author | wenzelm |
Mon, 23 Jun 2008 15:51:38 +0200 | |
changeset 27326 | d3beec370964 |
child 27328 | 1f0ac20db386 |
permissions | -rw-r--r-- |
27326
d3beec370964
moved src/HOL/Tools/induct_tacs.ML to src/Tools/induct_tacs.ML;
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1 |
(* Title: HOL/Tools/induct_tacs.ML |
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2 |
ID: $Id$ |
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3 |
Author: Makarius |
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|
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5 |
Unstructured induction and cases analysis. |
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6 |
*) |
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|
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8 |
signature INDUCT_TACS = |
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9 |
sig |
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val case_tac: Proof.context -> string -> int -> tactic |
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val case_rule_tac: Proof.context -> string -> thm -> int -> tactic |
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val induct_tac: Proof.context -> string option list list -> int -> tactic |
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val induct_rules_tac: Proof.context -> string option list list -> thm list -> int -> tactic |
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val setup: theory -> theory |
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15 |
end |
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16 |
|
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structure InductTacs: INDUCT_TACS = |
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18 |
struct |
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19 |
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(* case analysis *) |
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fun check_type ctxt t = |
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23 |
let |
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24 |
val u = singleton (Variable.polymorphic ctxt) t; |
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25 |
val U = Term.fastype_of u; |
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val _ = Term.is_TVar U andalso |
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error ("Cannot determine type of " ^ Syntax.string_of_term ctxt u); |
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in (u, U) end; |
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29 |
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fun gen_case_tac ctxt0 (s, opt_rule) i st = |
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31 |
let |
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val ((_, goal), ctxt) = Variable.focus_subgoal i st ctxt0; |
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val rule = |
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(case opt_rule of |
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SOME rule => rule |
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| NONE => |
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(case Induct.find_casesT ctxt |
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(#2 (check_type ctxt (ProofContext.read_term_schematic ctxt s))) of |
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rule :: _ => rule |
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| [] => @{thm case_split})); |
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val _ = Method.trace ctxt [rule]; |
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val xi = |
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(case Induct.vars_of (Thm.term_of (Thm.cprem_of rule 1)) of |
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Var (xi, _) :: _ => xi |
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| _ => raise THM ("Malformed cases rule", 0, [rule])); |
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in res_inst_tac ctxt [(xi, s)] rule i st end |
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handle THM _ => Seq.empty; |
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fun case_tac ctxt s = gen_case_tac ctxt (s, NONE); |
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fun case_rule_tac ctxt s rule = gen_case_tac ctxt (s, SOME rule); |
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(* induction *) |
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local |
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fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x) |
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| prep_var _ = NONE; |
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fun prep_inst (concl, xs) = |
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let val vs = Induct.vars_of concl |
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in map_filter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end; |
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in |
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fun gen_induct_tac ctxt0 (varss, opt_rules) i st = |
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let |
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val ((_, goal), ctxt) = Variable.focus_subgoal i st ctxt0; |
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val (prems, concl) = Logic.strip_horn (Thm.term_of goal); |
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fun induct_var name = |
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let |
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val t = Syntax.read_term ctxt name; |
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val (x, _) = Term.dest_Free t handle TERM _ => |
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error ("Induction argument not a variable: " ^ Syntax.string_of_term ctxt t); |
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val eq_x = fn Free (y, _) => x = y | _ => false; |
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val _ = |
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if Term.exists_subterm eq_x concl then () |
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else error ("No such variable in subgoal: " ^ Syntax.string_of_term ctxt t); |
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val _ = |
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if (exists o Term.exists_subterm) eq_x prems then |
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warning ("Induction variable occurs also among premises: " ^ Syntax.string_of_term ctxt t) |
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else (); |
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in #1 (check_type ctxt t) end; |
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86 |
|
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val argss = map (map (Option.map induct_var)) varss; |
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val _ = forall null argss andalso raise THM ("No induction arguments", 0, []); |
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89 |
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val rule = |
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(case opt_rules of |
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SOME rules => #2 (RuleCases.strict_mutual_rule ctxt rules) |
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| NONE => |
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94 |
(case map_filter (RuleCases.mutual_rule ctxt) (Induct.get_inductT ctxt argss) of |
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(_, rule) :: _ => rule |
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96 |
| [] => raise THM ("No induction rules", 0, []))); |
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97 |
|
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val rule' = rule |> Conv.fconv_rule (Conv.concl_conv ~1 ObjectLogic.atomize); |
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99 |
val _ = Method.trace ctxt [rule']; |
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100 |
|
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101 |
val concls = Logic.dest_conjunctions (Thm.concl_of rule); |
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102 |
val insts = maps prep_inst (concls ~~ varss) handle Library.UnequalLengths => |
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103 |
error "Induction rule has different numbers of variables"; |
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104 |
in res_inst_tac ctxt insts rule' i st end |
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handle THM _ => Seq.empty; |
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106 |
|
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end; |
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fun induct_tac ctxt args = gen_induct_tac ctxt (args, NONE); |
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fun induct_rules_tac ctxt args rules = gen_induct_tac ctxt (args, SOME rules); |
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(* method syntax *) |
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114 |
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local |
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116 |
|
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val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":"); |
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val opt_rule = Scan.option (rule_spec |-- Attrib.thm); |
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val opt_rules = Scan.option (rule_spec |-- Attrib.thms); |
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121 |
val varss = |
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Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name)))); |
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123 |
|
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124 |
in |
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125 |
|
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126 |
val setup = |
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Method.add_methods |
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[("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) gen_case_tac, |
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129 |
"unstructured case analysis on types"), |
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("induct_tac", Method.goal_args_ctxt' (varss -- opt_rules) gen_induct_tac, |
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"unstructured induction on types")]; |
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132 |
|
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133 |
end; |
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134 |
|
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135 |
end; |
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136 |