package coq

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package coq
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Inductive and coinductive types

Entry points for the vernacular commands Inductive and CoInductive

type uniform_inductive_flag =
  1. | UniformParameters
  2. | NonUniformParameters
val do_mutual_inductive : template:bool option -> Constrexpr.cumul_univ_decl_expr option -> (Vernacexpr.one_inductive_expr * Vernacexpr.decl_notation list) list -> cumulative:bool -> poly:bool -> ?typing_flags:Declarations.typing_flags -> private_ind:bool -> uniform:uniform_inductive_flag -> Declarations.recursivity_kind -> unit

User-interface API

Prepare a "match" template for a given inductive type. For each branch of the match, we list the constructor name followed by enough pattern variables. Not_found is raised if the given string isn't the qualid of a known inductive type.

val make_cases : Names.inductive -> string list list
module Mind_decl : sig ... end
val interp_mutual_inductive : env:Environ.env -> template:bool option -> Constrexpr.cumul_univ_decl_expr option -> (Vernacexpr.one_inductive_expr * Vernacexpr.decl_notation list) list -> cumulative:bool -> poly:bool -> ?typing_flags:Declarations.typing_flags -> private_ind:bool -> uniform:uniform_inductive_flag -> Declarations.recursivity_kind -> Mind_decl.t

elaborates an inductive declaration (the first half of do_mutual_inductive)

val interp_mutual_inductive_constr : sigma:Evd.evar_map -> template:bool option -> udecl:UState.universe_decl -> variances:Entries.variance_entry -> ctx_params:(EConstr.t, EConstr.t) Context.Rel.Declaration.pt list -> indnames:Names.Id.t list -> arities:EConstr.t list -> arityconcl:(bool * EConstr.ESorts.t) option list -> constructors:(Names.Id.t list * Constr.constr list) list -> env_ar_params:Environ.env -> cumulative:bool -> poly:bool -> private_ind:bool -> finite:Declarations.recursivity_kind -> Entries.mutual_inductive_entry * UnivNames.universe_binders * Univ.ContextSet.t

the post-elaboration part of interp_mutual_inductive, mainly dealing with universe levels

Internal API, exported for Record

val should_auto_template : Names.Id.t -> bool -> bool

should_auto_template x b is true when b is true and we automatically use template polymorphism. x is the name of the inductive under consideration.

val template_polymorphism_candidate : ctor_levels:Univ.Level.Set.t -> UState.universes_entry -> Constr.rel_context -> Sorts.t option -> bool

template_polymorphism_candidate ~ctor_levels uctx params conclsort is true iff an inductive with params params, conclusion conclsort and universe levels appearing in the constructor arguments ctor_levels would be definable as template polymorphic. It should have at least one universe in its monomorphic universe context that can be made parametric in its conclusion sort, if one is given.

val maybe_unify_params_in : Environ.env -> Evd.evar_map -> ninds:int -> nparams:int -> binders:int -> EConstr.t -> Evd.evar_map

nparams is the number of parameters which aren't treated as uniform, ie the length of params (including letins) where the env is uniform params, inductives, params, binders.

val variance_of_entry : cumulative:bool -> variances:Entries.variance_entry -> Entries.inductive_universes_entry -> Entries.variance_entry option

Will return None if non-cumulative, and resize if there are more universes than originally specified. If monomorphic, cumulative is treated as false.

module Internal : sig ... end