sig
module Z :
sig
type t = Integer.t
val zero : t
val one : t
val minus_one : t
val succ : t -> t
val pred : t -> t
val neg : t -> t
val add : t -> t -> t
val sub : t -> t -> t
val mul : t -> t -> t
val div : t -> t -> t
val rem : t -> t -> t
val div_rem : t -> t -> t * t
val equal : t -> t -> bool
val leq : t -> t -> bool
val lt : t -> t -> bool
val of_int : int -> t
val of_string : string -> t
val to_string : t -> string
val hash : t -> int
val compare : t -> t -> int
end
module QED :
sig
module Z :
sig
type t = Integer.t
val zero : t
val one : t
val minus_one : t
val succ : t -> t
val pred : t -> t
val neg : t -> t
val add : t -> t -> t
val sub : t -> t -> t
val mul : t -> t -> t
val div : t -> t -> t
val rem : t -> t -> t
val div_rem : t -> t -> t * t
val equal : t -> t -> bool
val leq : t -> t -> bool
val lt : t -> t -> bool
val of_int : int -> t
val of_string : string -> t
val to_string : t -> string
val hash : t -> int
val compare : t -> t -> int
end
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 bind
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 =
(Z.t, Field.t, ADT.t, Fun.t, var, bind, 'a) Qed.Logic.term_repr
type repr = term expression
type path = int list
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
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_zint : Z.t -> term
val e_real : Qed.R.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_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 : Fun.t -> term list -> term
val e_repr : 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_bind : Qed.Logic.binder -> var -> term -> term
val e_apply : term -> term list -> term
type sigma
val sigma : unit -> sigma
val e_subst : ?sigma:sigma -> (term -> term) -> term -> term
val e_subst_var : var -> term -> term -> term
val lc_bind : var -> term -> bind
val lc_open : var -> bind -> term
val lc_open_term : term -> bind -> term
val lc_closed : term -> bool
val lc_closed_at : int -> term -> bool
val lc_vars : term -> Qed.Bvars.t
val lc_repr : bind -> term
val binders : term -> Qed.Logic.binder list
val e_map : pool -> (term -> term) -> term -> term
val e_iter : pool -> (term -> unit) -> term -> unit
val f_map : (int -> term -> term) -> int -> term -> term
val f_iter : (int -> term -> unit) -> int -> term -> unit
val lc_map : (term -> term) -> term -> term
val lc_iter : (term -> unit) -> term -> unit
val typeof :
?field:(Field.t -> tau) ->
?record:(Field.t -> tau) -> ?call:(Fun.t -> tau) -> term -> tau
val set_builtin : Fun.t -> (term list -> term) -> unit
val set_builtin_eq : Fun.t -> (term -> term -> term) -> unit
val set_builtin_leq : Fun.t -> (term -> term -> term) -> unit
val consequence : term -> term -> term
val literal : term -> bool * term
val congruence_eq : term -> term -> (term * term) list option
val congruence_neq : term -> term -> (term * term) list option
val flattenable : term -> bool
val flattens : term -> term -> bool
val flatten : term -> term list
val affine : term -> (Z.t, 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
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
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 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_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_mthfloat : float -> Lang.F.term
val e_hexfloat : 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 : Lang.F.Z.t -> Lang.F.term
val e_real : Qed.R.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 : Lang.F.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_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 : 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
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_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 lift : (Lang.F.term -> Lang.F.term) -> Lang.F.pred -> Lang.F.pred
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 = Lang.F.QED.sigma
val sigma : unit -> Lang.F.sigma
val e_subst :
?sigma:Lang.F.sigma ->
(Lang.F.term -> Lang.F.term) -> Lang.F.term -> Lang.F.term
val p_subst :
?sigma:Lang.F.sigma ->
(Lang.F.term -> Lang.F.term) -> Lang.F.pred -> Lang.F.pred
val p_apply : 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 : Format.formatter -> Lang.F.tau -> unit
val pp_var : Format.formatter -> Lang.F.var -> unit
val pp_vars : Format.formatter -> Lang.F.Vars.t -> unit
val pp_term : Format.formatter -> Lang.F.term -> unit
val pp_pred : Format.formatter -> Lang.F.pred -> unit
val debugp : Format.formatter -> Lang.F.pred -> unit
type env
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 -> Format.formatter -> Lang.F.term -> unit
val pp_epred : Lang.F.env -> 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 p_iter :
(Lang.F.pred -> unit) -> (Lang.F.term -> unit) -> Lang.F.pred -> unit
val lc_closed : Lang.F.term -> bool
val lc_iter : (Lang.F.term -> unit) -> Lang.F.term -> unit
val lc_map : (Lang.F.term -> Lang.F.term) -> Lang.F.term -> Lang.F.term
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) -> Lang.F.term -> Lang.F.tau
val set_builtin : Lang.lfun -> (Lang.F.term list -> 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_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
module Check :
sig
val reset : unit -> unit
val set : string -> unit
val is_set : unit -> bool
val iter :
(qed:Lang.F.term -> raw:Lang.F.term -> goal:Lang.F.pred -> unit) ->
unit
end
end