Module Inductive

Extracting an inductive type from a construction
val find_rectype : Environ.env -> Constr.types -> Constr.pinductive * Constr.constr list
val find_inductive : Environ.env -> Constr.types -> Constr.pinductive * Constr.constr list
val find_coinductive : Environ.env -> Constr.types -> Constr.pinductive * Constr.constr list
type mind_specif = Declarations.mutual_inductive_body * Declarations.one_inductive_body
val lookup_mind_specif : Environ.env -> Names.inductive -> mind_specif

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

val inductive_paramdecls : Declarations.mutual_inductive_body Univ.puniverses -> Constr.rel_context

Returns the parameters of an inductive type with universes instantiated

val inductive_nonrec_rec_paramdecls : Declarations.mutual_inductive_body Univ.puniverses -> Constr.rel_context * Constr.rel_context

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 -> Univ.Instance.t -> Univ.Constraints.t
type param_univs = (unit -> Sorts.t) list
val make_param_univs : Environ.env -> Constr.constr array -> param_univs

The constr array is the types of the arguments to a template polymorphic inductive.

val constrained_type_of_inductive : mind_specif Univ.puniverses -> Constr.types Univ.constrained
val constrained_type_of_inductive_knowing_parameters : mind_specif Univ.puniverses -> param_univs -> Constr.types Univ.constrained
val relevance_of_inductive : Environ.env -> Names.inductive -> Sorts.relevance
val type_of_inductive : mind_specif Univ.puniverses -> Constr.types
val type_of_inductive_knowing_parameters : ?⁠polyprop:bool -> mind_specif Univ.puniverses -> param_univs -> Constr.types
val elim_sort : mind_specif ->
val is_private : mind_specif -> bool
val is_primitive_record : mind_specif -> bool
val constrained_type_of_constructor : Constr.pconstructor -> mind_specif -> Constr.types Univ.constrained
val type_of_constructor : Constr.pconstructor -> mind_specif -> Constr.types
val arities_of_constructors : Constr.pinductive -> mind_specif -> Constr.types array

Return constructor types in normal form

val type_of_constructors : Constr.pinductive -> 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 : mind_specif -> int
val expand_case : Environ.env -> -> Constr.case_info * Constr.constr * Constr.case_invert * Constr.constr * Constr.constr array

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 expand_case_specif : Declarations.mutual_inductive_body -> -> Constr.case_info * Constr.constr * Constr.case_invert * Constr.constr * Constr.constr array
val contract_case : Environ.env -> (Constr.case_info * Constr.constr * Constr.case_invert * Constr.constr * Constr.constr array) ->

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

val instantiate_context : Univ.Instance.t -> Vars.substl -> Names.Name.t Context.binder_annot array -> Constr.rel_context -> Constr.rel_context

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 type_case_branches : Environ.env -> (Constr.pinductive * Constr.constr list) -> Environ.unsafe_judgment -> Constr.constr -> Constr.types array * Constr.types

type_case_branches env (I,args) (p:A) c computes useful types about the following Cases expression: <p>Cases (c :: (I args)) of end It computes the type of every branch (pattern variables are introduced by products), the type for the whole expression, and the universe constraints generated.

val build_branches_type : Constr.pinductive -> (Declarations.mutual_inductive_body * Declarations.one_inductive_body) -> Constr.constr list -> Constr.constr -> Constr.types array
val mind_arity : Declarations.one_inductive_body -> Constr.rel_context *

Return the arity of an inductive type

val inductive_sort_family : Declarations.one_inductive_body ->
val check_case_info : Environ.env -> Constr.pinductive -> Sorts.relevance -> 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 : Environ.env -> Constr.fixpoint -> unit

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

val check_cofix : Environ.env -> Constr.cofixpoint -> unit
Support for sort-polymorphic inductive types
exception SingletonInductiveBecomesProp of Names.Id.t
val abstract_mind_lc : int -> int -> Names.MutInd.t -> (Constr.rel_context * Constr.constr) array -> Constr.constr array