author | wenzelm |
Sat, 17 Oct 2009 16:58:03 +0200 | |
changeset 32970 | fbd2bb2489a8 |
parent 32966 | 5b21661fe618 |
child 33149 | 2c8f1c450b47 |
permissions | -rw-r--r-- |
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(* Author: Lukas Bulwahn, TU Muenchen |
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Preprocessing definitions of predicates to introduction rules |
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*) |
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signature PREDICATE_COMPILE_PRED = |
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sig |
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(* preprocesses an equation to a set of intro rules; defines new constants *) |
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(* |
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val preprocess_pred_equation : thm -> theory -> thm list * theory |
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*) |
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val preprocess : string -> theory -> (thm list list * theory) |
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(* output is the term list of clauses of an unknown predicate *) |
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val preprocess_term : term -> theory -> (term list * theory) |
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(*val rewrite : thm -> thm*) |
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end; |
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(* : PREDICATE_COMPILE_PREPROC_PRED *) |
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structure Predicate_Compile_Pred = |
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struct |
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open Predicate_Compile_Aux |
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fun is_compound ((Const ("Not", _)) $ t) = |
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error "is_compound: Negation should not occur; preprocessing is defect" |
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| is_compound ((Const ("Ex", _)) $ _) = true |
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| is_compound ((Const (@{const_name "op |"}, _)) $ _ $ _) = true |
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| is_compound ((Const ("op &", _)) $ _ $ _) = |
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error "is_compound: Conjunction should not occur; preprocessing is defect" |
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| is_compound _ = false |
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fun flatten constname atom (defs, thy) = |
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if is_compound atom then |
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let |
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val constname = Name.variant (map (Long_Name.base_name o fst) defs) |
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((Long_Name.base_name constname) ^ "_aux") |
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val full_constname = Sign.full_bname thy constname |
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val (params, args) = List.partition (is_predT o fastype_of) |
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(map Free (Term.add_frees atom [])) |
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val constT = map fastype_of (params @ args) ---> HOLogic.boolT |
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val lhs = list_comb (Const (full_constname, constT), params @ args) |
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val def = Logic.mk_equals (lhs, atom) |
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val ([definition], thy') = thy |
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|> Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] |
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|> PureThy.add_defs false [((Binding.name (constname ^ "_def"), def), [])] |
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in |
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(lhs, ((full_constname, [definition]) :: defs, thy')) |
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end |
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else |
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(atom, (defs, thy)) |
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fun flatten_intros constname intros thy = |
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let |
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val ctxt = ProofContext.init thy |
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val ((_, intros), ctxt') = Variable.import true intros ctxt |
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val (intros', (local_defs, thy')) = (fold_map o fold_map_atoms) |
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(flatten constname) (map prop_of intros) ([], thy) |
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val tac = fn _ => Skip_Proof.cheat_tac thy' |
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val intros'' = map (fn t => Goal.prove ctxt' [] [] t tac) intros' |
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|> Variable.export ctxt' ctxt |
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in |
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(intros'', (local_defs, thy')) |
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end |
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(* TODO: same function occurs in inductive package *) |
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fun select_disj 1 1 = [] |
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| select_disj _ 1 = [rtac @{thm disjI1}] |
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| select_disj n i = (rtac @{thm disjI2})::(select_disj (n - 1) (i - 1)); |
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fun introrulify thy ths = |
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let |
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val ctxt = ProofContext.init thy |
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val ((_, ths'), ctxt') = Variable.import true ths ctxt |
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fun introrulify' th = |
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let |
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val (lhs, rhs) = Logic.dest_equals (prop_of th) |
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val frees = Term.add_free_names rhs [] |
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val disjuncts = HOLogic.dest_disj rhs |
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val nctxt = Name.make_context frees |
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fun mk_introrule t = |
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let |
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val ((ps, t'), nctxt') = focus_ex t nctxt |
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val prems = map HOLogic.mk_Trueprop (HOLogic.dest_conj t') |
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in |
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(ps, Logic.list_implies (prems, HOLogic.mk_Trueprop lhs)) |
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end |
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val x = ((cterm_of thy) o the_single o snd o strip_comb o HOLogic.dest_Trueprop o fst o |
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Logic.dest_implies o prop_of) @{thm exI} |
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fun prove_introrule (index, (ps, introrule)) = |
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let |
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val tac = Simplifier.simp_tac (HOL_basic_ss addsimps [th]) 1 |
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THEN EVERY1 (select_disj (length disjuncts) (index + 1)) |
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THEN (EVERY (map (fn y => |
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rtac (Drule.cterm_instantiate [(x, cterm_of thy (Free y))] @{thm exI}) 1) ps)) |
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THEN REPEAT_DETERM (rtac @{thm conjI} 1 THEN atac 1) |
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THEN TRY (atac 1) |
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in |
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Goal.prove ctxt' (map fst ps) [] introrule (fn {...} => tac) |
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end |
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in |
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map_index prove_introrule (map mk_introrule disjuncts) |
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end |
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in maps introrulify' ths' |> Variable.export ctxt' ctxt end |
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val rewrite = |
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Simplifier.simplify (HOL_basic_ss addsimps [@{thm Ball_def}, @{thm Bex_def}]) |
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#> Simplifier.simplify (HOL_basic_ss addsimps [@{thm all_not_ex}]) |
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#> Conv.fconv_rule nnf_conv |
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#> Simplifier.simplify (HOL_basic_ss addsimps [@{thm ex_disj_distrib}]) |
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val rewrite_intros = |
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Simplifier.simplify (HOL_basic_ss addsimps @{thms HOL.simp_thms(9)}) |
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fun preprocess (constname, specs) thy = |
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let |
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val ctxt = ProofContext.init thy |
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val intros = |
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if forall is_pred_equation specs then |
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introrulify thy (map rewrite specs) |
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else if forall (is_intro constname) specs then |
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map rewrite_intros specs |
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else |
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error ("unexpected specification for constant " ^ quote constname ^ ":\n" |
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^ commas (map (quote o Display.string_of_thm_global thy) specs)) |
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val _ = tracing ("Introduction rules of definitions before flattening: " |
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^ commas (map (Display.string_of_thm ctxt) intros)) |
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val _ = tracing "Defining local predicates and their intro rules..." |
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val (intros', (local_defs, thy')) = flatten_intros constname intros thy |
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val (intross, thy'') = fold_map preprocess local_defs thy' |
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in |
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(intros' :: flat intross,thy'') |
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end; |
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fun preprocess_term t thy = error "preprocess_pred_term: to implement" |
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end; |