aboutsummaryrefslogtreecommitdiffhomepage
path: root/tactics/contradiction.ml
blob: e12063fd44c2a4c070fb87c2039c16c164eeb6b2 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

open Constr
open EConstr
open Hipattern
open Tactics
open Coqlib
open Reductionops
open Proofview.Notations

module NamedDecl = Context.Named.Declaration

(* Absurd *)

let mk_absurd_proof coq_not t =
  let id = Namegen.default_dependent_ident in
  mkLambda (Names.Name id,mkApp(coq_not,[|t|]),
    mkLambda (Names.Name id,t,mkApp (mkRel 2,[|mkRel 1|])))

let absurd c =
  Proofview.Goal.enter begin fun gl ->
    let sigma = Proofview.Goal.sigma gl in
    let env = Proofview.Goal.env gl in
    let j = Retyping.get_judgment_of env sigma c in
    let sigma, j = Coercion.inh_coerce_to_sort env sigma j in
    let t = j.Environ.utj_val in
    Proofview.Unsafe.tclEVARS sigma <*>
    Tacticals.New.pf_constr_of_global (build_coq_not ()) >>= fun coqnot ->
    Tacticals.New.pf_constr_of_global (build_coq_False ()) >>= fun coqfalse ->
    Tacticals.New.tclTHENLIST [
      elim_type coqfalse;
      Simple.apply (mk_absurd_proof coqnot t)
    ]
  end

let absurd c = absurd c

(* Contradiction *)

(** [f] does not assume its argument to be [nf_evar]-ed. *)
let filter_hyp f tac =
  let rec seek = function
    | [] -> Proofview.tclZERO Not_found
    | d::rest when f (NamedDecl.get_type d) -> tac (NamedDecl.get_id d)
    | _::rest -> seek rest in
  Proofview.Goal.enter begin fun gl ->
    let hyps = Proofview.Goal.hyps gl in
    seek hyps
  end

let contradiction_context =
  Proofview.Goal.enter begin fun gl ->
    let sigma = Tacmach.New.project gl in
    let env = Proofview.Goal.env gl in
    let rec seek_neg l = match l with
      | [] ->  Tacticals.New.tclZEROMSG (Pp.str"No such contradiction")
      | d :: rest ->
          let id = NamedDecl.get_id d in
          let typ = nf_evar sigma (NamedDecl.get_type d) in
	  let typ = whd_all env sigma typ in
	  if is_empty_type sigma typ then
	    simplest_elim (mkVar id)
	  else match EConstr.kind sigma typ with
	  | Prod (na,t,u) when is_empty_type sigma u ->
             let is_unit_or_eq = match_with_unit_or_eq_type sigma t in
	     Tacticals.New.tclORELSE
               (match is_unit_or_eq with
               | Some _ ->
                   let hd,args = decompose_app sigma t in
                   let (ind,_ as indu) = destInd sigma hd in
                   let nparams = Inductiveops.inductive_nparams_env env ind in
                   let params = Util.List.firstn nparams args in
                   let p = applist ((mkConstructUi (indu,1)), params) in
                   (* Checking on the fly that it type-checks *)
                   simplest_elim (mkApp (mkVar id,[|p|]))
               | None ->
                 Tacticals.New.tclZEROMSG (Pp.str"Not a negated unit type."))
	      (Proofview.tclORELSE
                 (Proofview.Goal.enter begin fun gl ->
                   let is_conv_leq = Tacmach.New.pf_apply is_conv_leq gl in
	           filter_hyp (fun typ -> is_conv_leq typ t)
		     (fun id' -> simplest_elim (mkApp (mkVar id,[|mkVar id'|])))
                 end)
                 begin function (e, info) -> match e with
	           | Not_found -> seek_neg rest
                   | e -> Proofview.tclZERO ~info e
                 end)
	  | _ -> seek_neg rest
    in
    let hyps = Proofview.Goal.hyps gl in
    seek_neg hyps
  end

let is_negation_of env sigma typ t =
  match EConstr.kind sigma (whd_all env sigma t) with
    | Prod (na,t,u) ->
      is_empty_type sigma u && is_conv_leq env sigma typ t
    | _ -> false

let contradiction_term (c,lbind as cl) =
  Proofview.Goal.enter begin fun gl ->
    let sigma = Tacmach.New.project gl in
    let env = Proofview.Goal.env gl in
    let type_of = Tacmach.New.pf_unsafe_type_of gl in
    let typ = type_of c in
    let _, ccl = splay_prod env sigma typ in
    if is_empty_type sigma ccl then
      Tacticals.New.tclTHEN
        (elim false None cl None)
        (Tacticals.New.tclTRY assumption)
    else
      Proofview.tclORELSE
        begin
          if lbind = Tactypes.NoBindings then
            filter_hyp (fun c -> is_negation_of env sigma typ c)
              (fun id -> simplest_elim (mkApp (mkVar id,[|c|])))
          else
            Proofview.tclZERO Not_found
        end
        begin function (e, info) -> match e with
          | Not_found -> Tacticals.New.tclZEROMSG (Pp.str"Not a contradiction.")
          | e -> Proofview.tclZERO ~info e
        end
  end

let contradiction = function
  | None -> Tacticals.New.tclTHEN intros contradiction_context
  | Some c -> contradiction_term c