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Diffstat (limited to 'coq.mli')
| -rw-r--r-- | coq.mli | 231 |
1 files changed, 231 insertions, 0 deletions
@@ -0,0 +1,231 @@ +(***************************************************************************) +(* This is part of aac_tactics, it is distributed under the terms of the *) +(* GNU Lesser General Public License version 3 *) +(* (see file LICENSE for more details) *) +(* *) +(* Copyright 2009-2010: Thomas Braibant, Damien Pous. *) +(***************************************************************************) + +(** Interface with Coq where we define some handlers for Coq's API, + and we import several definitions from Coq's standard library. + + This general purpose library could be reused by other plugins. + + Some salient points: + - we use Caml's module system to mimic Coq's one, and avoid cluttering + the namespace; + - we also provide several handlers for standard coq tactics, in + order to provide a unified setting (we replace functions that + modify the evar_map by functions that operate on the whole + goal, and repack the modified evar_map with it). + +*) + +(** {2 Getting Coq terms from the environment} *) + +val init_constant : string list -> string -> Term.constr + +(** {2 General purpose functions} *) + +type goal_sigma = Proof_type.goal Tacmach.sigma +val goal_update : goal_sigma -> Evd.evar_map -> goal_sigma +val resolve_one_typeclass : Proof_type.goal Tacmach.sigma -> Term.types -> Term.constr * goal_sigma +val cps_resolve_one_typeclass: ?error:string -> Term.types -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic +val nf_evar : goal_sigma -> Term.constr -> Term.constr +val fresh_evar :goal_sigma -> Term.types -> Term.constr* goal_sigma +val evar_unit :goal_sigma ->Term.constr -> Term.constr* goal_sigma +val evar_binary: goal_sigma -> Term.constr -> Term.constr* goal_sigma +val evar_relation: goal_sigma -> Term.constr -> Term.constr* goal_sigma +val cps_evar_relation : Term.constr -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic +(** [cps_mk_letin name v] binds the constr [v] using a letin tactic *) +val cps_mk_letin : string -> Term.constr -> ( Term.constr -> Proof_type.tactic) -> Proof_type.tactic + + +val decomp_term : Term.constr -> (Term.constr , Term.types) Term.kind_of_term +val lapp : Term.constr lazy_t -> Term.constr array -> Term.constr + +(** {2 Bindings with Coq' Standard Library} *) + +(** Coq lists *) +module List: +sig + (** [of_list ty l] *) + val of_list:Term.constr ->Term.constr list ->Term.constr + + (** [type_of_list ty] *) + val type_of_list:Term.constr ->Term.constr +end + +(** Coq pairs *) +module Pair: +sig + val typ:Term.constr lazy_t + val pair:Term.constr lazy_t + val of_pair : Term.constr -> Term.constr -> Term.constr * Term.constr -> Term.constr +end + +module Bool : sig + val typ : Term.constr lazy_t + val of_bool : bool -> Term.constr +end + + +module Comparison : sig + val typ : Term.constr lazy_t + val eq : Term.constr lazy_t + val lt : Term.constr lazy_t + val gt : Term.constr lazy_t +end + +module Leibniz : sig + val eq_refl : Term.types -> Term.constr -> Term.constr +end + +module Option : sig + val some : Term.constr -> Term.constr -> Term.constr + val none : Term.constr -> Term.constr + val of_option : Term.constr -> Term.constr option -> Term.constr +end + +(** Coq positive numbers (pos) *) +module Pos: +sig + val typ:Term.constr lazy_t + val of_int: int ->Term.constr +end + +(** Coq unary numbers (peano) *) +module Nat: +sig + val typ:Term.constr lazy_t + val of_int: int ->Term.constr +end + +(** Coq typeclasses *) +module Classes: +sig + val mk_morphism: Term.constr -> Term.constr -> Term.constr -> Term.constr + val mk_equivalence: Term.constr -> Term.constr -> Term.constr + val mk_reflexive: Term.constr -> Term.constr -> Term.constr + val mk_transitive: Term.constr -> Term.constr -> Term.constr +end + +module Relation : sig + type t = {carrier : Term.constr; r : Term.constr;} + val make : Term.constr -> Term.constr -> t + val split : t -> Term.constr * Term.constr +end + +module Transitive : sig + type t = + { + carrier : Term.constr; + leq : Term.constr; + transitive : Term.constr; + } + val make : Term.constr -> Term.constr -> Term.constr -> t + val infer : goal_sigma -> Term.constr -> Term.constr -> t * goal_sigma + val from_relation : goal_sigma -> Relation.t -> t * goal_sigma + val cps_from_relation : Relation.t -> (t -> Proof_type.tactic) -> Proof_type.tactic + val to_relation : t -> Relation.t +end + +module Equivalence : sig + type t = + { + carrier : Term.constr; + eq : Term.constr; + equivalence : Term.constr; + } + val make : Term.constr -> Term.constr -> Term.constr -> t + val infer : goal_sigma -> Term.constr -> Term.constr -> t * goal_sigma + val from_relation : goal_sigma -> Relation.t -> t * goal_sigma + val cps_from_relation : Relation.t -> (t -> Proof_type.tactic) -> Proof_type.tactic + val to_relation : t -> Relation.t + val split : t -> Term.constr * Term.constr * Term.constr +end + +(** [match_as_equation ?context goal c] try to decompose c as a + relation applied to two terms. An optionnal rel_context can be + provided to ensure that the term remains typable *) +val match_as_equation : ?context:Term.rel_context -> goal_sigma -> Term.constr -> (Term.constr * Term.constr * Relation.t) option + +(** {2 Some tacticials} *) + +(** time the execution of a tactic *) +val tclTIME : string -> Proof_type.tactic -> Proof_type.tactic + +(** emit debug messages to see which tactics are failing *) +val tclDEBUG : string -> Proof_type.tactic -> Proof_type.tactic + +(** print the current goal *) +val tclPRINT : Proof_type.tactic -> Proof_type.tactic + + +(** {2 Error related mechanisms} *) + +val anomaly : string -> 'a +val user_error : string -> 'a +val warning : string -> unit + + +(** {2 Rewriting tactics used in aac_rewrite} *) + +module Rewrite : sig + +(** The rewriting tactics used in aac_rewrite, build as handlers of the usual [setoid_rewrite]*) + + +(** {2 Datatypes} *) + +(** We keep some informations about the hypothesis, with an (informal) + invariant: + - [typeof hyp = typ] + - [typ = forall context, body] + - [body = rel left right] + +*) +type hypinfo = + { + hyp : Term.constr; (** the actual constr corresponding to the hypothese *) + hyptype : Term.constr; (** the type of the hypothesis *) + context : Term.rel_context; (** the quantifications of the hypothese *) + body : Term.constr; (** the body of the hypothese*) + rel : Relation.t; (** the relation *) + left : Term.constr; (** left hand side *) + right : Term.constr; (** right hand side *) + l2r : bool; (** rewriting from left to right *) + } + +(** [get_hypinfo H l2r ?check_type k] analyse the hypothesis H, and + build the related hypinfo, in CPS style. Moreover, an optionnal + function can be provided to check the type of every free + variable of the body of the hypothesis. *) +val get_hypinfo :Term.constr -> l2r:bool -> ?check_type:(Term.types -> bool) -> (hypinfo -> Proof_type.tactic) -> Proof_type.tactic + +(** {2 Rewriting with bindings} + + The problem : Given a term to rewrite of type [H :forall xn ... x1, + t], we have to instanciate the subset of [xi] of type + [carrier]. [subst : (int * constr)] is the mapping the De Bruijn + indices in [t] to the [constrs]. We need to handle the rest of the + indexes. Two ways : + + - either using fresh evars and rewriting [H tn ?1 tn-2 ?2 ] + - either building a term like [fun 1 2 => H tn 1 tn-2 2] + + Both these terms have the same type. +*) + +(** build the constr to rewrite, in CPS style, with lambda abstractions *) +val build : hypinfo -> (int * Term.constr) list -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic + +(** build the constr to rewrite, in CPS style, with evars *) +val build_with_evar : hypinfo -> (int * Term.constr) list -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic + +(** [rewrite ?abort hypinfo subst] builds the rewriting tactic + associated with the given [subst] and [hypinfo], and feeds it to + the given continuation. If [abort] is set to [true], we build + [tclIDTAC] instead. *) +val rewrite : ?abort:bool -> hypinfo -> (int * Term.constr) list -> (Proof_type.tactic -> Proof_type.tactic) -> Proof_type.tactic +end |