(************************************************************************) (* * The Coq Proof Assistant / The Coq Development Team *) (* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) (* bool [@@ocaml.deprecated "Alias for [Constr.isRel]"] val isRelN : int -> constr -> bool [@@ocaml.deprecated "Alias for [Constr.isRelN]"] val isVar : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isVar]"] val isVarId : Id.t -> constr -> bool [@@ocaml.deprecated "Alias for [Constr.isVarId]"] val isInd : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isInd]"] val isEvar : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isEvar]"] val isMeta : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isMeta]"] val isEvar_or_Meta : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isEvar_or_Meta]"] val isSort : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isSort]"] val isCast : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isCast]"] val isApp : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isApp]"] val isLambda : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isLambda]"] val isLetIn : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isletIn]"] val isProd : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isProp]"] val isConst : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isConst]"] val isConstruct : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isConstruct]"] val isFix : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isFix]"] val isCoFix : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isCoFix]"] val isCase : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isCase]"] val isProj : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isProj]"] val is_Prop : constr -> bool [@@ocaml.deprecated "Alias for [Constr.is_Prop]"] val is_Set : constr -> bool [@@ocaml.deprecated "Alias for [Constr.is_Set]"] val isprop : constr -> bool [@@ocaml.deprecated "Alias for [Constr.isprop]"] val is_Type : constr -> bool [@@ocaml.deprecated "Alias for [Constr.is_Type]"] val iskind : constr -> bool [@@ocaml.deprecated "Alias for [Constr.is_kind]"] val is_small : Sorts.t -> bool [@@ocaml.deprecated "Alias for [Constr.is_small]"] (** {5 Term destructors } *) (** Destructor operations are partial functions and @raise DestKO if the term has not the expected form. *) (** Destructs a de Bruijn index *) val destRel : constr -> int [@@ocaml.deprecated "Alias for [Constr.destRel]"] (** Destructs an existential variable *) val destMeta : constr -> metavariable [@@ocaml.deprecated "Alias for [Constr.destMeta]"] (** Destructs a variable *) val destVar : constr -> Id.t [@@ocaml.deprecated "Alias for [Constr.destVar]"] (** Destructs a sort. [is_Prop] recognizes the sort {% \textsf{%}Prop{% }%}, whether [isprop] recognizes both {% \textsf{%}Prop{% }%} and {% \textsf{%}Set{% }%}. *) val destSort : constr -> Sorts.t [@@ocaml.deprecated "Alias for [Constr.destSort]"] (** Destructs a casted term *) val destCast : constr -> constr * cast_kind * constr [@@ocaml.deprecated "Alias for [Constr.destCast]"] (** Destructs the product {% $ %}(x:t_1)t_2{% $ %} *) val destProd : types -> Name.t * types * types [@@ocaml.deprecated "Alias for [Constr.destProd]"] (** Destructs the abstraction {% $ %}[x:t_1]t_2{% $ %} *) val destLambda : constr -> Name.t * types * constr [@@ocaml.deprecated "Alias for [Constr.destLambda]"] (** Destructs the let {% $ %}[x:=b:t_1]t_2{% $ %} *) val destLetIn : constr -> Name.t * constr * types * constr [@@ocaml.deprecated "Alias for [Constr.destLetIn]"] (** Destructs an application *) val destApp : constr -> constr * constr array [@@ocaml.deprecated "Alias for [Constr.destApp]"] (** Obsolete synonym of destApp *) val destApplication : constr -> constr * constr array [@@ocaml.deprecated "Alias for [Constr.destApplication]"] (** Decompose any term as an applicative term; the list of args can be empty *) val decompose_app : constr -> constr * constr list [@@ocaml.deprecated "Alias for [Constr.decompose_app]"] (** Same as [decompose_app], but returns an array. *) val decompose_appvect : constr -> constr * constr array [@@ocaml.deprecated "Alias for [Constr.decompose_appvect]"] (** Destructs a constant *) val destConst : constr -> Constant.t Univ.puniverses [@@ocaml.deprecated "Alias for [Constr.destConst]"] (** Destructs an existential variable *) val destEvar : constr -> existential [@@ocaml.deprecated "Alias for [Constr.destEvar]"] (** Destructs a (co)inductive type *) val destInd : constr -> inductive Univ.puniverses [@@ocaml.deprecated "Alias for [Constr.destInd]"] (** Destructs a constructor *) val destConstruct : constr -> constructor Univ.puniverses [@@ocaml.deprecated "Alias for [Constr.destConstruct]"] (** Destructs a [match c as x in I args return P with ... | Ci(...yij...) => ti | ... end] (or [let (..y1i..) := c as x in I args return P in t1], or [if c then t1 else t2]) @return [(info,c,fun args x => P,[|...|fun yij => ti| ...|])] where [info] is pretty-printing information *) val destCase : constr -> case_info * constr * constr * constr array [@@ocaml.deprecated "Alias for [Constr.destCase]"] (** Destructs a projection *) val destProj : constr -> Projection.t * constr [@@ocaml.deprecated "Alias for [Constr.destProj]"] (** Destructs the {% $ %}i{% $ %}th function of the block [Fixpoint f{_ 1} ctx{_ 1} = b{_ 1} with f{_ 2} ctx{_ 2} = b{_ 2} ... with f{_ n} ctx{_ n} = b{_ n}], where the length of the {% $ %}j{% $ %}th context is {% $ %}ij{% $ %}. *) val destFix : constr -> fixpoint [@@ocaml.deprecated "Alias for [Constr.destFix]"] val destCoFix : constr -> cofixpoint [@@ocaml.deprecated "Alias for [Constr.destCoFix]"] (** {5 Derived constructors} *) (** non-dependent product [t1 -> t2], an alias for [forall (_:t1), t2]. Beware [t_2] is NOT lifted. Eg: in context [A:Prop], [A->A] is built by [(mkArrow (mkRel 1) (mkRel 2))] *) val mkArrow : types -> types -> constr (** Named version of the functions from [Term]. *) val mkNamedLambda : Id.t -> types -> constr -> constr val mkNamedLetIn : Id.t -> constr -> types -> constr -> constr val mkNamedProd : Id.t -> types -> types -> types (** Constructs either [(x:t)c] or [[x=b:t]c] *) val mkProd_or_LetIn : Context.Rel.Declaration.t -> types -> types val mkProd_wo_LetIn : Context.Rel.Declaration.t -> types -> types val mkNamedProd_or_LetIn : Context.Named.Declaration.t -> types -> types val mkNamedProd_wo_LetIn : Context.Named.Declaration.t -> types -> types (** Constructs either [[x:t]c] or [[x=b:t]c] *) val mkLambda_or_LetIn : Context.Rel.Declaration.t -> constr -> constr val mkNamedLambda_or_LetIn : Context.Named.Declaration.t -> constr -> constr (** {5 Other term constructors. } *) (** [applist (f,args)] and its variants work as [mkApp] *) val applist : constr * constr list -> constr val applistc : constr -> constr list -> constr val appvect : constr * constr array -> constr val appvectc : constr -> constr array -> constr (** [prodn n l b] = [forall (x_1:T_1)...(x_n:T_n), b] where [l] is [(x_n,T_n)...(x_1,T_1)...]. *) val prodn : int -> (Name.t * constr) list -> constr -> constr (** [compose_prod l b] @return [forall (x_1:T_1)...(x_n:T_n), b] where [l] is [(x_n,T_n)...(x_1,T_1)]. Inverse of [decompose_prod]. *) val compose_prod : (Name.t * constr) list -> constr -> constr (** [lamn n l b] @return [fun (x_1:T_1)...(x_n:T_n) => b] where [l] is [(x_n,T_n)...(x_1,T_1)...]. *) val lamn : int -> (Name.t * constr) list -> constr -> constr (** [compose_lam l b] @return [fun (x_1:T_1)...(x_n:T_n) => b] where [l] is [(x_n,T_n)...(x_1,T_1)]. Inverse of [it_destLam] *) val compose_lam : (Name.t * constr) list -> constr -> constr (** [to_lambda n l] @return [fun (x_1:T_1)...(x_n:T_n) => T] where [l] is [forall (x_1:T_1)...(x_n:T_n), T] *) val to_lambda : int -> constr -> constr (** [to_prod n l] @return [forall (x_1:T_1)...(x_n:T_n), T] where [l] is [fun (x_1:T_1)...(x_n:T_n) => T] *) val to_prod : int -> constr -> constr val it_mkLambda_or_LetIn : constr -> Context.Rel.t -> constr val it_mkProd_or_LetIn : types -> Context.Rel.t -> types (** In [lambda_applist c args], [c] is supposed to have the form [λΓ.c] with [Γ] without let-in; it returns [c] with the variables of [Γ] instantiated by [args]. *) val lambda_applist : constr -> constr list -> constr val lambda_appvect : constr -> constr array -> constr (** In [lambda_applist_assum n c args], [c] is supposed to have the form [λΓ.c] with [Γ] of length [n] and possibly with let-ins; it returns [c] with the assumptions of [Γ] instantiated by [args] and the local definitions of [Γ] expanded. *) val lambda_applist_assum : int -> constr -> constr list -> constr val lambda_appvect_assum : int -> constr -> constr array -> constr (** pseudo-reduction rule *) (** [prod_appvect] [forall (x1:B1;...;xn:Bn), B] [a1...an] @return [B[a1...an]] *) val prod_appvect : types -> constr array -> types val prod_applist : types -> constr list -> types (** In [prod_appvect_assum n c args], [c] is supposed to have the form [∀Γ.c] with [Γ] of length [n] and possibly with let-ins; it returns [c] with the assumptions of [Γ] instantiated by [args] and the local definitions of [Γ] expanded. *) val prod_appvect_assum : int -> types -> constr array -> types val prod_applist_assum : int -> types -> constr list -> types (** {5 Other term destructors. } *) (** Transforms a product term {% $ %}(x_1:T_1)..(x_n:T_n)T{% $ %} into the pair {% $ %}([(x_n,T_n);...;(x_1,T_1)],T){% $ %}, where {% $ %}T{% $ %} is not a product. *) val decompose_prod : constr -> (Name.t*constr) list * constr (** Transforms a lambda term {% $ %}[x_1:T_1]..[x_n:T_n]T{% $ %} into the pair {% $ %}([(x_n,T_n);...;(x_1,T_1)],T){% $ %}, where {% $ %}T{% $ %} is not a lambda. *) val decompose_lam : constr -> (Name.t*constr) list * constr (** Given a positive integer n, decompose a product term {% $ %}(x_1:T_1)..(x_n:T_n)T{% $ %} into the pair {% $ %}([(xn,Tn);...;(x1,T1)],T){% $ %}. Raise a user error if not enough products. *) val decompose_prod_n : int -> constr -> (Name.t * constr) list * constr (** Given a positive integer {% $ %}n{% $ %}, decompose a lambda term {% $ %}[x_1:T_1]..[x_n:T_n]T{% $ %} into the pair {% $ %}([(x_n,T_n);...;(x_1,T_1)],T){% $ %}. Raise a user error if not enough lambdas. *) val decompose_lam_n : int -> constr -> (Name.t * constr) list * constr (** Extract the premisses and the conclusion of a term of the form "(xi:Ti) ... (xj:=cj:Tj) ..., T" where T is not a product nor a let *) val decompose_prod_assum : types -> Context.Rel.t * types (** Idem with lambda's and let's *) val decompose_lam_assum : constr -> Context.Rel.t * constr (** Idem but extract the first [n] premisses, counting let-ins. *) val decompose_prod_n_assum : int -> types -> Context.Rel.t * types (** Idem for lambdas, _not_ counting let-ins *) val decompose_lam_n_assum : int -> constr -> Context.Rel.t * constr (** Idem, counting let-ins *) val decompose_lam_n_decls : int -> constr -> Context.Rel.t * constr (** Return the premisses/parameters of a type/term (let-in included) *) val prod_assum : types -> Context.Rel.t val lam_assum : constr -> Context.Rel.t (** Return the first n-th premisses/parameters of a type (let included and counted) *) val prod_n_assum : int -> types -> Context.Rel.t (** Return the first n-th premisses/parameters of a term (let included but not counted) *) val lam_n_assum : int -> constr -> Context.Rel.t (** Remove the premisses/parameters of a type/term *) val strip_prod : types -> types val strip_lam : constr -> constr (** Remove the first n-th premisses/parameters of a type/term *) val strip_prod_n : int -> types -> types val strip_lam_n : int -> constr -> constr (** Remove the premisses/parameters of a type/term (including let-in) *) val strip_prod_assum : types -> types val strip_lam_assum : constr -> constr (** {5 ... } *) (** An "arity" is a term of the form [[x1:T1]...[xn:Tn]s] with [s] a sort. Such a term can canonically be seen as the pair of a context of types and of a sort *) type arity = Context.Rel.t * Sorts.t (** Build an "arity" from its canonical form *) val mkArity : arity -> types (** Destruct an "arity" into its canonical form *) val destArity : types -> arity (** Tell if a term has the form of an arity *) val isArity : types -> bool (** {5 Kind of type} *) type ('constr, 'types) kind_of_type = | SortType of Sorts.t | CastType of 'types * 'types | ProdType of Name.t * 'types * 'types | LetInType of Name.t * 'constr * 'types * 'types | AtomicType of 'constr * 'constr array val kind_of_type : types -> (constr, types) kind_of_type (** {5 Redeclaration of stuff from module [Sorts]} *) val set_sort : Sorts.t [@@ocaml.deprecated "Alias for Sorts.set"] val prop_sort : Sorts.t [@@ocaml.deprecated "Alias for Sorts.prop"] val type1_sort : Sorts.t [@@ocaml.deprecated "Alias for Sorts.type1"] val sorts_ord : Sorts.t -> Sorts.t -> int [@@ocaml.deprecated "Alias for Sorts.compare"] val is_prop_sort : Sorts.t -> bool [@@ocaml.deprecated "Alias for Sorts.is_prop"] val family_of_sort : Sorts.t -> Sorts.family [@@ocaml.deprecated "Alias for Sorts.family"] (** {5 Redeclaration of stuff from module [Constr]} See module [Constr] for further info. *) (** {6 Term constructors. } *) val mkRel : int -> constr [@@ocaml.deprecated "Alias for Constr.mkRel"] val mkVar : Id.t -> constr [@@ocaml.deprecated "Alias for Constr.mkVar"] val mkMeta : metavariable -> constr [@@ocaml.deprecated "Alias for Constr.mkMeta"] val mkEvar : existential -> constr [@@ocaml.deprecated "Alias for Constr.mkEvar"] val mkSort : Sorts.t -> types [@@ocaml.deprecated "Alias for Constr.mkSort"] val mkProp : types [@@ocaml.deprecated "Alias for Constr.mkProp"] val mkSet : types [@@ocaml.deprecated "Alias for Constr.mkSet"] val mkType : Univ.Universe.t -> types [@@ocaml.deprecated "Alias for Constr.mkType"] val mkCast : constr * cast_kind * constr -> constr [@@ocaml.deprecated "Alias for Constr"] val mkProd : Name.t * types * types -> types [@@ocaml.deprecated "Alias for Constr"] val mkLambda : Name.t * types * constr -> constr [@@ocaml.deprecated "Alias for Constr"] val mkLetIn : Name.t * constr * types * constr -> constr [@@ocaml.deprecated "Alias for Constr"] val mkApp : constr * constr array -> constr [@@ocaml.deprecated "Alias for Constr"] val mkConst : Constant.t -> constr [@@ocaml.deprecated "Alias for Constr"] val mkProj : Projection.t * constr -> constr [@@ocaml.deprecated "Alias for Constr"] val mkInd : inductive -> constr [@@ocaml.deprecated "Alias for Constr"] val mkConstruct : constructor -> constr [@@ocaml.deprecated "Alias for Constr"] val mkConstU : Constant.t Univ.puniverses -> constr [@@ocaml.deprecated "Alias for Constr"] val mkIndU : inductive Univ.puniverses -> constr [@@ocaml.deprecated "Alias for Constr"] val mkConstructU : constructor Univ.puniverses -> constr [@@ocaml.deprecated "Alias for Constr"] val mkConstructUi : (pinductive * int) -> constr [@@ocaml.deprecated "Alias for Constr"] val mkCase : case_info * constr * constr * constr array -> constr [@@ocaml.deprecated "Alias for Constr.mkCase"] val mkFix : fixpoint -> constr [@@ocaml.deprecated "Alias for Constr.mkFix"] val mkCoFix : cofixpoint -> constr [@@ocaml.deprecated "Alias for Constr.mkCoFix"] (** {6 Aliases} *) val eq_constr : constr -> constr -> bool [@@ocaml.deprecated "Alias for Constr.equal"] (** [eq_constr_univs u a b] is [true] if [a] equals [b] modulo alpha, casts, application grouping and the universe constraints in [u]. *) val eq_constr_univs : constr UGraph.check_function [@@ocaml.deprecated "Alias for Constr.eq_constr_univs"] (** [leq_constr_univs u a b] is [true] if [a] is convertible to [b] modulo alpha, casts, application grouping and the universe constraints in [u]. *) val leq_constr_univs : constr UGraph.check_function [@@ocaml.deprecated "Alias for Constr.leq_constr_univs"] (** [eq_constr_univs a b] [true, c] if [a] equals [b] modulo alpha, casts, application grouping and ignoring universe instances. *) val eq_constr_nounivs : constr -> constr -> bool [@@ocaml.deprecated "Alias for Constr.qe_constr_nounivs"] val kind_of_term : constr -> (constr, types, Sorts.t, Univ.Instance.t) kind_of_term [@@ocaml.deprecated "Alias for Constr.kind"] val compare : constr -> constr -> int [@@ocaml.deprecated "Alias for [Constr.compare]"] val constr_ord : constr -> constr -> int [@@ocaml.deprecated "Alias for [Term.compare]"] val fold_constr : ('a -> constr -> 'a) -> 'a -> constr -> 'a [@@ocaml.deprecated "Alias for [Constr.fold]"] val map_constr : (constr -> constr) -> constr -> constr [@@ocaml.deprecated "Alias for [Constr.map]"] val map_constr_with_binders : ('a -> 'a) -> ('a -> constr -> constr) -> 'a -> constr -> constr [@@ocaml.deprecated "Alias for [Constr.map_with_binders]"] val map_puniverses : ('a -> 'b) -> 'a Univ.puniverses -> 'b Univ.puniverses [@@ocaml.deprecated "Alias for [Constr.map_puniverses]"] val univ_of_sort : Sorts.t -> Univ.Universe.t [@@ocaml.deprecated "Alias for [Sorts.univ_of_sort]"] val sort_of_univ : Univ.Universe.t -> Sorts.t [@@ocaml.deprecated "Alias for [Sorts.sort_of_univ]"] val iter_constr : (constr -> unit) -> constr -> unit [@@ocaml.deprecated "Alias for [Constr.iter]"] val iter_constr_with_binders : ('a -> 'a) -> ('a -> constr -> unit) -> 'a -> constr -> unit [@@ocaml.deprecated "Alias for [Constr.iter_with_binders]"] val compare_constr : (int -> constr -> constr -> bool) -> int -> constr -> constr -> bool [@@ocaml.deprecated "Alias for [Constr.compare_head]"] type constr = Constr.constr [@@ocaml.deprecated "Alias for Constr.t"] (** Alias types, for compatibility. *) type types = Constr.types [@@ocaml.deprecated "Alias for Constr.types"] type contents = Sorts.contents = Pos | Null [@@ocaml.deprecated "Alias for Sorts.contents"] type sorts = Sorts.t = | Prop of Sorts.contents (** Prop and Set *) | Type of Univ.Universe.t (** Type *) [@@ocaml.deprecated "Alias for Sorts.t"] type sorts_family = Sorts.family = InProp | InSet | InType [@@ocaml.deprecated "Alias for Sorts.family"] type 'a puniverses = 'a Univ.puniverses [@@ocaml.deprecated "Alias for Constr.puniverses"] (** Simply type aliases *) type pconstant = Constr.pconstant [@@ocaml.deprecated "Alias for Constr.pconstant"] type pinductive = Constr.pinductive [@@ocaml.deprecated "Alias for Constr.pinductive"] type pconstructor = Constr.pconstructor [@@ocaml.deprecated "Alias for Constr.pconstructor"] type existential_key = Evar.t [@@ocaml.deprecated "Alias for Evar.t"] type existential = Constr.existential [@@ocaml.deprecated "Alias for Constr.existential"] type metavariable = Constr.metavariable [@@ocaml.deprecated "Alias for Constr.metavariable"] type case_style = Constr.case_style = LetStyle | IfStyle | LetPatternStyle | MatchStyle | RegularStyle [@@ocaml.deprecated "Alias for Constr.case_style"] type case_printing = Constr.case_printing = { ind_tags : bool list; cstr_tags : bool list array; style : Constr.case_style } [@@ocaml.deprecated "Alias for Constr.case_printing"] type case_info = Constr.case_info = { ci_ind : inductive; ci_npar : int; ci_cstr_ndecls : int array; ci_cstr_nargs : int array; ci_pp_info : Constr.case_printing } [@@ocaml.deprecated "Alias for Constr.case_info"] type cast_kind = Constr.cast_kind = VMcast | NATIVEcast | DEFAULTcast | REVERTcast [@@ocaml.deprecated "Alias for Constr.cast_kind"] type rec_declaration = Constr.rec_declaration [@@ocaml.deprecated "Alias for Constr.rec_declaration"] type fixpoint = Constr.fixpoint [@@ocaml.deprecated "Alias for Constr.fixpoint"] type cofixpoint = Constr.cofixpoint [@@ocaml.deprecated "Alias for Constr.cofixpoint"] type 'constr pexistential = 'constr Constr.pexistential [@@ocaml.deprecated "Alias for Constr.pexistential"] type ('constr, 'types) prec_declaration = ('constr, 'types) Constr.prec_declaration [@@ocaml.deprecated "Alias for Constr.prec_declaration"] type ('constr, 'types) pfixpoint = ('constr, 'types) Constr.pfixpoint [@@ocaml.deprecated "Alias for Constr.pfixpoint"] type ('constr, 'types) pcofixpoint = ('constr, 'types) Constr.pcofixpoint [@@ocaml.deprecated "Alias for Constr.pcofixpoint"] type ('constr, 'types, 'sort, 'univs) kind_of_term = ('constr, 'types, 'sort, 'univs) Constr.kind_of_term = | Rel of int | Var of Id.t | Meta of Constr.metavariable | Evar of 'constr Constr.pexistential | Sort of 'sort | Cast of 'constr * Constr.cast_kind * 'types | Prod of Name.t * 'types * 'types | Lambda of Name.t * 'types * 'constr | LetIn of Name.t * 'constr * 'types * 'constr | App of 'constr * 'constr array | Const of (Constant.t * 'univs) | Ind of (inductive * 'univs) | Construct of (constructor * 'univs) | Case of Constr.case_info * 'constr * 'constr * 'constr array | Fix of ('constr, 'types) Constr.pfixpoint | CoFix of ('constr, 'types) Constr.pcofixpoint | Proj of Projection.t * 'constr [@@ocaml.deprecated "Alias for Constr.kind_of_term"] type values = Vmvalues.values [@@ocaml.deprecated "Alias for Vmvalues.values"] val hash_constr : Constr.constr -> int [@@ocaml.deprecated "Alias for Constr.hash"] val hcons_sorts : Sorts.t -> Sorts.t [@@ocaml.deprecated "Alias for [Sorts.hcons]"] val hcons_constr : Constr.constr -> Constr.constr [@@ocaml.deprecated "Alias for [Constr.hcons]"] val hcons_types : Constr.types -> Constr.types [@@ocaml.deprecated "Alias for [Constr.hcons]"]