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Main tactics defined in ML. This file is huge and should probably be split in more reasonable units at some point. Because of its size and age, the implementation features various styles and stages of the proof engine. This has to be uniformized someday.

General functions.
val is_quantified_hypothesis : Names.Id.t -> Proofview.Goal.t -> bool
Primitive tactics.
val introduction : Names.Id.t -> unit Proofview.tactic
val convert_concl : check:bool -> EConstr.types -> Constr.cast_kind -> unit Proofview.tactic
val convert_hyp : check:bool -> reorder:bool -> EConstr.named_declaration -> unit Proofview.tactic
val mutual_fix : Names.Id.t -> int -> (Names.Id.t * int * EConstr.constr) list -> int -> unit Proofview.tactic
val fix : Names.Id.t -> int -> unit Proofview.tactic
val mutual_cofix : Names.Id.t -> (Names.Id.t * EConstr.constr) list -> int -> unit Proofview.tactic
val cofix : Names.Id.t -> unit Proofview.tactic
val convert_leq : EConstr.constr -> EConstr.constr -> unit Proofview.tactic
Introduction tactics.
val fresh_id_in_env : Names.Id.Set.t -> Names.Id.t -> Environ.env -> Names.Id.t
val fresh_id : Names.Id.Set.t -> Names.Id.t -> Goal.goal Evd.sigma -> Names.Id.t
val find_intro_names : EConstr.rel_context -> Goal.goal Evd.sigma -> Names.Id.t list
val intro : unit Proofview.tactic
val introf : unit Proofview.tactic
val intro_move : Names.Id.t option -> Names.Id.t Logic.move_location -> unit Proofview.tactic
val intro_move_avoid : Names.Id.t option -> Names.Id.Set.t -> Names.Id.t Logic.move_location -> unit Proofview.tactic
val intro_avoiding : Names.Id.Set.t -> unit Proofview.tactic

intro_avoiding idl acts as intro but prevents the new Id.t to belong to idl

val intro_replacing : Names.Id.t -> unit Proofview.tactic
val intro_using : Names.Id.t -> unit Proofview.tactic
  • deprecated Prefer [intro_using_then] to avoid renaming issues.
val intro_using_then : Names.Id.t -> (Names.Id.t -> unit Proofview.tactic) -> unit Proofview.tactic
val intro_mustbe_force : Names.Id.t -> unit Proofview.tactic
val intros_mustbe_force : Names.Id.t list -> unit Proofview.tactic
val intro_then : (Names.Id.t -> unit Proofview.tactic) -> unit Proofview.tactic
val intros_using : Names.Id.t list -> unit Proofview.tactic
  • deprecated Prefer [intros_using_then] to avoid renaming issues.
val intros_using_then : Names.Id.t list -> (Names.Id.t list -> unit Proofview.tactic) -> unit Proofview.tactic
val intros_replacing : Names.Id.t list -> unit Proofview.tactic
val intros_possibly_replacing : Names.Id.t list -> unit Proofview.tactic
val auto_intros_tac : Names.Name.t list -> unit Proofview.tactic

auto_intros_tac names handles Automatic Introduction of binders

val intros : unit Proofview.tactic
val intros_clearing : bool list -> unit Proofview.tactic

Assuming a tactic tac depending on an hypothesis Id.t, try_intros_until tac arg first assumes that arg denotes a quantified hypothesis (denoted by name or by index) and try to introduce it in context before to apply tac, otherwise assume the hypothesis is already in context and directly apply tac

type evars_flag = bool
type rec_flag = bool
type advanced_flag = bool
type clear_flag = bool option

Apply a tactic on a quantified hypothesis, an hypothesis in context or a term with bindings

type 'a core_destruction_arg =
  1. | ElimOnConstr of 'a
  2. | ElimOnIdent of Names.lident
  3. | ElimOnAnonHyp of int
type 'a destruction_arg = clear_flag * 'a core_destruction_arg

Tell if a used hypothesis should be cleared by default or not

val use_clear_hyp_by_default : unit -> bool
Introduction tactics with eliminations.
val intro_patterns : evars_flag -> Tactypes.intro_patterns -> unit Proofview.tactic
val intro_patterns_bound_to : evars_flag -> int -> Names.Id.t Logic.move_location -> Tactypes.intro_patterns -> unit Proofview.tactic
val intros_patterns : evars_flag -> Tactypes.intro_patterns -> unit Proofview.tactic

Implements user-level "intros", with standing for "**"

Exact tactics.
val assumption : unit Proofview.tactic
val exact_no_check : EConstr.constr -> unit Proofview.tactic
val vm_cast_no_check : EConstr.constr -> unit Proofview.tactic
val native_cast_no_check : EConstr.constr -> unit Proofview.tactic
val exact_check : EConstr.constr -> unit Proofview.tactic
val exact_proof : Constrexpr.constr_expr -> unit Proofview.tactic
Reduction tactics.
type tactic_reduction = Reductionops.reduction_function
type e_tactic_reduction = Reductionops.e_reduction_function
val make_change_arg : EConstr.constr -> change_arg
val reduct_in_hyp : check:bool -> reorder:bool -> tactic_reduction -> Locus.hyp_location -> unit Proofview.tactic
val reduct_option : check:bool -> (tactic_reduction * Constr.cast_kind) -> Locus.goal_location -> unit Proofview.tactic
val reduct_in_concl : check:bool -> (tactic_reduction * Constr.cast_kind) -> unit Proofview.tactic
val e_reduct_in_concl : check:bool -> (e_tactic_reduction * Constr.cast_kind) -> unit Proofview.tactic
val change_in_concl : check:bool -> (Locus.occurrences * Pattern.constr_pattern) option -> change_arg -> unit Proofview.tactic
val change_concl : EConstr.constr -> unit Proofview.tactic
val change_in_hyp : check:bool -> (Locus.occurrences * Pattern.constr_pattern) option -> change_arg -> Locus.hyp_location -> unit Proofview.tactic
val red_in_concl : unit Proofview.tactic
val red_in_hyp : Locus.hyp_location -> unit Proofview.tactic
val red_option : Locus.goal_location -> unit Proofview.tactic
val hnf_in_concl : unit Proofview.tactic
val hnf_in_hyp : Locus.hyp_location -> unit Proofview.tactic
val hnf_option : Locus.goal_location -> unit Proofview.tactic
val simpl_in_concl : unit Proofview.tactic
val simpl_in_hyp : Locus.hyp_location -> unit Proofview.tactic
val simpl_option : Locus.goal_location -> unit Proofview.tactic
val normalise_in_concl : unit Proofview.tactic
val normalise_in_hyp : Locus.hyp_location -> unit Proofview.tactic
val normalise_option : Locus.goal_location -> unit Proofview.tactic
val normalise_vm_in_concl : unit Proofview.tactic
val change : check:bool -> Pattern.constr_pattern option -> change_arg -> Locus.clause -> unit Proofview.tactic
val pattern_option : (Locus.occurrences * EConstr.constr) list -> Locus.goal_location -> unit Proofview.tactic
val unfold_constr : Names.GlobRef.t -> unit Proofview.tactic
Modification of the local context.
val clear : Names.Id.t list -> unit Proofview.tactic
val clear_body : Names.Id.t list -> unit Proofview.tactic
val unfold_body : Names.Id.t -> unit Proofview.tactic
val keep : Names.Id.t list -> unit Proofview.tactic
val apply_clear_request : clear_flag -> bool -> EConstr.constr -> unit Proofview.tactic
val rename_hyp : (Names.Id.t * Names.Id.t) list -> unit Proofview.tactic
val revert : Names.Id.t list -> unit Proofview.tactic
Resolution tactics.
val apply_type : typecheck:bool -> EConstr.constr -> EConstr.constr list -> unit Proofview.tactic
val bring_hyps : EConstr.named_context -> unit Proofview.tactic
val apply : EConstr.constr -> unit Proofview.tactic
val eapply : EConstr.constr -> unit Proofview.tactic
val apply_with_delayed_bindings_gen : advanced_flag -> evars_flag -> (clear_flag * Tactypes.delayed_open_constr_with_bindings CAst.t) list -> unit Proofview.tactic
val apply_with_bindings : EConstr.constr Tactypes.with_bindings -> unit Proofview.tactic
val eapply_with_bindings : EConstr.constr Tactypes.with_bindings -> unit Proofview.tactic
val cut_and_apply : EConstr.constr -> unit Proofview.tactic
Elimination tactics.
type elim_scheme = {
  1. elimt : EConstr.types;
  2. indref : Names.GlobRef.t option;
  3. params : EConstr.rel_context;
    (*

    (prm1,tprm1);(prm2,tprm2)...(prmp,tprmp)

    *)
  4. nparams : int;
    (*

    number of parameters

    *)
  5. predicates : EConstr.rel_context;
    (*

    (Qq, (Tq_1 -> Tq_2 ->...-> Tq_nq)), (Q1,...)

    *)
  6. npredicates : int;
    (*

    Number of predicates

    *)
  7. branches : EConstr.rel_context;
    (*

    branchr,...,branch1

    *)
  8. nbranches : int;
    (*

    Number of branches

    *)
  9. args : EConstr.rel_context;
    (*

    (xni, Ti_ni) ... (x1, Ti_1)

    *)
  10. nargs : int;
    (*

    number of arguments

    *)
  11. indarg : EConstr.rel_declaration option;
    (*

    Some (H,I prm1..prmp x1...xni) if HI is in premisses, None otherwise

    *)
  12. concl : EConstr.types;
    (*

    Qi x1...xni HI (f...), HI and (f...) are optional and mutually exclusive

    *)
  13. indarg_in_concl : bool;
    (*

    true if HI appears at the end of conclusion

    *)
  14. farg_in_concl : bool;
    (*

    true if (f...) appears at the end of conclusion

    *)
}

rel_contexts and rel_declaration actually contain triples, and lists are actually in reverse order to fit compose_prod.

val compute_elim_sig : Evd.evar_map -> EConstr.types -> elim_scheme
type eliminator =
  1. | ElimTerm of EConstr.constr
  2. | ElimClause of EConstr.constr Tactypes.with_bindings
val general_elim_clause : evars_flag -> Unification.unify_flags -> Names.Id.t option -> Clenv.clausenv -> eliminator -> unit Proofview.tactic
val simplest_elim : EConstr.constr -> unit Proofview.tactic
Case analysis tactics.
val simplest_case : EConstr.constr -> unit Proofview.tactic
Generic case analysis / induction tactics.

Implements user-level "destruct" and "induction"

Eliminations giving the type instead of the proof.
val case_type : EConstr.types -> unit Proofview.tactic
val elim_type : EConstr.types -> unit Proofview.tactic
Constructor tactics.
val constructor_tac : evars_flag -> int option -> int -> EConstr.constr Tactypes.bindings -> unit Proofview.tactic
val any_constructor : evars_flag -> unit Proofview.tactic option -> unit Proofview.tactic
val one_constructor : int -> EConstr.constr Tactypes.bindings -> unit Proofview.tactic
val left_with_bindings : evars_flag -> EConstr.constr Tactypes.bindings -> unit Proofview.tactic
val right_with_bindings : evars_flag -> EConstr.constr Tactypes.bindings -> unit Proofview.tactic
val split_with_bindings : evars_flag -> EConstr.constr Tactypes.bindings list -> unit Proofview.tactic
val split_with_delayed_bindings : evars_flag -> EConstr.constr Tactypes.bindings Tactypes.delayed_open list -> unit Proofview.tactic
val simplest_left : unit Proofview.tactic
val simplest_right : unit Proofview.tactic
val simplest_split : unit Proofview.tactic
Equality tactics.
val setoid_reflexivity : unit Proofview.tactic Hook.t
val reflexivity_red : bool -> unit Proofview.tactic
val reflexivity : unit Proofview.tactic
val intros_reflexivity : unit Proofview.tactic
val setoid_symmetry : unit Proofview.tactic Hook.t
val symmetry_red : bool -> unit Proofview.tactic
val symmetry : unit Proofview.tactic
val setoid_symmetry_in : (Names.Id.t -> unit Proofview.tactic) Hook.t
val intros_symmetry : Locus.clause -> unit Proofview.tactic
val setoid_transitivity : (EConstr.constr option -> unit Proofview.tactic) Hook.t
val transitivity_red : bool -> EConstr.constr option -> unit Proofview.tactic
val transitivity : EConstr.constr -> unit Proofview.tactic
val etransitivity : unit Proofview.tactic
val intros_transitivity : EConstr.constr option -> unit Proofview.tactic
Cut tactics.
val assert_before_replacing : Names.Id.t -> EConstr.types -> unit Proofview.tactic
val assert_after_replacing : Names.Id.t -> EConstr.types -> unit Proofview.tactic
val assert_before : Names.Name.t -> EConstr.types -> unit Proofview.tactic
val assert_after : Names.Name.t -> EConstr.types -> unit Proofview.tactic
val assert_as : bool -> Names.Id.t option -> Tactypes.intro_pattern option -> EConstr.constr -> unit Proofview.tactic

Implements the tactics assert, enough and pose proof; note that "by" applies on the first goal for both assert and enough

val assert_by : Names.Name.t -> EConstr.types -> unit Proofview.tactic -> unit Proofview.tactic
val enough_by : Names.Name.t -> EConstr.types -> unit Proofview.tactic -> unit Proofview.tactic
val pose_proof : Names.Name.t -> EConstr.constr -> unit Proofview.tactic

Common entry point for user-level "assert", "enough" and "pose proof"

val forward : bool -> unit Proofview.tactic option option -> Tactypes.intro_pattern option -> EConstr.constr -> unit Proofview.tactic

Implements the tactic cut, actually a modus ponens rule

Tactics for adding local definitions.
val pose_tac : Names.Name.t -> EConstr.constr -> unit Proofview.tactic
val letin_tac : (bool * Tactypes.intro_pattern_naming) option -> Names.Name.t -> EConstr.constr -> EConstr.types option -> Locus.clause -> unit Proofview.tactic

Common entry point for user-level "set", "pose" and "remember"

Generalize tactics.
val generalize : EConstr.constr list -> unit Proofview.tactic
val new_generalize_gen : ((Locus.occurrences * EConstr.constr) * Names.Name.t) list -> unit Proofview.tactic
val generalize_dep : ?with_let:bool -> EConstr.constr -> unit Proofview.tactic
Other tactics.
val constr_eq : strict:bool -> EConstr.constr -> EConstr.constr -> unit Proofview.tactic

Syntactic equality up to universes. With strict the universe constraints must be already true to succeed, without strict they are added to the evar map.

val abstract_generalize : ?generalize_vars:bool -> ?force_dep:bool -> Names.Id.t -> unit Proofview.tactic
val specialize_eqs : Names.Id.t -> unit Proofview.tactic
val general_rewrite_clause : (bool -> evars_flag -> EConstr.constr Tactypes.with_bindings -> Locus.clause -> unit Proofview.tactic) Hook.t
val subst_one : (bool -> Names.Id.t -> (Names.Id.t * EConstr.constr * bool) -> unit Proofview.tactic) Hook.t
val declare_intro_decomp_eq : ((int -> unit Proofview.tactic) -> (Coqlib.coq_eq_data * EConstr.types * (EConstr.types * EConstr.constr * EConstr.constr)) -> (EConstr.constr * EConstr.types) -> unit Proofview.tactic) -> unit
val with_set_strategy : (Conv_oracle.level * Names.GlobRef.t list) list -> 'a Proofview.tactic -> 'a Proofview.tactic

Tactic analogous to the Strategy vernacular, but only applied locally to the tactic argument

Simple form of basic tactics.
module Simple : sig ... end

Simplified version of some of the above tactics

Tacticals defined directly in term of Proofview
module New : sig ... end
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