1 (* Copyright (C) 2002, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
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15 * GNU General Public License for more details.
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27 module PEH = ProofEngineHelpers
30 module TC = CicTypeChecker
31 module PET = ProofEngineTypes
32 module S = CicSubstitution
33 module PT = PrimitiveTactics
35 module FNG = FreshNamesGenerator
36 module MI = CicMkImplicit
37 module PESR = ProofEngineStructuralRules
39 let fail_msg0 = "unexported clearbody: invalid argument"
40 let fail_msg1 = "fwd: argument is not premise in the current goal"
41 let fail_msg2 = "fwd: no applicable simplification"
43 let error msg = raise (PET.Fail msg)
45 (* unexported tactics *******************************************************)
48 let id_tac (proof,goal) =
50 let _, metasenv, _, _ = proof in
51 let _, _, _ = CicUtil.lookup_meta goal metasenv in
53 with CicUtil.Meta_not_found _ -> (proof, [])
57 let clearbody ~index =
58 let rec find_name index = function
59 | Some (Cic.Name name, _) :: _ when index = 1 -> name
60 | _ :: tail when index > 1 -> find_name (pred index) tail
61 | _ -> error fail_msg0
63 let clearbody status =
64 let (proof, goal) = status in
65 let _, metasenv, _, _ = proof in
66 let _, context, _ = CicUtil.lookup_meta goal metasenv in
67 PET.apply_tactic (PESR.clearbody ~hyp:(find_name index context)) status
69 PET.mk_tactic clearbody
71 (* lapply *******************************************************************)
73 let strip_prods metasenv context ?how_many to_what term =
74 let irl = MI.identity_relocation_list_for_metavariable context in
75 let mk_meta metasenv its_type =
76 let index = MI.new_meta metasenv [] in
77 let metasenv = [index, context, its_type] @ metasenv in
78 metasenv, Cic.Meta (index, irl), index
80 let update_counters = function
81 | None, [] -> None, false, id_tac, []
82 | None, to_what :: tail -> None, true, PT.apply_tac ~term:to_what, tail
83 | Some hm, [] -> Some (pred hm), false, id_tac, []
84 | Some hm, to_what :: tail -> Some (pred hm), true, PT.apply_tac ~term:to_what, tail
86 let rec aux metasenv metas conts tw = function
87 | Some hm, _ when hm <= 0 -> metasenv, metas, conts
88 | xhm, Cic.Prod (Cic.Name _, t1, t2) ->
89 let metasenv, meta, index = mk_meta metasenv t1 in
90 aux metasenv (meta :: metas) (conts @ [id_tac, index]) tw (xhm, (S.subst meta t2))
91 | xhm, Cic.Prod (Cic.Anonymous, t1, t2) ->
92 let xhm, pos, tac, tw = update_counters (xhm, tw) in
93 let metasenv, meta, index = mk_meta metasenv t1 in
94 let conts = if pos then (tac, index) :: conts else conts @ [tac, index] in
95 aux metasenv (meta :: metas) conts tw (xhm, (S.subst meta t2))
96 | _, t -> metasenv, metas, conts
98 aux metasenv [] [] to_what (how_many, term)
100 let lapply_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
101 (* ?(substs = []) *) ?how_many ?(to_what = []) what =
102 let letin_tac term = PT.letin_tac ~mk_fresh_name_callback term in
103 let lapply_tac (proof, goal) =
104 let xuri, metasenv, u, t = proof in
105 let _, context, _ = CicUtil.lookup_meta goal metasenv in
106 let lemma, _ = TC.type_of_aux' metasenv context what U.empty_ugraph in
107 let lemma = FNG.clean_dummy_dependent_types lemma in
108 let metasenv, metas, conts = strip_prods metasenv context ?how_many to_what lemma in
109 let conclusion = Cic.Appl (what :: List.rev metas) in
110 let tac = T.thens ~start:(letin_tac conclusion)
111 ~continuations:[clearbody ~index:1]
113 let proof = (xuri, metasenv, u, t) in
114 let aux (proof, goals) (tac, goal) =
115 let proof, new_goals = PET.apply_tactic tac (proof, goal) in
116 proof, goals @ new_goals
118 List.fold_left aux (proof, []) ((tac, goal) :: conts)
120 PET.mk_tactic lapply_tac
122 (* fwd **********************************************************************)
125 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
128 let find_type metasenv context =
129 let rec aux p = function
130 | Some (Cic.Name name, Cic.Decl t) :: _ when name = hyp -> p, t
131 | Some (Cic.Name name, Cic.Def (_, Some t)) :: _ when name = hyp -> p, t
132 | Some (Cic.Name name, Cic.Def (u, _)) :: tail when name = hyp ->
133 p, fst (TC.type_of_aux' metasenv tail u U.empty_ugraph)
134 | _ :: tail -> aux (succ p) tail
135 | [] -> error fail_msg1
139 let lapply_tac to_what lemma =
140 lapply_tac ~mk_fresh_name_callback ~how_many:1 ~to_what:[to_what] lemma
142 let fwd_simpl_tac status =
143 let (proof, goal) = status in
144 let _, metasenv, _, _ = proof in
145 let _, context, ty = CicUtil.lookup_meta goal metasenv in
146 let index, major = find_type metasenv context in
147 match MetadataQuery.fwd_simpl ~dbd major with
148 | [] -> error fail_msg2
150 Printf.eprintf "fwd: %s\n" (UriManager.string_of_uri uri); flush stderr;
151 let start = lapply_tac (Cic.Rel index) (Cic.Const (uri, [])) in
152 let tac = T.thens ~start ~continuations:[PESR.clear hyp] in
153 PET.apply_tactic tac status
155 PET.mk_tactic fwd_simpl_tac