path: root/tactics/hipattern.ml

(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* $Id$ *)

open Pp
open Util
open Names
open Nameops
open Term
open Termops
open Reductionops
open Inductiveops
open Evd
open Environ
open Proof_trees
open Clenv
open Pattern
open Matching
open Coqlib
open Declarations

(* I implemented the following functions which test whether a term t
   is an inductive but non-recursive type, a general conjuction, a
   general disjunction, or a type with no constructors.

   They are more general than matching with or_term, and_term, etc, 
   since they do not depend on the name of the type. Hence, they 
   also work on ad-hoc disjunctions introduced by the user.
  
  -- Eduardo (6/8/97). *)

type 'a matching_function = constr -> 'a option

type testing_function  = constr -> bool

let mkmeta n = Nameops.make_ident "X" (Some n)
let mkPMeta n = PMeta (Some (mkmeta n))
let meta1 = mkmeta 1
let meta2 = mkmeta 2
let meta3 = mkmeta 3
let meta4 = mkmeta 4

let op2bool = function Some _ -> true | None -> false

let match_with_non_recursive_type t = 
  match kind_of_term t with 
    | App _ -> 
        let (hdapp,args) = decompose_app t in
        (match kind_of_term hdapp with
           | Ind ind -> 
               if not (Global.lookup_mind (fst ind)).mind_finite then 
		 Some (hdapp,args) 
	       else 
		 None 
           | _ -> None)
    | _ -> None

let is_non_recursive_type t = op2bool (match_with_non_recursive_type t)

(* A general conjunction type is a non-recursive inductive type with
   only one constructor. *)

let match_with_conjunction t =
  let (hdapp,args) = decompose_app t in 
  match kind_of_term hdapp with
    | Ind ind -> 
	let (mib,mip) = Global.lookup_inductive ind in
	if (Array.length mip.mind_consnames = 1)
	  && (not (mis_is_recursive (ind,mib,mip)))
          && (mip.mind_nrealargs = 0)
        then 
	  Some (hdapp,args)
        else 
	  None
    | _ -> None

let is_conjunction t = op2bool (match_with_conjunction t)
    
(* A general disjunction type is a non-recursive inductive type all
   whose constructors have a single argument. *)

let match_with_disjunction t =
  let (hdapp,args) = decompose_app t in 
  match kind_of_term hdapp with
    | Ind ind  ->
        let car = mis_constr_nargs ind in
	if array_for_all (fun ar -> ar = 1) car &&
	   (let (mib,mip) = Global.lookup_inductive ind in
            not (mis_is_recursive (ind,mib,mip)))
        then 
	  Some (hdapp,args)
        else 
	  None
    | _ -> None

let is_disjunction t = op2bool (match_with_disjunction t)

let match_with_empty_type t =
  let (hdapp,args) = decompose_app t in
  match (kind_of_term hdapp) with
    | Ind ind -> 
        let (mib,mip) = Global.lookup_inductive ind in
        let nconstr = Array.length mip.mind_consnames in  
	if nconstr = 0 then Some hdapp else None
    | _ ->  None
	  
let is_empty_type t = op2bool (match_with_empty_type t)

let match_with_unit_type t =
  let (hdapp,args) = decompose_app t in
  match (kind_of_term hdapp) with
    | Ind ind  -> 
        let (mib,mip) = Global.lookup_inductive ind in
        let constr_types = mip.mind_nf_lc in 
        let nconstr = Array.length mip.mind_consnames in
        let zero_args c =
          nb_prod c = mip.mind_nparams in  
	if nconstr = 1 && array_for_all zero_args constr_types then 
	  Some hdapp
        else 
	  None
    | _ -> None

let is_unit_type t = op2bool (match_with_unit_type t)

(* Checks if a given term is an application of an
   inductive binary relation R, so that R has only one constructor
   establishing its reflexivity.  *)

(* ["(A : ?)(x:A)(? A x x)"] and ["(x : ?)(? x x)"] *)
let x = Name (id_of_string "x")
let y = Name (id_of_string "y")
let name_A = Name (id_of_string "A")
let coq_refl_rel1_pattern =
  PProd
    (name_A, PMeta None,
    PProd (x, PRel 1, PApp (PMeta None, [|PRel 2; PRel 1; PRel 1|])))
let coq_refl_rel2_pattern =
  PProd (x, PMeta None, PApp (PMeta None, [|PRel 1; PRel 1|]))

let coq_refl_reljm_pattern =
PProd
    (name_A, PMeta None,
    PProd (x, PRel 1, PApp (PMeta None, [|PRel 2; PRel 1; PRel 2;PRel 1|])))

let match_with_equation t =
  let (hdapp,args) = decompose_app t in
  match (kind_of_term hdapp) with
    | Ind ind -> 
        let (mib,mip) = Global.lookup_inductive ind in
        let constr_types = mip.mind_nf_lc in 
        let nconstr = Array.length mip.mind_consnames in
	if nconstr = 1 &&
           (is_matching coq_refl_rel1_pattern constr_types.(0) ||
            is_matching coq_refl_rel2_pattern constr_types.(0) ||
            is_matching coq_refl_reljm_pattern constr_types.(0)) 
        then 
	  Some (hdapp,args)
        else 
	  None
    | _ -> None

let is_equation t = op2bool (match_with_equation  t)

(* ["(?1 -> ?2)"] *)
let imp a b = PProd (Anonymous, a, b)
let coq_arrow_pattern = imp (mkPMeta 1) (mkPMeta 2)
let match_arrow_pattern t =
  match matches coq_arrow_pattern t with
    | [(m1,arg);(m2,mind)] -> assert (m1=meta1 & m2=meta2); (arg, mind)
    | _ -> anomaly "Incorrect pattern matching" 

let match_with_nottype t =
  try
    let (arg,mind) = match_arrow_pattern t in
    if is_empty_type mind then Some (mind,arg) else None
  with PatternMatchingFailure -> None  

let is_nottype t = op2bool (match_with_nottype t)
		     
let match_with_forall_term c=
  match kind_of_term c with
    | Prod (nam,a,b) -> Some (nam,a,b)
    | _            -> None

let is_forall_term c = op2bool (match_with_forall_term c) 

let match_with_imp_term c=
  match kind_of_term c with
    | Prod (_,a,b) when not (dependent (mkRel 1) b) ->Some (a,b)
    | _              -> None

let is_imp_term c = op2bool (match_with_imp_term c) 

let rec has_nodep_prod_after n c =
  match kind_of_term c with
    | Prod (_,_,b) -> 
	( n>0 || not (dependent (mkRel 1) b)) 
	&& (has_nodep_prod_after (n-1) b)
    | _            -> true
	  
let has_nodep_prod = has_nodep_prod_after 0
	
let match_with_nodep_ind t =
  let (hdapp,args) = decompose_app t in
    match (kind_of_term hdapp) with
      | Ind ind  -> 
          let (mib,mip) = Global.lookup_inductive ind in
	    if Array.length (mib.mind_packets)>1 then None else
	      let nodep_constr = has_nodep_prod_after mip.mind_nparams in
		if array_for_all nodep_constr mip.mind_nf_lc then
		  let params=
		    if mip.mind_nrealargs=0 then args else
		      fst (list_chop mip.mind_nparams args) in
		    Some (hdapp,params,mip.mind_nrealargs)
		else 
		  None
      | _ -> None
	  
let is_nodep_ind t=op2bool (match_with_nodep_ind t)

let match_with_sigma_type t=
  let (hdapp,args) = decompose_app t in
  match (kind_of_term hdapp) with
    | Ind ind  -> 
        let (mib,mip) = Global.lookup_inductive ind in
          if (Array.length (mib.mind_packets)=1) &&
	    (mip.mind_nrealargs=0) &&
	    (Array.length mip.mind_consnames=1) &&
	    has_nodep_prod_after (mip.mind_nparams+1) mip.mind_nf_lc.(0) then
	      (*allowing only 1 existential*) 
	      Some (hdapp,args)
	  else 
	    None
    | _ -> None

let is_sigma_type t=op2bool (match_with_sigma_type t)

(***** Destructing patterns bound to some theory *)

let rec first_match matcher = function
  | [] -> raise PatternMatchingFailure
  | (pat,build_set)::l ->
      try (build_set (),matcher pat)
      with PatternMatchingFailure -> first_match matcher l

(*** Equality *)

(* Patterns "(eq ?1 ?2 ?3)", "(eqT ?1 ?2 ?3)" and "(idT ?1 ?2 ?3)" *)
let coq_eq_pattern_gen eq = 
  lazy (PApp(PRef (Lazy.force eq), [|mkPMeta 1;mkPMeta 2;mkPMeta 3|]))
let coq_eq_pattern = coq_eq_pattern_gen coq_eq_ref
(*let coq_eqT_pattern = coq_eq_pattern_gen coq_eqT_ref*)
let coq_idT_pattern = coq_eq_pattern_gen coq_idT_ref

let match_eq eqn eq_pat =
  match matches (Lazy.force eq_pat) eqn with
    | [(m1,t);(m2,x);(m3,y)] ->
	assert (m1 = meta1 & m2 = meta2 & m3 = meta3);
	(t,x,y)
    | _ -> anomaly "match_eq: an eq pattern should match 3 terms"

let equalities =
  [coq_eq_pattern, build_coq_eq_data;
(*   coq_eqT_pattern, build_coq_eqT_data;*)
   coq_idT_pattern, build_coq_idT_data]

let find_eq_data_decompose eqn = (* fails with PatternMatchingFailure *)
  first_match (match_eq eqn) equalities

open Tacmach
open Tacticals

let match_eq_nf gls eqn eq_pat =
  match pf_matches gls (Lazy.force eq_pat) eqn with
    | [(m1,t);(m2,x);(m3,y)] ->
	assert (m1 = meta1 & m2 = meta2 & m3 = meta3);
	(t,pf_whd_betadeltaiota gls x,pf_whd_betadeltaiota gls y)
    | _ -> anomaly "match_eq: an eq pattern should match 3 terms"

let dest_nf_eq gls eqn =
  try
    snd (first_match (match_eq_nf gls eqn) equalities)
  with PatternMatchingFailure ->
    error "Not an equality"

(*** Sigma-types *)

(* Patterns "(existS ?1 ?2 ?3 ?4)" and "(existT ?1 ?2 ?3 ?4)" *)
let coq_ex_pattern_gen ex =
  lazy(PApp(PRef (Lazy.force ex), [|mkPMeta 1;mkPMeta 2;mkPMeta 3;mkPMeta 4|]))
let coq_existS_pattern = coq_ex_pattern_gen coq_existS_ref
let coq_existT_pattern = coq_ex_pattern_gen coq_existT_ref

let match_sigma ex ex_pat =
  match matches (Lazy.force ex_pat) ex with
    | [(m1,a);(m2,p);(m3,car);(m4,cdr)] as l ->
	assert (m1=meta1 & m2=meta2 & m3=meta3 & m4=meta4);
	(a,p,car,cdr)
    | _ ->
	anomaly "match_sigma: a successful sigma pattern should match 4 terms"

let find_sigma_data_decompose ex = (* fails with PatternMatchingFailure *)
  first_match (match_sigma ex) 
    [coq_existS_pattern, build_sigma_set; 
     coq_existT_pattern, build_sigma_type]

(* Pattern "(sig ?1 ?2)" *)
let coq_sig_pattern = 
  lazy (PApp (PRef (Lazy.force coq_sig_ref), [| (mkPMeta 1); (mkPMeta 2) |]))

let match_sigma t =
  match matches (Lazy.force coq_sig_pattern) t with
    | [(_,a); (_,p)] -> (a,p)
    | _ -> anomaly "Unexpected pattern"

let is_matching_sigma t = is_matching (Lazy.force coq_sig_pattern) t

(*** Decidable equalities *)

(* Pattern "(sumbool (eq ?1 ?2 ?3) ?4)" *)
let coq_eqdec_partial_pattern =
  lazy
    (PApp
       (PRef (Lazy.force coq_sumbool_ref),
	[| Lazy.force coq_eq_pattern; (mkPMeta 4) |]))

let match_eqdec_partial t =
  match matches (Lazy.force coq_eqdec_partial_pattern) t with
    | [_; (_,lhs); (_,rhs); _] -> (lhs,rhs)
    | _ -> anomaly "Unexpected pattern"

(* The expected form of the goal for the tactic Decide Equality *)

(* Pattern "(x,y:?1){<?1>x=y}+{~(<?1>x=y)}" *)
(* i.e. "(x,y:?1)(sumbool (eq ?1 x y) ~(eq ?1 x y))" *)
let x = Name (id_of_string "x")
let y = Name (id_of_string "y")
let coq_eqdec_pattern =
  lazy
    (PProd (x, (mkPMeta 1), PProd (y, (mkPMeta 1), 
    PApp (PRef (Lazy.force coq_sumbool_ref),
	  [| PApp (PRef (Lazy.force coq_eq_ref),
		   [| (mkPMeta 1); PRel 2; PRel 1 |]);
	     PApp (PRef (Lazy.force coq_not_ref), 
		   [|PApp (PRef (Lazy.force coq_eq_ref),
 			   [| (mkPMeta 1); PRel 2; PRel 1 |])|]) |]))))

let match_eqdec t =
  match matches (Lazy.force coq_eqdec_pattern) t with
    | [(_,typ)] -> typ
    | _ -> anomaly "Unexpected pattern"

(* Patterns "~ ?" and "? -> False" *)
let coq_not_pattern = lazy(PApp(PRef (Lazy.force coq_not_ref), [|PMeta None|]))
let coq_imp_False_pattern =
  lazy (imp (PMeta None) (PRef (Lazy.force coq_False_ref)))

let is_matching_not t = is_matching (Lazy.force coq_not_pattern) t
let is_matching_imp_False t = is_matching (Lazy.force coq_imp_False_pattern) t