Module Reductionops

Reduction Functions.

exception Elimconst
val debug_RAKAM : CDebug.t
module CredNative : Primred.RedNative with type elem = EConstr.t and type args = EConstr.t array and type evd = Evd.evar_map and type uinstance = EConstr.EInstance.t
module ReductionBehaviour : sig ... end

Machinery to customize the behavior of the reduction

Support for reduction effects
type effect_name = string
val declare_reduction_effect : effect_name -> (Environ.env -> Evd.evar_map -> Constr.constr -> unit) -> unit
val set_reduction_effect : Libobject.locality -> Names.Constant.t -> effect_name -> unit
val reduction_effect_hook : Environ.env -> Evd.evar_map -> Names.Constant.t -> Constr.constr Stdlib.Lazy.t -> unit
module Stack : sig ... end
type reduction_function = Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr
type e_reduction_function = Environ.env -> Evd.evar_map -> EConstr.constr -> Evd.evar_map * EConstr.constr
type stack_reduction_function = Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr * EConstr.constr list
Generic Optimized Reduction Function using Closures
val clos_norm_flags : RedFlags.reds -> reduction_function
val clos_whd_flags : RedFlags.reds -> reduction_function
val nf_beta : reduction_function

Same as (strong whd_beta[delta][iota]), but much faster on big terms

val nf_betaiota : reduction_function
val nf_betaiotazeta : reduction_function
val nf_zeta : reduction_function
val nf_all : reduction_function

Lazy strategy, weak head reduction

val whd_nored : reduction_function
val whd_beta : reduction_function
val whd_betaiota : reduction_function
val whd_betaiotazeta : reduction_function
val whd_all : reduction_function
val whd_allnolet : reduction_function
val whd_betalet : reduction_function
val whd_nored_stack : stack_reduction_function

Removes cast and put into applicative form

val whd_beta_stack : stack_reduction_function
val whd_betaiota_stack : stack_reduction_function
val whd_betaiotazeta_stack : stack_reduction_function
val whd_all_stack : stack_reduction_function
val whd_allnolet_stack : stack_reduction_function
val whd_betalet_stack : stack_reduction_function
Head normal forms
val whd_delta_stack : stack_reduction_function
val whd_delta : reduction_function
val whd_betadeltazeta_stack : stack_reduction_function
val whd_betadeltazeta : reduction_function
val whd_zeta_stack : stack_reduction_function
val whd_zeta : reduction_function

Various reduction functions

val beta_applist : Evd.evar_map -> (EConstr.constr * EConstr.constr list) -> EConstr.constr
val hnf_prod_appvect : Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr array -> EConstr.constr
val hnf_prod_applist : Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr list -> EConstr.constr
val hnf_lam_appvect : Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr array -> EConstr.constr

Decompose a type into a sequence of products and a non-product conclusion in head normal form, using head-reduction to expose the products

Decompose a term into a sequence of lambdas and a non-lambda conclusion in head normal form, using head-reduction to expose the lambdas

val whd_decompose_prod_decls : Environ.env -> Evd.evar_map -> EConstr.types -> EConstr.rel_context * EConstr.types

Decompose a type into a context and a conclusion not starting with a product or let-in, using head-reduction without zeta to expose the products and let-ins

Like whd_decompose_prod but limited at n products; raises Invalid_argument if not enough products

Like whd_decompose_lambda but limited at n lambdas; raises Invalid_argument if not enough lambdas

Decompose an arity reducing let-ins; Raises Reduction.NotArity

Decompose an arity preserving let-ins; Raises Reduction.NotArity

Raises Reduction.NotArity

val whd_decompose_prod_n_assum : Environ.env -> Evd.evar_map -> int -> EConstr.types -> EConstr.rel_context * EConstr.types

Extract the n first products of a type, preserving let-ins (but not counting them); Raises Invalid_argument if not enough products

val whd_decompose_prod_n_decls : Environ.env -> Evd.evar_map -> int -> EConstr.types -> EConstr.rel_context * EConstr.types

Extract the n first products of a type, counting and preserving let-ins; Raises Invalid_argument if not enough products or let-ins

val whd_decompose_lambda_n_assum : Environ.env -> Evd.evar_map -> int -> EConstr.constr -> EConstr.rel_context * EConstr.constr

Extract the n first lambdas of a term, preserving let-ins (but not counting them); Raises Invalid_argument if not enough lambdas

val reducible_mind_case : Evd.evar_map -> EConstr.constr -> bool
val is_arity : Environ.env -> Evd.evar_map -> EConstr.constr -> bool
val is_sort : Environ.env -> Evd.evar_map -> EConstr.types -> bool
val is_transparent : Environ.env -> Evaluable.t -> bool

Querying the kernel conversion oracle: opaque/transparent constants

Conversion Functions (uses closures, lazy strategy)
type conversion_test = Univ.Constraints.t -> Univ.Constraints.t
val is_conv_leq : ?reds:TransparentState.t -> Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr -> bool

check_conv Checks universe constraints only. pb defaults to CUMUL and ts to a full transparent state.

val infer_conv : ?catch_incon:bool -> ?pb:Evd.conv_pb -> ?ts:TransparentState.t -> Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr -> Evd.evar_map option

infer_conv Adds necessary universe constraints to the evar map. pb defaults to CUMUL and ts to a full transparent state.

  • raises UniverseInconsistency

    iff catch_incon is set to false, otherwise returns false in that case.

val infer_conv_ustate : ?catch_incon:bool -> ?pb:Evd.conv_pb -> ?ts:TransparentState.t -> Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr -> UnivProblem.Set.t option
val vm_infer_conv : ?pb:Evd.conv_pb -> Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr -> Evd.evar_map option

Conversion with inference of universe constraints

val native_infer_conv : ?pb:Evd.conv_pb -> Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr -> Evd.evar_map option
type genconv = {
genconv : a err. Evd.conv_pb -> l2r:bool -> Evd.evar_map -> TransparentState.t -> Environ.env -> ('a'err) Conversion.generic_conversion_function;
}
val infer_conv_gen : genconv -> ?catch_incon:bool -> ?pb:Evd.conv_pb -> ?ts:TransparentState.t -> Environ.env -> Evd.evar_map -> EConstr.constr -> EConstr.constr -> Evd.evar_map option

infer_conv_gen behaves like infer_conv but is parametrized by a conversion function. Used to pretype vm and native casts.

val check_hyps_inclusion : Environ.env -> Evd.evar_map -> Names.GlobRef.t -> Constr.named_context -> unit

Typeops.check_hyps_inclusion but handles evars in the environment.

Heuristic for Conversion with Evar
type state = EConstr.constr * Stack.t
type state_reduction_function = Environ.env -> Evd.evar_map -> state -> state
val pr_state : Environ.env -> Evd.evar_map -> state -> Pp.t
val whd_nored_state : state_reduction_function
val whd_betaiota_deltazeta_for_iota_state : TransparentState.t -> state_reduction_function
exception PatternFailure
val is_head_evar : Environ.env -> Evd.evar_map -> EConstr.constr -> bool

Meta-related reduction functions

exception AnomalyInConversion of exn

Deprecated

Re-deprecated in 8.19

val hnf_decompose_prod_decls : Environ.env -> Evd.evar_map -> EConstr.types -> EConstr.rel_context * EConstr.types
val hnf_decompose_prod_n_decls : Environ.env -> Evd.evar_map -> int -> EConstr.types -> EConstr.rel_context * EConstr.types
val hnf_decompose_lambda_n_assum : Environ.env -> Evd.evar_map -> int -> EConstr.constr -> EConstr.rel_context * EConstr.constr