src/Tools/case_product.ML
author noschinl
Wed Dec 08 18:18:36 2010 +0100 (2010-12-08)
changeset 41826 18d4d2b60016
child 41883 392364739e5d
permissions -rw-r--r--
introduce attribute case_prod for combining case rules
* * *
[PATCH 1/9] Make tac independent of consumes

From 1a53ef4c070f924ff8e69529b0c1b13fa2844722 Mon Sep 17 00:00:00 2001
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case_product.ML | 11 ++++++-----
1 files changed, 6 insertions(+), 5 deletions(-)
* * *
[PATCH 2/9] Replace MRS by OF

From da55d08ae287bfdc18dec554067b45a3e298c243 Mon Sep 17 00:00:00 2001
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case_product.ML | 4 ++--
1 files changed, 2 insertions(+), 2 deletions(-)
* * *
[PATCH 3/9] Clean up tactic

From d26d50caaa3526c8c0625d7395467c6914f1a8d9 Mon Sep 17 00:00:00 2001
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case_product.ML | 13 +++++--------
1 files changed, 5 insertions(+), 8 deletions(-)
* * *
[PATCH 4/9] Move out get_consumes a bit more

From 6ed5415f29cc43cea30c216edb1e74ec6c0f6c33 Mon Sep 17 00:00:00 2001
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case_product.ML | 4 +++-
1 files changed, 3 insertions(+), 1 deletions(-)
* * *
[PATCH 5/9] Clean up tactic

From d301cfe6377e9f7db74b190fb085e0e66eeadfb5 Mon Sep 17 00:00:00 2001
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case_product.ML | 3 +--
1 files changed, 1 insertions(+), 2 deletions(-)
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[PATCH 6/9] Cleanup build_concl_prems

From c30889e131e74a92caac5b1e6d3d816890406ca7 Mon Sep 17 00:00:00 2001
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case_product.ML | 18 ++++++++----------
1 files changed, 8 insertions(+), 10 deletions(-)
* * *
[PATCH 7/9] Split logic & annotation a bit

From e065606118308c96e013fad72ab9ad89b5a4b945 Mon Sep 17 00:00:00 2001
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case_product.ML | 26 ++++++++++++++++++--------
1 files changed, 18 insertions(+), 8 deletions(-)
* * *
[PATCH 8/9] Remove dependency on consumes attribute

From e2a4de044481586d6127bbabd0ef48d0e3ab57c0 Mon Sep 17 00:00:00 2001
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case_product.ML | 46 ++++++++++++++++++++++------------------------
1 files changed, 22 insertions(+), 24 deletions(-)
* * *
[PATCH 9/9] whitespace

From 59f5036bd8f825da4a362970292a34ec06c0f1a2 Mon Sep 17 00:00:00 2001
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case_product.ML | 2 +-
1 files changed, 1 insertions(+), 1 deletions(-)
     1 (*   Title: case_product.ML
     2      Author: Lars Noschinski
     3 
     4 Combines two case rules into a single one.
     5 
     6 Assumes that the theorems are of the form
     7   "[| C1; ...; Cm; A1 ==> P; ...; An ==> P |] ==> P"
     8 where m is given by the "consumes" attribute of the theorem.
     9 *)
    10 
    11 signature CASE_PRODUCT =
    12   sig
    13 
    14   val combine: Proof.context -> thm -> thm -> thm
    15   val combine_annotated: Proof.context -> thm -> thm -> thm
    16   val setup: theory -> theory
    17 end;
    18 
    19 structure Case_Product: CASE_PRODUCT =
    20 struct
    21 
    22 (*Instantiates the conclusion of thm2 to the one of thm1.*)
    23 fun inst_concl thm1 thm2 =
    24   let
    25     val cconcl_of = Drule.strip_imp_concl o Thm.cprop_of
    26   in Thm.instantiate (Thm.match (cconcl_of thm2, cconcl_of thm1)) thm2 end
    27 
    28 fun inst_thms thm1 thm2 ctxt =
    29   let
    30     val import = yield_singleton (apfst snd oo Variable.import true)
    31     val (i_thm1, ctxt') = import thm1 ctxt
    32     val (i_thm2, ctxt'') = import (inst_concl i_thm1 thm2) ctxt'
    33   in ((i_thm1, i_thm2), ctxt'') end
    34 
    35 (*
    36 Returns list of prems, where loose bounds have been replaced by frees.
    37 FIXME: Focus
    38 *)
    39 fun free_prems t ctxt =
    40   let
    41     val bs = Term.strip_all_vars t
    42     val (names, ctxt') = Variable.variant_fixes (map fst bs) ctxt
    43     val subst = map Free (names ~~ map snd bs)
    44     val t' = map (Term.subst_bounds o pair (rev subst)) (Logic.strip_assums_hyp t)
    45   in ((t', subst), ctxt') end
    46 
    47 fun build_concl_prems thm1 thm2 ctxt =
    48   let
    49     val concl = Thm.concl_of thm1
    50 
    51     fun is_consumes t = not (Logic.strip_assums_concl t aconv concl)
    52     val (p_cons1, p_cases1) = chop_while is_consumes (Thm.prems_of thm1)
    53     val (p_cons2, p_cases2) = chop_while is_consumes (Thm.prems_of thm2)
    54 
    55     val p_cases_prod = map (fn p1 => map (fn p2 =>
    56       let
    57         val (((t1, subst1), (t2, subst2)), _) = ctxt
    58           |> free_prems p1 ||>> free_prems p2
    59       in
    60         Logic.list_implies (t1 @ t2, concl)
    61         |> fold_rev Logic.all (subst1 @ subst2)
    62       end
    63       ) p_cases2) p_cases1
    64 
    65     val prems = p_cons1 :: p_cons2 :: p_cases_prod
    66   in
    67     (concl, prems)
    68   end
    69 
    70 fun case_product_tac prems struc thm1 thm2 =
    71   let
    72     val (p_cons1 :: p_cons2 :: premss) = unflat struc prems
    73     val thm2' = thm2 OF p_cons2
    74   in
    75     (Tactic.rtac (thm1 OF p_cons1)
    76      THEN' EVERY' (map (fn p =>
    77        Tactic.rtac thm2'
    78        THEN' EVERY' (map (ProofContext.fact_tac o single) p)) premss)
    79     )
    80   end
    81 
    82 fun combine ctxt thm1 thm2 =
    83   let
    84     val ((i_thm1, i_thm2), ctxt') = inst_thms thm1 thm2 ctxt
    85     val (concl, prems_rich) = build_concl_prems i_thm1 i_thm2 ctxt'
    86   in
    87     Goal.prove ctxt' [] (flat prems_rich) concl (fn {prems, ...} =>
    88       case_product_tac prems prems_rich i_thm1 i_thm2 1)
    89     |> singleton (Variable.export ctxt' ctxt)
    90   end;
    91 
    92 fun annotation thm1 thm2 =
    93   let
    94     val (names1, cons1) = apfst (map fst) (Rule_Cases.get thm1)
    95     val (names2, cons2) = apfst (map fst) (Rule_Cases.get thm2)
    96     val names = map_product (fn x => fn y => x ^ "_" ^y) names1 names2
    97   in
    98     Rule_Cases.case_names names o Rule_Cases.consumes (cons1 + cons2)
    99   end
   100 
   101 fun combine_annotated ctxt thm1 thm2 =
   102   combine ctxt thm1 thm2
   103   |> snd o annotation thm1 thm2 o pair (Context.Proof ctxt)
   104 
   105 (* Attribute setup *)
   106 
   107 val case_prod_attr = let
   108     fun combine_list ctxt = fold (fn x => fn y => combine_annotated ctxt y x)
   109   in
   110     Attrib.thms >> (fn thms => Thm.rule_attribute (fn ctxt => fn thm =>
   111       combine_list (Context.proof_of ctxt) thms thm))
   112   end
   113 
   114 val setup =
   115  Attrib.setup @{binding "case_product"} case_prod_attr "product with other case rules"
   116 
   117 end;