Module Inductive

Extracting an inductive type from a construction

find_m*type env sigma c coerce c to an recursive type (I args). find_rectype, find_inductive and find_coinductive respectively accepts any recursive type, only an inductive type and only a coinductive type. They raise Not_found if not convertible to a recursive type.

val find_coinductive : ?evars:CClosure.evar_handler -> Environ.env -> Constr.types -> Constr.pinductive * Constr.constr list

Fetching information in the environment about an inductive type. Raises an anomaly if the inductive type is not found.

Returns the parameters of an inductive type with universes instantiated

Returns the parameters of an inductive type with universes instantiated, splitting it into the contexts of recursively uniform and recursively non-uniform parameters

val instantiate_inductive_constraints : Declarations.mutual_inductive_body -> UVars.Instance.t -> Univ.Constraints.t
type template_univ =
| TemplateProp
| TemplateUniv of Univ.Universe.t
type param_univs = (expected:Univ.Level.t -> template_univ) list
val constrained_type_of_inductive_knowing_parameters : Declarations.mind_specif UVars.puniverses -> param_univs -> Constr.types Univ.constrained
val relevance_of_ind_body : Declarations.one_inductive_body -> UVars.Instance.t -> Sorts.relevance
val relevance_of_inductive : Environ.env -> Constr.pinductive -> Sorts.relevance
val type_of_inductive_knowing_parameters : ?polyprop:bool -> Declarations.mind_specif UVars.puniverses -> param_univs -> Constr.types
val quality_leq : Sorts.Quality.t -> Sorts.Quality.t -> bool

For squashing.

type squash =
| SquashToSet
| SquashToQuality of Sorts.Quality.t
val is_allowed_elimination : Declarations.mind_specif UVars.puniverses -> Sorts.t -> bool
val is_private : Declarations.mind_specif -> bool
val is_primitive_record : Declarations.mind_specif -> bool

Return type as quoted by the user

val arities_of_constructors : Constr.pinductive -> Declarations.mind_specif -> Constr.types array

Return constructor types in normal form

val type_of_constructors : Constr.pinductive -> Declarations.mind_specif -> Constr.types array

Return constructor types in user form

val abstract_constructor_type_relatively_to_inductive_types_context : int -> Names.MutInd.t -> Constr.types -> Constr.types

Turns a constructor type recursively referring to inductive types into the same constructor type referring instead to a context made from the abstract declaration of the inductive types (e.g. turns nat->nat into mkArrowR (Rel 1) (Rel 2)); takes as arguments the number of inductive types in the block and the name of the block

val inductive_params : Declarations.mind_specif -> int

Given an inductive type and its parameters, builds the context of the return clause, including the inductive being eliminated. The additional binder array is only used to set the names of the context variables, we use the less general type to make it easy to use this function on Case nodes.

val expand_branch_contexts : Declarations.mind_specif -> UVars.Instance.t -> Constr.constr array -> (Names.Name.t Context.binder_annot array * 'a) array -> Constr.rel_context array

Given an inductive type and its parameters, builds the context of the return clause, including the inductive being eliminated. The additional binder array is only used to set the names of the context variables, we use the less general type to make it easy to use this function on Case nodes.

type ('constr, 'types) pexpanded_case = Constr.case_info * ('constr * Sorts.relevance) * 'constr Constr.pcase_invert * 'constr * 'constr array
type expanded_case = (Constr.constr, Constr.types) pexpanded_case
val expand_case : Environ.env -> Constr.case -> expanded_case

Given a pattern-matching represented compactly, expands it so as to produce lambda and let abstractions in front of the return clause and the pattern branches.

val contract_case : Environ.env -> expanded_case -> Constr.case

Dual operation of the above. Fails if the return clause or branch has not the expected form.

instantiate_context u subst nas ctx applies both u and subst to ctx while replacing names using nas (order reversed). In particular, assumes that ctx and nas have the same length.

val check_case_info : Environ.env -> Constr.pinductive -> Constr.case_info -> unit

Check a case_info actually correspond to a Case expression on the given inductive type.

Guard conditions for fix and cofix-points.
val is_primitive_positive_container : Environ.env -> Names.Constant.t -> bool

is_primitive_positive_container env c tells if the constant c is registered as a primitive type that can be seen as a container where the occurrences of its parameters are positive, in which case the positivity and guard conditions are extended to allow inductive types to nest their subterms in these containers.

val check_fix : ?evars:CClosure.evar_handler -> Environ.env -> Constr.fixpoint -> unit

When chk is false, the guard condition is not actually checked.

val check_cofix : ?evars:CClosure.evar_handler -> Environ.env -> Constr.cofixpoint -> unit
Support for sort-polymorphic inductive types

The "polyprop" optional argument below controls the "Prop-polymorphism". By default, it is allowed. But when "polyprop=false", the following exception is raised when a polymorphic singleton inductive type becomes Prop due to parameter instantiation. This is used by the Ocaml extraction, which cannot handle (yet?) Prop-polymorphism.

exception SingletonInductiveBecomesProp of Names.Id.t
val abstract_mind_lc : int -> int -> Names.MutInd.t -> (Constr.rel_context * Constr.constr) array -> Constr.constr array