.term -> bool
val lc_iter : (Wp.Lang.F.term -> unit) -> Wp.Lang.F.term -> unit
val decide : Wp.Lang.F.term -> bool
val basename : Wp.Lang.F.term -> string
val is_true : Wp.Lang.F.term -> Qed.Logic.maybe
val is_false : Wp.Lang.F.term -> Qed.Logic.maybe
val is_prop : Wp.Lang.F.term -> bool
val is_int : Wp.Lang.F.term -> bool
val is_real : Wp.Lang.F.term -> bool
val is_arith : Wp.Lang.F.term -> bool
val is_closed : Wp.Lang.F.term -> bool
val is_simple : Wp.Lang.F.term -> bool
val is_atomic : Wp.Lang.F.term -> bool
val is_primitive : Wp.Lang.F.term -> bool
val is_neutral : Wp.Lang.Fun.t -> Wp.Lang.F.term -> bool
val is_absorbant : Wp.Lang.Fun.t -> Wp.Lang.F.term -> bool
val record_with :
Wp.Lang.F.record -> (Wp.Lang.F.term * Wp.Lang.F.record) option
val are_equal : Wp.Lang.F.term -> Wp.Lang.F.term -> Qed.Logic.maybe
val eval_eq : Wp.Lang.F.term -> Wp.Lang.F.term -> bool
val eval_neq : Wp.Lang.F.term -> Wp.Lang.F.term -> bool
val eval_lt : Wp.Lang.F.term -> Wp.Lang.F.term -> bool
val eval_leq : Wp.Lang.F.term -> Wp.Lang.F.term -> bool
val repr : Wp.Lang.F.term -> Wp.Lang.F.QED.repr
val sort : Wp.Lang.F.term -> Qed.Logic.sort
val vars : Wp.Lang.F.term -> Wp.Lang.F.Vars.t
val varsp : Wp.Lang.F.pred -> Wp.Lang.F.Vars.t
val occurs : Wp.Lang.F.var -> Wp.Lang.F.term -> bool
val occursp : Wp.Lang.F.var -> Wp.Lang.F.pred -> bool
val intersect : Wp.Lang.F.term -> Wp.Lang.F.term -> bool
val intersectp : Wp.Lang.F.pred -> Wp.Lang.F.pred -> bool
val is_subterm : Wp.Lang.F.term -> Wp.Lang.F.term -> bool
val typeof :
?field:(Wp.Lang.Field.t -> Wp.Lang.F.tau) ->
?record:(Wp.Lang.Field.t -> Wp.Lang.F.tau) ->
?call:(Wp.Lang.Fun.t -> Wp.Lang.F.tau option list -> Wp.Lang.F.tau) ->
Wp.Lang.F.term -> Wp.Lang.F.tau
val set_builtin :
Wp.Lang.lfun -> (Wp.Lang.F.term list -> Wp.Lang.F.term) -> unit
val set_builtin_get :
Wp.Lang.lfun ->
(Wp.Lang.F.term list ->
Wp.Lang.F.tau option -> Wp.Lang.F.term -> Wp.Lang.F.term) ->
unit
val set_builtin_1 : Wp.Lang.lfun -> Wp.Lang.F.unop -> unit
val set_builtin_2 : Wp.Lang.lfun -> Wp.Lang.F.binop -> unit
val set_builtin_2' :
Wp.Lang.lfun ->
(Wp.Lang.F.term ->
Wp.Lang.F.term -> Wp.Lang.F.tau option -> Wp.Lang.F.term) ->
unit
val set_builtin_eq : Wp.Lang.lfun -> Wp.Lang.F.binop -> unit
val set_builtin_leq : Wp.Lang.lfun -> Wp.Lang.F.binop -> unit
val set_builtin_eqp : Wp.Lang.lfun -> Wp.Lang.F.cmp -> unit
val release : unit -> unit
end