(* 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_pred_equation : thm -> theory -> thm list * theory
*)
val preprocess : string -> theory -> (thm list list * theory)
(* output is the term list of clauses of an unknown predicate *)
val preprocess_term : term -> theory -> (term list * theory)
(*val rewrite : thm -> thm*)
end;
(* : PREDICATE_COMPILE_PREPROC_PRED *) (* FIXME *)
structure Predicate_Compile_Pred =
struct
open Predicate_Compile_Aux
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 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
(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}])
val rewrite_intros =
(* Simplifier.simplify (HOL_basic_ss addsimps @{thms HOL.simp_thms(9)}) *)
Simplifier.full_simplify (HOL_basic_ss addsimps [@{thm not_not}])
fun preprocess (constname, specs) thy =
let
val ctxt = ProofContext.init thy
val intros =
if forall is_pred_equation specs then
introrulify thy (map rewrite specs)
else if forall (is_intro constname) specs then
map rewrite_intros specs
else
error ("unexpected specification for constant " ^ quote constname ^ ":\n"
^ commas (map (quote o Display.string_of_thm_global thy) specs))
val (intros', (local_defs, thy')) = flatten_intros constname intros thy
val (intross, thy'') = fold_map preprocess local_defs thy'
in
((constname, intros') :: flat intross,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 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 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 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;