(* Title: HOL/Tools/Predicate_Compile/predicate_compile_pred.ML
Author: Lukas Bulwahn, TU Muenchen
Preprocessing definitions of predicates to introduction rules.
*)
signature PREDICATE_COMPILE_PRED =
sig
(* preprocesses an equation to a set of intro rules; defines new constants *)
val preprocess : Predicate_Compile_Aux.options -> (string * thm list) -> theory
-> ((string * thm list) list * theory)
val flat_higher_order_arguments : ((string * thm list) list * theory)
-> ((string * thm list) list * ((string * thm list) list * theory))
end;
structure Predicate_Compile_Pred : PREDICATE_COMPILE_PRED =
struct
open Predicate_Compile_Aux
fun datatype_names_of_case_name thy case_name =
map (#1 o #2) (#descr (the (Datatype_Data.info_of_case thy case_name)))
fun make_case_distribs new_type_names descr sorts thy =
let
val case_combs = Datatype_Prop.make_case_combs new_type_names descr sorts thy "f";
fun make comb =
let
val Type ("fun", [T, T']) = fastype_of comb;
val (Const (case_name, _), fs) = strip_comb comb
val used = Term.add_tfree_names comb []
val U = TFree (Name.variant used "'t", HOLogic.typeS)
val x = Free ("x", T)
val f = Free ("f", T' --> U)
fun apply_f f' =
let
val Ts = binder_types (fastype_of f')
val bs = map Bound ((length Ts - 1) downto 0)
in
fold (curry absdummy) (rev Ts) (f $ (list_comb (f', bs)))
end
val fs' = map apply_f fs
val case_c' = Const (case_name, (map fastype_of fs') @ [T] ---> U)
in
HOLogic.mk_eq (f $ (comb $ x), list_comb (case_c', fs') $ x)
end
in
map make case_combs
end
fun case_rewrites thy Tcon =
let
val info = Datatype.the_info thy Tcon
val descr = #descr info
val sorts = #sorts info
val typ_names = the_default [Tcon] (#alt_names info)
in
map (Drule.export_without_context o Skip_Proof.make_thm thy o HOLogic.mk_Trueprop)
(make_case_distribs typ_names [descr] sorts thy)
end
fun instantiated_case_rewrites thy Tcon =
let
val rew_ths = case_rewrites thy Tcon
val ctxt = ProofContext.init thy
fun instantiate th =
let
val f = (fst (strip_comb (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of th))))))
val Type ("fun", [uninst_T, uninst_T']) = fastype_of f
val ([tname, tname', uname, yname], ctxt') = Variable.add_fixes ["'t", "'t'", "'u", "y"] ctxt
val T = TFree (tname, HOLogic.typeS)
val T' = TFree (tname', HOLogic.typeS)
val U = TFree (uname, HOLogic.typeS)
val y = Free (yname, U)
val f' = absdummy (U --> T', Bound 0 $ y)
val th' = Thm.certify_instantiate
([(dest_TVar uninst_T, U --> T'), (dest_TVar uninst_T', T')],
[((fst (dest_Var f), (U --> T') --> T'), f')]) th
val [th'] = Variable.export ctxt' ctxt [th']
in
th'
end
in
map instantiate rew_ths
end
fun is_compound ((Const ("Not", _)) $ t) =
error "is_compound: Negation should not occur; preprocessing is defect"
| is_compound ((Const ("Ex", _)) $ _) = true
| is_compound ((Const (@{const_name "op |"}, _)) $ _ $ _) = true
| is_compound ((Const ("op &", _)) $ _ $ _) =
error "is_compound: Conjunction should not occur; preprocessing is defect"
| is_compound _ = false
fun flatten constname atom (defs, thy) =
if is_compound atom then
let
val atom = Envir.beta_norm (Pattern.eta_long [] atom)
val constname = Name.variant (map (Long_Name.base_name o fst) defs)
((Long_Name.base_name constname) ^ "_aux")
val full_constname = Sign.full_bname thy constname
val (params, args) = List.partition (is_predT o fastype_of)
(map Free (Term.add_frees atom []))
val constT = map fastype_of (params @ args) ---> HOLogic.boolT
val lhs = list_comb (Const (full_constname, constT), params @ args)
val def = Logic.mk_equals (lhs, atom)
val ([definition], thy') = thy
|> Sign.add_consts_i [(Binding.name constname, constT, NoSyn)]
|> PureThy.add_defs false [((Binding.name (constname ^ "_def"), def), [])]
in
(lhs, ((full_constname, [definition]) :: defs, thy'))
end
else
(case (fst (strip_comb atom)) of
(Const (@{const_name If}, _)) => let
val if_beta = @{lemma "(if c then x else y) z = (if c then x z else y z)" by simp}
val atom' = MetaSimplifier.rewrite_term thy
(map (fn th => th RS @{thm eq_reflection}) [@{thm if_bool_eq_disj}, if_beta]) [] atom
val _ = assert (not (atom = atom'))
in
flatten constname atom' (defs, thy)
end
| _ =>
if (has_split_thm thy (fst (strip_comb atom))) then
let
val (f, args) = strip_comb atom
val split_thm = prepare_split_thm (ProofContext.init thy) (the (find_split_thm' thy f))
(* TODO: contextify things - this line is to unvarify the split_thm *)
(*val ((_, [isplit_thm]), _) = Variable.import true [split_thm] (ProofContext.init thy)*)
val (assms, concl) = Logic.strip_horn (Thm.prop_of split_thm)
val (P, [split_t]) = strip_comb (HOLogic.dest_Trueprop concl)
val Tcons = datatype_names_of_case_name thy (fst (dest_Const f))
val ths = maps (instantiated_case_rewrites thy) Tcons
val atom = MetaSimplifier.rewrite_term thy
(map (fn th => th RS @{thm eq_reflection}) ths) [] atom
val (f, args) = strip_comb atom
val subst = Pattern.match thy (split_t, atom) (Vartab.empty, Vartab.empty)
val (_, split_args) = strip_comb split_t
val match = split_args ~~ args
val names = Term.add_free_names atom []
val frees = map Free (Term.add_frees atom [])
val constname = Name.variant (map (Long_Name.base_name o fst) defs)
((Long_Name.base_name constname) ^ "_aux")
val full_constname = Sign.full_bname thy constname
val constT = map fastype_of frees ---> HOLogic.boolT
val lhs = list_comb (Const (full_constname, constT), frees)
fun new_def assm =
let
val (vTs, assm') = strip_all (Envir.beta_norm (Envir.subst_term subst assm))
val var_names = Name.variant_list names (map fst vTs)
val vars = map Free (var_names ~~ (map snd vTs))
val (prems', pre_res) = Logic.strip_horn (subst_bounds (rev vars, assm'))
fun partition_prem_subst prem =
case HOLogic.dest_eq (HOLogic.dest_Trueprop prem) of
(Free (x, T), r) => (NONE, SOME ((x, T), r))
| _ => (SOME prem, NONE)
fun partition f xs =
let
fun partition' acc1 acc2 [] = (rev acc1, rev acc2)
| partition' acc1 acc2 (x :: xs) =
let
val (y, z) = f x
val acc1' = case y of NONE => acc1 | SOME y' => y' :: acc1
val acc2' = case z of NONE => acc2 | SOME z' => z' :: acc2
in partition' acc1' acc2' xs end
in partition' [] [] xs end
val (prems'', subst) = partition partition_prem_subst prems'
val (_, [inner_t]) = strip_comb (HOLogic.dest_Trueprop pre_res)
val pre_def = Logic.mk_equals (lhs,
fold (curry HOLogic.mk_conj) (map HOLogic.dest_Trueprop prems'') inner_t)
val def = Envir.expand_term_frees subst pre_def
in
def
end
val new_defs = map new_def assms
val (definition, thy') = thy
|> Sign.add_consts_i [(Binding.name constname, constT, NoSyn)]
|> fold_map Drule.add_axiom (map_index
(fn (i, t) => (Binding.name (constname ^ "_def" ^ string_of_int i), t)) new_defs)
in
(lhs, ((full_constname, definition) :: defs, thy'))
end
else
(atom, (defs, thy)))
fun flatten_intros constname intros thy =
let
val ctxt = ProofContext.init thy
val ((_, intros), ctxt') = Variable.import true intros ctxt
val (intros', (local_defs, thy')) = (fold_map o fold_map_atoms)
(flatten constname) (map prop_of intros) ([], thy)
val tac = fn _ => Skip_Proof.cheat_tac thy'
val intros'' = map (fn t => Goal.prove ctxt' [] [] t tac) intros'
|> Variable.export ctxt' ctxt
in
(intros'', (local_defs, thy'))
end
(* TODO: same function occurs in inductive package *)
fun select_disj 1 1 = []
| select_disj _ 1 = [rtac @{thm disjI1}]
| select_disj n i = (rtac @{thm disjI2})::(select_disj (n - 1) (i - 1));
fun introrulify thy ths =
let
val ctxt = ProofContext.init thy
val ((_, ths'), ctxt') = Variable.import true ths ctxt
fun introrulify' th =
let
val (lhs, rhs) = Logic.dest_equals (prop_of th)
val frees = Term.add_free_names rhs []
val disjuncts = HOLogic.dest_disj rhs
val nctxt = Name.make_context frees
fun mk_introrule t =
let
val ((ps, t'), nctxt') = focus_ex t nctxt
val prems = map HOLogic.mk_Trueprop (HOLogic.dest_conj t')
in
(ps, Logic.list_implies (prems, HOLogic.mk_Trueprop lhs))
end
val x = ((cterm_of thy) o the_single o snd o strip_comb o HOLogic.dest_Trueprop o fst o
Logic.dest_implies o prop_of) @{thm exI}
fun prove_introrule (index, (ps, introrule)) =
let
val tac = Simplifier.simp_tac (HOL_basic_ss addsimps [th]) 1
THEN EVERY1 (select_disj (length disjuncts) (index + 1))
THEN (EVERY (map (fn y =>
rtac (Drule.cterm_instantiate [(x, cterm_of thy (Free y))] @{thm exI}) 1) ps))
THEN REPEAT_DETERM (rtac @{thm conjI} 1 THEN atac 1)
THEN TRY (atac 1)
in
Goal.prove ctxt' (map fst ps) [] introrule (fn _ => tac)
end
in
map_index prove_introrule (map mk_introrule disjuncts)
end
in maps introrulify' ths' |> Variable.export ctxt' ctxt end
val rewrite =
Simplifier.simplify (HOL_basic_ss addsimps [@{thm Ball_def}, @{thm Bex_def}])
#> Simplifier.simplify (HOL_basic_ss addsimps [@{thm all_not_ex}])
#> Conv.fconv_rule nnf_conv
#> Simplifier.simplify (HOL_basic_ss addsimps [@{thm ex_disj_distrib}])
fun split_conjs thy t =
let
fun split_conjunctions (Const (@{const_name "op &"}, _) $ t1 $ t2) =
(split_conjunctions t1) @ (split_conjunctions t2)
| split_conjunctions t = [t]
in
map HOLogic.mk_Trueprop (split_conjunctions (HOLogic.dest_Trueprop t))
end
fun rewrite_intros thy =
Simplifier.full_simplify (HOL_basic_ss addsimps [@{thm all_not_ex}])
#> Simplifier.full_simplify (HOL_basic_ss addsimps @{thms bool_simps} addsimps @{thms nnf_simps})
#> map_term thy (maps_premises (split_conjs thy))
fun print_specs options thy msg ths =
if show_intermediate_results options then
(tracing (msg); tracing (commas (map (Display.string_of_thm_global thy) ths)))
else
()
(*
fun split_cases thy th =
let
in
map_term thy th
end
*)
fun preprocess options (constname, specs) thy =
(* case Predicate_Compile_Data.processed_specs thy constname of
SOME specss => (specss, thy)
| NONE =>*)
let
val ctxt = ProofContext.init thy
val intros =
if forall is_pred_equation specs then
map (map_term thy (maps_premises (split_conjs thy))) (introrulify thy (map rewrite specs))
else if forall (is_intro constname) specs then
map (rewrite_intros thy) specs
else
error ("unexpected specification for constant " ^ quote constname ^ ":\n"
^ commas (map (quote o Display.string_of_thm_global thy) specs))
val _ = print_specs options thy "normalized intros" intros
(*val intros = maps (split_cases thy) intros*)
val (intros', (local_defs, thy')) = flatten_intros constname intros thy
val (intross, thy'') = fold_map (preprocess options) local_defs thy'
val full_spec = (constname, intros') :: flat intross
(*val thy''' = Predicate_Compile_Data.store_processed_specs (constname, full_spec) thy''*)
in
(full_spec, thy'')
end;
fun preprocess_term t thy = error "preprocess_pred_term: to implement"
fun is_Abs (Abs _) = true
| is_Abs _ = false
fun flat_higher_order_arguments (intross, thy) =
let
fun process constname atom (new_defs, thy) =
let
val (pred, args) = strip_comb atom
fun replace_abs_arg (abs_arg as Abs _ ) (new_defs, thy) =
let
val vars = map Var (Term.add_vars abs_arg [])
val abs_arg' = Logic.unvarify_global abs_arg
val frees = map Free (Term.add_frees abs_arg' [])
val constname = Name.variant (map (Long_Name.base_name o fst) new_defs)
((Long_Name.base_name constname) ^ "_hoaux")
val full_constname = Sign.full_bname thy constname
val constT = map fastype_of frees ---> (fastype_of abs_arg')
val const = Const (full_constname, constT)
val lhs = list_comb (const, frees)
val def = Logic.mk_equals (lhs, abs_arg')
val ([definition], thy') = thy
|> Sign.add_consts_i [(Binding.name constname, constT, NoSyn)]
|> PureThy.add_defs false [((Binding.name (constname ^ "_def"), def), [])]
in
(list_comb (Logic.varify_global const, vars),
((full_constname, [definition])::new_defs, thy'))
end
| replace_abs_arg arg (new_defs, thy) =
if (is_predT (fastype_of arg)) then
process constname arg (new_defs, thy)
else
(arg, (new_defs, thy))
val (args', (new_defs', thy')) = fold_map replace_abs_arg
(map Envir.beta_eta_contract args) (new_defs, thy)
in
(list_comb (pred, args'), (new_defs', thy'))
end
fun flat_intro intro (new_defs, thy) =
let
val constname = fst (dest_Const (fst (strip_comb
(HOLogic.dest_Trueprop (Logic.strip_imp_concl (prop_of intro))))))
val (intro_ts, (new_defs, thy)) = fold_map_atoms (process constname) (prop_of intro) (new_defs, thy)
val th = Skip_Proof.make_thm thy intro_ts
in
(th, (new_defs, thy))
end
fun fold_map_spec f [] s = ([], s)
| fold_map_spec f ((c, ths) :: specs) s =
let
val (ths', s') = f ths s
val (specs', s'') = fold_map_spec f specs s'
in ((c, ths') :: specs', s'') end
val (intross', (new_defs, thy')) = fold_map_spec (fold_map flat_intro) intross ([], thy)
in
(intross', (new_defs, thy'))
end
end;