Module `Clenv`

This file defines clausenv, which is a deprecated way to handle open terms in the proof engine. Most of the API here is legacy except for the evar-based clauses.

The Type of Constructions clausale environments.

type clausenv = { env : Environ.env; the typing context evd : Evd.evar_map; the mapping from metavar and evar numbers to their types and values templval : EConstr.constr Evd.freelisted; the template which we are trying to fill out templtyp : EConstr.constr Evd.freelisted; its type }

val clenv_value : clausenv -> EConstr.constr: subject of clenv (instantiated)

val clenv_type : clausenv -> EConstr.types: type of clenv (instantiated)

val clenv_nf_meta : clausenv -> EConstr.constr -> EConstr.constr: substitute resolved metas

val clenv_meta_type : clausenv -> Constr.metavariable -> EConstr.types: type of a meta in clenv context

val mk_clenv_from : Proofview.Goal.t -> (EConstr.constr * EConstr.types) -> clausenv
val mk_clenv_from_n : Proofview.Goal.t -> int option -> (EConstr.constr * EConstr.types) -> clausenv
val mk_clenv_from_env : Environ.env -> Evd.evar_map -> int option -> (EConstr.constr * EConstr.types) -> clausenv
val refresh_undefined_univs : clausenv -> clausenv * Univ.universe_level_subst: Refresh the universes in a clenv

linking of clenvs

val clenv_fchain : ?⁠with_univs:bool -> ?⁠flags:Unification.unify_flags -> Constr.metavariable -> clausenv -> clausenv -> clausenv

Unification with clenvs

val clenv_unify : ?⁠flags:Unification.unify_flags -> Evd.conv_pb -> EConstr.constr -> EConstr.constr -> clausenv -> clausenv: Unifies two terms in a clenv. The boolean is allow_K (see Unification)

val clenv_unique_resolver : ?⁠flags:Unification.unify_flags -> clausenv -> Proofview.Goal.t -> clausenv: unifies the concl of the goal with the type of the clenv

val clenv_dependent : clausenv -> Constr.metavariable list
val clenv_pose_metas_as_evars : clausenv -> Constr.metavariable list -> clausenv * Evar.t list

Bindings

type arg_bindings = EConstr.constr Tactypes.explicit_bindings

val clenv_independent : clausenv -> Constr.metavariable list: bindings where the key is the position in the template of the clenv (dependent or not). Positions can be negative meaning to start from the rightmost argument of the template.

val clenv_missing : clausenv -> Constr.metavariable list

exception NoSuchBinding: for the purpose of inversion tactics

val clenv_constrain_last_binding : EConstr.constr -> clausenv -> clausenv
val clenv_unify_meta_types : ?⁠flags:Unification.unify_flags -> clausenv -> clausenv

val make_clenv_binding_env_apply : Environ.env -> Evd.evar_map -> int option -> (EConstr.constr * EConstr.constr) -> EConstr.constr Tactypes.bindings -> clausenv: the arity of the lemma is fixed the optional int tells how many prods of the lemma have to be used use all of them if None

val make_clenv_binding_apply : Environ.env -> Evd.evar_map -> int option -> (EConstr.constr * EConstr.constr) -> EConstr.constr Tactypes.bindings -> clausenv
val make_clenv_binding_env : Environ.env -> Evd.evar_map -> (EConstr.constr * EConstr.constr) -> EConstr.constr Tactypes.bindings -> clausenv
val make_clenv_binding : Environ.env -> Evd.evar_map -> (EConstr.constr * EConstr.constr) -> EConstr.constr Tactypes.bindings -> clausenv

exception NotExtensibleClause: if the clause is a product, add an extra meta for this product

val clenv_push_prod : clausenv -> clausenv
val pr_clenv : clausenv -> Pp.t: Pretty-print (debug only)

Evar-based clauses

The following code is an adaptation of the make_clenv_* functions above, except that it uses evars instead of metas, and naturally fits in the new refinement monad. It should eventually replace all uses of the aforementioned functions.

A clause is constructed as follows: assume a type t := forall (x1 : A1) ... (xn : An), T, we instantiate all the xi with a fresh evar ei and return T(xi := ei) together with the ei enriched with a bit of additional data. This is the simple part done by make_evar_clause.

The problem lies in the fact we want to solve such holes with some constr bindings. This entails some subtleties, because the provided terms may only be well-typed up to a coercion, which we can only infer if we have enough typing information. The meta machinery could insert coercions through tricky instantiation delays. The only solution we have now is to delay the tentative resolution of clauses by providing the solve_evar_clause function, to be called at a smart enough time.

type hole = { hole_evar : EConstr.constr; The hole itself. Guaranteed to be an evar. hole_type : EConstr.types; Type of the hole in the current environment. hole_deps : bool; Whether the remainder of the clause was dependent in the hole. Note that because let binders are substituted, it does not mean that it actually appears somewhere in the returned clause. hole_name : Names.Name.t; Name of the hole coming from its binder. }
type clause = { cl_holes : hole list; cl_concl : EConstr.types; }

val make_evar_clause : Environ.env -> Evd.evar_map -> ?⁠len:int -> EConstr.types -> Evd.evar_map * clause: An evar version of make_clenv_binding. Given a type t, evar_environments env sigma ~len t bl tries to eliminate at most len products of the type t by filling it with evars. It returns the resulting type together with the list of holes generated. Assumes that t is well-typed in the environment.

val solve_evar_clause : Environ.env -> Evd.evar_map -> bool -> clause -> EConstr.constr Tactypes.bindings -> Evd.evar_map: solve_evar_clause env sigma hyps cl bl tries to solve the holes contained in cl according to the bl argument. Assumes that bl are well-typed in the environment. The boolean hyps is a compatibility flag that allows to consider arguments to be dependent only when they appear in hypotheses and not in the conclusion. This boolean is only used when bl is of the form ImplicitBindings _.

`env : Environ.env;`	the typing context
`evd : Evd.evar_map;`	the mapping from metavar and evar numbers to their types and values
`templval : EConstr.constr Evd.freelisted;`	the template which we are trying to fill out
`templtyp : EConstr.constr Evd.freelisted;`	its type

`hole_evar : EConstr.constr;`	The hole itself. Guaranteed to be an evar.
`hole_type : EConstr.types;`	Type of the hole in the current environment.
`hole_deps : bool;`	Whether the remainder of the clause was dependent in the hole. Note that because let binders are substituted, it does not mean that it actually appears somewhere in the returned clause.
`hole_name : Names.Name.t;`	Name of the hole coming from its binder.

Pretty-print (debug only)