Module Termops

This file defines various utilities for term manipulation that are not needed in the kernel.

about contexts

val lookup_rel_id : Names.Id.t -> ('c, 't, 'r) 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.

val rel_vect : int -> int -> Constr.constr array

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_list : int -> int -> EConstr.constr list

Prod/Lambda/LetIn destructors on constr

val it_mkNamedProd_wo_LetIn : Constr.types -> Constr.named_context -> Constr.types
val it_mkLambda_or_LetIn_from_no_LetIn : Constr.constr -> Constr.rel_context -> Constr.constr
Generic iterators on constr
val map_constr_with_binders_left_to_right : Environ.env -> Evd.evar_map -> (EConstr.rel_declaration -> 'a -> 'a) -> ('a -> EConstr.constr -> EConstr.constr) -> 'a -> EConstr.constr -> EConstr.constr
val map_constr_with_full_binders : Environ.env -> Evd.evar_map -> (EConstr.rel_declaration -> 'a -> 'a) -> ('a -> EConstr.constr -> EConstr.constr) -> 'a -> EConstr.constr -> EConstr.constr
val fold_constr_with_full_binders : Environ.env -> Evd.evar_map -> (EConstr.rel_declaration -> 'a -> 'a) -> ('a -> 'b -> EConstr.constr -> 'b) -> 'a -> 'b -> EConstr.constr -> 'b
val strip_head_cast : Evd.evar_map -> EConstr.constr -> EConstr.constr
val drop_extra_implicit_args : Evd.evar_map -> EConstr.constr -> EConstr.constr

occur checks

exception Occur
val occur_meta : Evd.evar_map -> EConstr.constr -> bool
val occur_existential : Evd.evar_map -> EConstr.constr -> bool
val occur_meta_or_existential : Evd.evar_map -> EConstr.constr -> bool
val occur_metavariable : Evd.evar_map -> Constr.metavariable -> EConstr.constr -> bool
val occur_evar : Evd.evar_map -> Evar.t -> EConstr.constr -> bool
val occur_var : Environ.env -> Evd.evar_map -> Names.Id.t -> EConstr.constr -> bool
val occur_var_indirectly : Environ.env -> Evd.evar_map -> Names.Id.t -> EConstr.constr -> Names.GlobRef.t option
val occur_var_in_decl : Environ.env -> Evd.evar_map -> Names.Id.t -> EConstr.named_declaration -> bool
val occur_vars : Environ.env -> Evd.evar_map -> Names.Id.Set.t -> EConstr.constr -> bool
val occur_vars_in_decl : Environ.env -> Evd.evar_map -> Names.Id.Set.t -> EConstr.named_declaration -> bool
val local_occur_var : Evd.evar_map -> Names.Id.t -> EConstr.constr -> bool

As occur_var but assume the identifier not to be a section variable

val local_occur_var_in_decl : Evd.evar_map -> Names.Id.t -> EConstr.named_declaration -> bool
val free_rels : Evd.evar_map -> EConstr.constr -> Int.Set.t
val dependent : Evd.evar_map -> EConstr.constr -> EConstr.constr -> bool

dependent m t tests whether m is a subterm of t

val dependent_no_evar : Evd.evar_map -> EConstr.constr -> EConstr.constr -> bool
val dependent_in_decl : Evd.evar_map -> EConstr.constr -> EConstr.named_declaration -> bool
val count_occurrences : Evd.evar_map -> EConstr.constr -> EConstr.constr -> int
val collect_metas : Evd.evar_map -> EConstr.constr -> int list
val collect_vars : Evd.evar_map -> EConstr.constr -> Names.Id.Set.t

for visible vars only

type meta_value_map = (Constr.metavariable * Constr.constr) list
val isMetaOf : Evd.evar_map -> Constr.metavariable -> EConstr.constr -> bool
type meta_type_map = (Constr.metavariable * Constr.types) list

Type assignment for metavariables

pop c lifts by -1 the positive indexes in c

...

Substitution of an arbitrary large term. Uses equality modulo reduction of let

val replace_term_gen : Evd.evar_map -> (Evd.evar_map -> int -> EConstr.constr -> bool) -> int -> EConstr.constr -> EConstr.constr -> EConstr.constr

replace_term_gen eq arity e c replaces matching subterms according to eq by e in c. If arity is non-zero applications of larger length are handled atomically.

subst_term d c replaces d by Rel 1 in c

replace_term d e c replaces d by e in c

val base_sort_cmp : Conversion.conv_pb -> Sorts.t -> Sorts.t -> bool

Alternative term equalities

val eq_constr : Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr -> bool
val eta_reduce_head : Evd.evar_map -> EConstr.constr -> EConstr.constr
val eta_expand_instantiation : ?evars:CClosure.evar_handler -> Environ.env -> Constr.constr array -> Constr.rel_context -> Constr.constr array
val prod_applist : Evd.evar_map -> EConstr.constr -> EConstr.constr list -> EConstr.constr

prod_applist forall (x1:B1;...;xn:Bn), B a1...an

  • returns

    B[a1...an]

val prod_applist_decls : Evd.evar_map -> int -> EConstr.constr -> EConstr.constr list -> EConstr.constr

In prod_applist_decls n c args, c is supposed to have the form ∀Γ.c with Γ of length m and possibly with let-ins; it returns c with the assumptions of Γ instantiated by args and the local definitions of Γ expanded. Note that n counts both let-ins and prods, while the length of args only counts prods. In other words, varying n changes how many trailing let-ins are expanded.

val strip_outer_cast : Evd.evar_map -> EConstr.constr -> EConstr.constr

Remove recursively the casts around a term i.e. strip_outer_cast (Cast (Cast ... (Cast c, t) ... )) is c.

val nb_lam : Evd.evar_map -> EConstr.constr -> int

nb_lam sigma t counts the number of head lambda abstractions in t, ignoring casts. For instance on fun x1 x2 x3 => c (where c is not itself a lambda abstraction) it returns 3.

val nb_prod : Evd.evar_map -> EConstr.constr -> int

nb_prod sigma t counts the number of head products in t, ignoring casts.

val nb_prod_modulo_zeta : Evd.evar_map -> EConstr.constr -> int

Variant of nb_prod which also does zeta-reduction (i.e. reduces let-ins) along the way.

last_arg sigma t returns the last argument of t. Fails if t is not an application.

val adjust_app_array_size : EConstr.constr -> EConstr.constr array -> EConstr.constr -> EConstr.constr array -> EConstr.constr * EConstr.constr array * EConstr.constr * EConstr.constr array
type names_context = Names.Name.t list

name contexts

val lookup_name_of_rel : int -> names_context -> Names.Name.t
val lookup_rel_of_name : Names.Id.t -> names_context -> int
val empty_names_context : names_context
val ids_of_rel_context : ('c, 't, 'r) Context.Rel.pt -> Names.Id.t list
val ids_of_named_context : ('c, 't, 'r) Context.Named.pt -> Names.Id.t list
val ids_of_context : Environ.env -> Names.Id.t list
val names_of_rel_context : Environ.env -> names_context
val env_rel_context_chop : int -> Environ.env -> Environ.env * EConstr.rel_context
val vars_of_env : Environ.env -> Names.Id.Set.t

Set of local names

other signature iterators

val assums_of_rel_context : ('c, 't, 'r) Context.Rel.pt -> ((Names.Name.t, 'r) Context.pbinder_annot * 't) list
val fold_named_context_both_sides : ('a -> Constr.named_declaration -> Constr.named_declaration list -> 'a) -> Constr.named_context -> init:'a -> 'a
val mem_named_context_val : Names.Id.t -> Environ.named_context_val -> bool
val clear_named_body : Names.Id.t -> Environ.env -> Environ.env
val global_vars_set : Environ.env -> Evd.evar_map -> EConstr.constr -> Names.Id.Set.t
val global_vars_set_of_decl : Environ.env -> Evd.evar_map -> EConstr.named_declaration -> Names.Id.Set.t
val dependency_closure : Environ.env -> Evd.evar_map -> EConstr.named_context -> Names.Id.Set.t -> Names.Id.t list

Gives an ordered list of hypotheses, closed by dependencies, containing a given set

val is_section_variable : Environ.env -> Names.Id.t -> bool

This tests if the ident is known in the given env, intended to be used with the global env.

  • deprecated Use is_section_variable_env on the local env instead of is_section_variable on the global env.
val is_section_variable_sign : ?check:bool -> Environ.named_context_val -> Names.Id.t -> bool

Check if the ident has SecVar status in this enviroment. By default check=true and produce anomaly if it is not bound. If check=false returns false if it is not bound.

val is_section_variable_env : ?check:bool -> Environ.env -> Names.Id.t -> bool
val is_template_polymorphic_ref : Environ.env -> Evd.evar_map -> EConstr.constr -> bool
val is_template_polymorphic_ind : Environ.env -> Evd.evar_map -> EConstr.constr -> bool
val is_Prop : Evd.evar_map -> EConstr.constr -> bool
val is_Set : Evd.evar_map -> EConstr.constr -> bool
val is_Type : Evd.evar_map -> EConstr.constr -> bool
val reference_of_level : Evd.evar_map -> Univ.Level.t -> Libnames.qualid option
Debug pretty-printers
val pr_global_env : Environ.env -> Names.GlobRef.t -> Pp.t
val pr_existential_key : Environ.env -> Evd.evar_map -> Evar.t -> Pp.t
val evar_string : Environ.env -> Evd.evar_map -> Evar.t -> string
val evar_suggested_name : Environ.env -> Evd.evar_map -> Evar.t -> Names.Id.t
val pr_evar_info : Environ.env -> Evd.evar_map -> 'a Evd.evar_info -> Pp.t
val pr_evar_constraints : Evd.evar_map -> Evd.evar_constraint list -> Pp.t
val pr_evar_map : ?with_univs:bool -> int option -> Environ.env -> Evd.evar_map -> Pp.t
val pr_evar_map_filter : ?with_univs:bool -> (Evar.t -> Evd.any_evar_info -> bool) -> Environ.env -> Evd.evar_map -> Pp.t
val pr_evd_level : Evd.evar_map -> Univ.Level.t -> Pp.t
val pr_evd_qglobal : Evd.evar_map -> Sorts.QGlobal.t -> Pp.t
val pr_evd_qvar : Evd.evar_map -> Sorts.QVar.t -> Pp.t
val pr_evd_quality : Evd.evar_map -> Sorts.Quality.t -> Pp.t
module ConstrData : sig ... end
module Internal : sig ... end

NOTE: to print terms you always want to use functions in Printer, not these ones which are for very special cases.

val pr_evar_universe_context : UState.t -> Pp.t
  • deprecated (9.0) Use [UState.pr] instead