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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(** This file defines various utilities for term manipulation that are not
needed in the kernel. *)
open Pp
open Names
open Term
open Environ
open EConstr
(** printers *)
val print_sort : sorts -> std_ppcmds
val pr_sort_family : sorts_family -> std_ppcmds
val pr_fix : ('a -> std_ppcmds) -> ('a, 'a) pfixpoint -> std_ppcmds
(** about contexts *)
val push_rel_assum : Name.t * types -> env -> env
val push_rels_assum : (Name.t * Constr.types) list -> env -> env
val push_named_rec_types : Name.t array * Constr.types array * 'a -> env -> env
val lookup_rel_id : Id.t -> ('c, 't) Context.Rel.pt -> int * 'c option * 't
(** Associates the contents of an identifier in a [rel_context]. Raise
[Not_found] if there is no such identifier. *)
(** Functions that build argument lists matching a block of binders or a context.
[rel_vect n m] builds [|Rel (n+m);...;Rel(n+1)|]
*)
val rel_vect : int -> int -> Constr.constr array
val rel_list : int -> int -> constr list
(** iterators/destructors on terms *)
val mkProd_or_LetIn : rel_declaration -> types -> types
val mkProd_wo_LetIn : rel_declaration -> types -> types
val it_mkProd : types -> (Name.t * types) list -> types
val it_mkLambda : constr -> (Name.t * types) list -> constr
val it_mkProd_or_LetIn : types -> rel_context -> types
val it_mkProd_wo_LetIn : types -> rel_context -> types
val it_mkLambda_or_LetIn : Constr.constr -> Context.Rel.t -> Constr.constr
val it_mkNamedProd_or_LetIn : types -> named_context -> types
val it_mkNamedProd_wo_LetIn : Constr.types -> Context.Named.t -> Constr.types
val it_mkNamedLambda_or_LetIn : constr -> named_context -> constr
(* Ad hoc version reinserting letin, assuming the body is defined in
the context where the letins are expanded *)
val it_mkLambda_or_LetIn_from_no_LetIn : Constr.constr -> Context.Rel.t -> Constr.constr
(** {6 Generic iterators on constr} *)
val map_constr_with_binders_left_to_right :
Evd.evar_map ->
(rel_declaration -> 'a -> 'a) ->
('a -> constr -> constr) ->
'a -> constr -> constr
val map_constr_with_full_binders :
Evd.evar_map ->
(rel_declaration -> 'a -> 'a) ->
('a -> constr -> constr) -> 'a -> constr -> constr
(** [fold_constr_with_binders g f n acc c] folds [f n] on the immediate
subterms of [c] starting from [acc] and proceeding from left to
right according to the usual representation of the constructions as
[fold_constr] but it carries an extra data [n] (typically a lift
index) which is processed by [g] (which typically add 1 to [n]) at
each binder traversal; it is not recursive *)
val fold_constr_with_binders : Evd.evar_map ->
('a -> 'a) -> ('a -> 'b -> constr -> 'b) -> 'a -> 'b -> constr -> 'b
val fold_constr_with_full_binders : Evd.evar_map ->
(Context.Rel.Declaration.t -> 'a -> 'a) -> ('a -> 'b -> constr -> 'b) ->
'a -> 'b -> constr -> 'b
val iter_constr_with_full_binders :
(Context.Rel.Declaration.t -> 'a -> 'a) -> ('a -> Constr.constr -> unit) -> 'a ->
Constr.constr -> unit
(**********************************************************************)
val strip_head_cast : Evd.evar_map -> constr -> constr
val drop_extra_implicit_args : Evd.evar_map -> constr -> constr
(** occur checks *)
exception Occur
val occur_meta : Evd.evar_map -> constr -> bool
val occur_existential : Evd.evar_map -> constr -> bool
val occur_meta_or_existential : Evd.evar_map -> constr -> bool
val occur_evar : Evd.evar_map -> existential_key -> constr -> bool
val occur_var : env -> Evd.evar_map -> Id.t -> constr -> bool
val occur_var_in_decl :
env -> Evd.evar_map ->
Id.t -> named_declaration -> bool
(** As {!occur_var} but assume the identifier not to be a section variable *)
val local_occur_var : Evd.evar_map -> Id.t -> constr -> bool
val free_rels : Evd.evar_map -> constr -> Int.Set.t
(** [dependent m t] tests whether [m] is a subterm of [t] *)
val dependent : Evd.evar_map -> constr -> constr -> bool
val dependent_no_evar : Evd.evar_map -> constr -> constr -> bool
val dependent_univs : Evd.evar_map -> constr -> constr -> bool
val dependent_univs_no_evar : Evd.evar_map -> constr -> constr -> bool
val dependent_in_decl : Evd.evar_map -> constr -> named_declaration -> bool
val count_occurrences : Evd.evar_map -> constr -> constr -> int
val collect_metas : Evd.evar_map -> constr -> int list
val collect_vars : Evd.evar_map -> constr -> Id.Set.t (** for visible vars only *)
val vars_of_global_reference : env -> Globnames.global_reference -> Id.Set.t
val occur_term : Evd.evar_map -> constr -> constr -> bool (** Synonymous of dependent *)
(* Substitution of metavariables *)
type meta_value_map = (metavariable * Constr.constr) list
val subst_meta : meta_value_map -> Constr.constr -> Constr.constr
val isMetaOf : Evd.evar_map -> metavariable -> constr -> bool
(** Type assignment for metavariables *)
type meta_type_map = (metavariable * Constr.types) list
(** [pop c] lifts by -1 the positive indexes in [c] *)
val pop : constr -> constr
(** {6 ... } *)
(** Substitution of an arbitrary large term. Uses equality modulo
reduction of let *)
(** [subst_term_gen eq d c] replaces [d] by [Rel 1] in [c] using [eq]
as equality *)
val subst_term_gen : Evd.evar_map ->
(Evd.evar_map -> constr -> constr -> bool) -> constr -> constr -> constr
(** [replace_term_gen eq d e c] replaces [d] by [e] in [c] using [eq]
as equality *)
val replace_term_gen :
Evd.evar_map -> (Evd.evar_map -> constr -> constr -> bool) ->
constr -> constr -> constr -> constr
(** [subst_term d c] replaces [d] by [Rel 1] in [c] *)
val subst_term : Evd.evar_map -> constr -> constr -> constr
(** [replace_term d e c] replaces [d] by [e] in [c] *)
val replace_term : Evd.evar_map -> constr -> constr -> constr -> constr
(** Alternative term equalities *)
val base_sort_cmp : Reduction.conv_pb -> sorts -> sorts -> bool
val compare_constr_univ : Evd.evar_map -> (Reduction.conv_pb -> constr -> constr -> bool) ->
Reduction.conv_pb -> constr -> constr -> bool
val constr_cmp : Evd.evar_map -> Reduction.conv_pb -> constr -> constr -> bool
val eq_constr : Evd.evar_map -> constr -> constr -> bool (* FIXME rename: erases universes*)
val eta_reduce_head : Evd.evar_map -> constr -> constr
(** Flattens application lists *)
val collapse_appl : Evd.evar_map -> constr -> constr
val prod_applist : Evd.evar_map -> constr -> constr list -> constr
(** Remove recursively the casts around a term i.e.
[strip_outer_cast (Cast (Cast ... (Cast c, t) ... ))] is [c]. *)
val strip_outer_cast : Evd.evar_map -> constr -> constr
exception CannotFilter
(** Lightweight first-order filtering procedure. Unification
variables ar represented by (untyped) Evars.
[filtering c1 c2] returns the substitution n'th evar ->
(context,term), or raises [CannotFilter].
Warning: Outer-kernel sort subtyping are taken into account: c1 has
to be smaller than c2 wrt. sorts. *)
type subst = (rel_context * constr) Evar.Map.t
val filtering : Evd.evar_map -> rel_context -> Reduction.conv_pb -> constr -> constr -> subst
val decompose_prod_letin : Evd.evar_map -> constr -> int * rel_context * constr
val align_prod_letin : Evd.evar_map -> constr -> constr -> rel_context * constr
(** [nb_lam] {% $ %}[x_1:T_1]...[x_n:T_n]c{% $ %} where {% $ %}c{% $ %} is not an abstraction
gives {% $ %}n{% $ %} (casts are ignored) *)
val nb_lam : Evd.evar_map -> constr -> int
(** Similar to [nb_lam], but gives the number of products instead *)
val nb_prod : Evd.evar_map -> constr -> int
(** Similar to [nb_prod], but zeta-contracts let-in on the way *)
val nb_prod_modulo_zeta : Evd.evar_map -> constr -> int
(** Get the last arg of a constr intended to be an application *)
val last_arg : Evd.evar_map -> constr -> constr
(** Force the decomposition of a term as an applicative one *)
val decompose_app_vect : Evd.evar_map -> constr -> constr * constr array
val adjust_app_list_size : constr -> constr list -> constr -> constr list ->
(constr * constr list * constr * constr list)
val adjust_app_array_size : constr -> constr array -> constr -> constr array ->
(constr * constr array * constr * constr array)
(** name contexts *)
type names_context = Name.t list
val add_name : Name.t -> names_context -> names_context
val lookup_name_of_rel : int -> names_context -> Name.t
val lookup_rel_of_name : Id.t -> names_context -> int
val empty_names_context : names_context
val ids_of_rel_context : ('c, 't) Context.Rel.pt -> Id.t list
val ids_of_named_context : ('c, 't) Context.Named.pt -> Id.t list
val ids_of_context : env -> Id.t list
val names_of_rel_context : env -> names_context
(* [context_chop n Γ] returns (Γ₁,Γ₂) such that [Γ]=[Γ₂Γ₁], [Γ₁] has
[n] hypotheses, excluding local definitions, and [Γ₁], if not empty,
starts with an hypothesis (i.e. [Γ₁] has the form empty or [x:A;Γ₁'] *)
val context_chop : int -> Context.Rel.t -> Context.Rel.t * Context.Rel.t
(* [env_rel_context_chop n env] extracts out the [n] top declarations
of the rel_context part of [env], counting both local definitions and
hypotheses *)
val env_rel_context_chop : int -> env -> env * rel_context
(** Set of local names *)
val vars_of_env: env -> Id.Set.t
val add_vname : Id.Set.t -> Name.t -> Id.Set.t
(** other signature iterators *)
val process_rel_context : (rel_declaration -> env -> env) -> env -> env
val assums_of_rel_context : ('c, 't) Context.Rel.pt -> (Name.t * 't) list
val lift_rel_context : int -> Context.Rel.t -> Context.Rel.t
val substl_rel_context : Constr.constr list -> Context.Rel.t -> Context.Rel.t
val smash_rel_context : Context.Rel.t -> Context.Rel.t (** expand lets in context *)
val map_rel_context_in_env :
(env -> Constr.constr -> Constr.constr) -> env -> Context.Rel.t -> Context.Rel.t
val map_rel_context_with_binders :
(int -> 'c -> 'c) -> ('c, 'c) Context.Rel.pt -> ('c, 'c) Context.Rel.pt
val fold_named_context_both_sides :
('a -> Context.Named.Declaration.t -> Context.Named.Declaration.t list -> 'a) ->
Context.Named.t -> init:'a -> 'a
val mem_named_context_val : Id.t -> named_context_val -> bool
val compact_named_context : Context.Named.t -> Context.Compacted.t
val map_rel_decl : ('a -> 'b) -> ('a, 'a) Context.Rel.Declaration.pt -> ('b, 'b) Context.Rel.Declaration.pt
val map_named_decl : ('a -> 'b) -> ('a, 'a) Context.Named.Declaration.pt -> ('b, 'b) Context.Named.Declaration.pt
val clear_named_body : Id.t -> env -> env
val global_vars : env -> Evd.evar_map -> constr -> Id.t list
val global_vars_set : env -> Evd.evar_map -> constr -> Id.Set.t
val global_vars_set_of_decl : env -> Evd.evar_map -> named_declaration -> Id.Set.t
val global_app_of_constr : Evd.evar_map -> constr -> Globnames.global_reference puniverses * constr option
(** Gives an ordered list of hypotheses, closed by dependencies,
containing a given set *)
val dependency_closure : env -> Evd.evar_map -> named_context -> Id.Set.t -> Id.t list
(** Test if an identifier is the basename of a global reference *)
val is_section_variable : Id.t -> bool
val global_of_constr : Evd.evar_map -> constr -> Globnames.global_reference puniverses
val is_global : Evd.evar_map -> Globnames.global_reference -> constr -> bool
val isGlobalRef : Evd.evar_map -> constr -> bool
val is_template_polymorphic : env -> Evd.evar_map -> constr -> bool
val is_Prop : Evd.evar_map -> constr -> bool
(** Combinators on judgments *)
val on_judgment : ('a -> 'b) -> ('a, 'a) punsafe_judgment -> ('b, 'b) punsafe_judgment
val on_judgment_value : ('c -> 'c) -> ('c, 't) punsafe_judgment -> ('c, 't) punsafe_judgment
val on_judgment_type : ('t -> 't) -> ('c, 't) punsafe_judgment -> ('c, 't) punsafe_judgment
(** {6 Functions to deal with impossible cases } *)
val set_impossible_default_clause : (unit -> (Constr.constr * Constr.types) Univ.in_universe_context_set) -> unit
val coq_unit_judge : unit -> unsafe_judgment Univ.in_universe_context_set
(** {5 Debug pretty-printers} *)
open Evd
val pr_existential_key : evar_map -> evar -> Pp.std_ppcmds
val pr_evar_suggested_name : existential_key -> evar_map -> Id.t
val pr_evar_info : evar_info -> Pp.std_ppcmds
val pr_evar_constraints : evar_constraint list -> Pp.std_ppcmds
val pr_evar_map : ?with_univs:bool -> int option -> evar_map -> Pp.std_ppcmds
val pr_evar_map_filter : ?with_univs:bool -> (Evar.t -> evar_info -> bool) ->
evar_map -> Pp.std_ppcmds
val pr_metaset : Metaset.t -> Pp.std_ppcmds
val pr_evar_universe_context : evar_universe_context -> Pp.std_ppcmds
val pr_evd_level : evar_map -> Univ.Level.t -> Pp.std_ppcmds
(** debug printer: do not use to display terms to the casual user... *)
val set_print_constr : (env -> Evd.evar_map -> constr -> std_ppcmds) -> unit
val print_constr : constr -> std_ppcmds
val print_constr_env : env -> Evd.evar_map -> constr -> std_ppcmds
val print_named_context : env -> std_ppcmds
val pr_rel_decl : env -> Context.Rel.Declaration.t -> std_ppcmds
val print_rel_context : env -> std_ppcmds
val print_env : env -> std_ppcmds
|
