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(* Title: HOL/Statespace/state_fun.ML
Author: Norbert Schirmer, TU Muenchen
*)
signature STATE_FUN =
sig
val lookupN : string
val updateN : string
val mk_constr : theory -> typ -> term
val mk_destr : theory -> typ -> term
val lookup_simproc : simproc
val update_simproc : simproc
val ex_lookup_eq_simproc : simproc
val ex_lookup_ss : simpset
val lazy_conj_simproc : simproc
val string_eq_simp_tac : Proof.context -> int -> tactic
end;
structure StateFun: STATE_FUN =
struct
val lookupN = \<^const_name>\<open>StateFun.lookup\<close>;
val updateN = \<^const_name>\<open>StateFun.update\<close>;
val sel_name = HOLogic.dest_string;
fun mk_name i t =
(case try sel_name t of
SOME name => name
| NONE =>
(case t of
Free (x, _) => x
| Const (x, _) => x
| _ => "x" ^ string_of_int i));
local
val conj1_False = @{thm conj1_False};
val conj2_False = @{thm conj2_False};
val conj_True = @{thm conj_True};
val conj_cong = @{thm conj_cong};
fun isFalse (Const (\<^const_name>\<open>False\<close>, _)) = true
| isFalse _ = false;
fun isTrue (Const (\<^const_name>\<open>True\<close>, _)) = true
| isTrue _ = false;
in
val lazy_conj_simproc =
Simplifier.make_simproc \<^context> "lazy_conj_simp"
{lhss = [\<^term>\<open>P & Q\<close>],
proc = fn _ => fn ctxt => fn ct =>
(case Thm.term_of ct of
Const (\<^const_name>\<open>HOL.conj\<close>,_) $ P $ Q =>
let
val P_P' = Simplifier.rewrite ctxt (Thm.cterm_of ctxt P);
val P' = P_P' |> Thm.prop_of |> Logic.dest_equals |> #2;
in
if isFalse P' then SOME (conj1_False OF [P_P'])
else
let
val Q_Q' = Simplifier.rewrite ctxt (Thm.cterm_of ctxt Q);
val Q' = Q_Q' |> Thm.prop_of |> Logic.dest_equals |> #2;
in
if isFalse Q' then SOME (conj2_False OF [Q_Q'])
else if isTrue P' andalso isTrue Q' then SOME (conj_True OF [P_P', Q_Q'])
else if P aconv P' andalso Q aconv Q' then NONE
else SOME (conj_cong OF [P_P', Q_Q'])
end
end
| _ => NONE)};
fun string_eq_simp_tac ctxt =
simp_tac (put_simpset HOL_basic_ss ctxt
addsimps @{thms list.inject list.distinct char.inject
cong_exp_iff_simps simp_thms}
addsimprocs [lazy_conj_simproc]
|> Simplifier.add_cong @{thm block_conj_cong});
end;
val lookup_ss =
simpset_of (put_simpset HOL_basic_ss \<^context>
addsimps (@{thms list.inject} @ @{thms char.inject}
@ @{thms list.distinct} @ @{thms simp_thms}
@ [@{thm StateFun.lookup_update_id_same}, @{thm StateFun.id_id_cancel},
@{thm StateFun.lookup_update_same}, @{thm StateFun.lookup_update_other}])
addsimprocs [lazy_conj_simproc]
addSolver StateSpace.distinctNameSolver
|> fold Simplifier.add_cong @{thms block_conj_cong});
val ex_lookup_ss =
simpset_of (put_simpset HOL_ss \<^context> addsimps @{thms StateFun.ex_id});
structure Data = Generic_Data
(
type T = simpset * simpset * bool; (*lookup simpset, ex_lookup simpset, are simprocs installed*)
val empty = (empty_ss, empty_ss, false);
val extend = I;
fun merge ((ss1, ex_ss1, b1), (ss2, ex_ss2, b2)) =
(merge_ss (ss1, ss2), merge_ss (ex_ss1, ex_ss2), b1 orelse b2);
);
val _ = Theory.setup (Context.theory_map (Data.put (lookup_ss, ex_lookup_ss, false)));
val lookup_simproc =
Simplifier.make_simproc \<^context> "lookup_simp"
{lhss = [\<^term>\<open>lookup d n (update d' c m v s)\],
proc = fn _ => fn ctxt => fn ct =>
(case Thm.term_of ct of (Const (\<^const_name>\<open>StateFun.lookup\<close>, lT) $ destr $ n $
(s as Const (\<^const_name>\<open>StateFun.update\<close>, uT) $ _ $ _ $ _ $ _ $ _)) =>
(let
val (_::_::_::_::sT::_) = binder_types uT;
val mi = Term.maxidx_of_term (Thm.term_of ct);
fun mk_upds (Const (\<^const_name>\<open>StateFun.update\<close>, uT) $ d' $ c $ m $ v $ s) =
let
val (_ :: _ :: _ :: fT :: _ :: _) = binder_types uT;
val vT = domain_type fT;
val (s', cnt) = mk_upds s;
val (v', cnt') =
(case v of
Const (\<^const_name>\<open>K_statefun\<close>, KT) $ v'' =>
(case v'' of
(Const (\<^const_name>\<open>StateFun.lookup\<close>, _) $
(d as (Const (\<^const_name>\<open>Fun.id\<close>, _))) $ n' $ _) =>
if d aconv c andalso n aconv m andalso m aconv n'
then (v,cnt) (* Keep value so that
lookup_update_id_same can fire *)
else
(Const (\<^const_name>\<open>StateFun.K_statefun\<close>, KT) $
Var (("v", cnt), vT), cnt + 1)
| _ =>
(Const (\<^const_name>\<open>StateFun.K_statefun\<close>, KT) $
Var (("v", cnt), vT), cnt + 1))
| _ => (v, cnt));
in (Const (\<^const_name>\<open>StateFun.update\<close>, uT) $ d' $ c $ m $ v' $ s', cnt') end
| mk_upds s = (Var (("s", mi + 1), sT), mi + 2);
val ct =
Thm.cterm_of ctxt
(Const (\<^const_name>\<open>StateFun.lookup\<close>, lT) $ destr $ n $ fst (mk_upds s));
val basic_ss = #1 (Data.get (Context.Proof ctxt));
val ctxt' = ctxt |> Config.put simp_depth_limit 100 |> put_simpset basic_ss;
val thm = Simplifier.rewrite ctxt' ct;
in
if (op aconv) (Logic.dest_equals (Thm.prop_of thm))
then NONE
else SOME thm
end
handle Option.Option => NONE)
| _ => NONE)};
local
val meta_ext = @{thm StateFun.meta_ext};
val ss' =
simpset_of (put_simpset HOL_ss \<^context> addsimps
(@{thm StateFun.update_apply} :: @{thm Fun.o_apply} :: @{thms list.inject} @ @{thms char.inject}
@ @{thms list.distinct})
addsimprocs [lazy_conj_simproc, StateSpace.distinct_simproc]
|> fold Simplifier.add_cong @{thms block_conj_cong});
in
val update_simproc =
Simplifier.make_simproc \<^context> "update_simp"
{lhss = [\<^term>\<open>update d c n v s\<close>],
proc = fn _ => fn ctxt => fn ct =>
(case Thm.term_of ct of
Const (\<^const_name>\<open>StateFun.update\<close>, uT) $ _ $ _ $ _ $ _ $ _ =>
let
val (_ :: _ :: _ :: _ :: sT :: _) = binder_types uT;
(*"('v => 'a1) => ('a2 => 'v) => 'n => ('a1 => 'a2) => ('n => 'v) => ('n => 'v)"*)
fun init_seed s = (Bound 0, Bound 0, [("s", sT)], [], false);
fun mk_comp f fT g gT =
let val T = domain_type fT --> range_type gT
in (Const (\<^const_name>\<open>Fun.comp\<close>, gT --> fT --> T) $ g $ f, T) end;
fun mk_comps fs = foldl1 (fn ((f, fT), (g, gT)) => mk_comp g gT f fT) fs;
fun append n c cT f fT d dT comps =
(case AList.lookup (op aconv) comps n of
SOME gTs => AList.update (op aconv) (n, [(c, cT), (f, fT), (d, dT)] @ gTs) comps
| NONE => AList.update (op aconv) (n, [(c, cT), (f, fT), (d, dT)]) comps);
fun split_list (x :: xs) = let val (xs', y) = split_last xs in (x, xs', y) end
| split_list _ = error "StateFun.split_list";
fun merge_upds n comps =
let val ((c, cT), fs, (d, dT)) = split_list (the (AList.lookup (op aconv) comps n))
in ((c, cT), fst (mk_comps fs), (d, dT)) end;
(* mk_updterm returns
* - (orig-term-skeleton,simplified-term-skeleton, vars, b)
* where boolean b tells if a simplification has occurred.
"orig-term-skeleton = simplified-term-skeleton" is
* the desired simplification rule.
* The algorithm first walks down the updates to the seed-state while
* memorising the updates in the already-table. While walking up the
* updates again, the optimised term is constructed.
*)
fun mk_updterm already
((upd as Const (\<^const_name>\<open>StateFun.update\<close>, uT)) $ d $ c $ n $ v $ s) =
let
fun rest already = mk_updterm already;
val (dT :: cT :: nT :: vT :: sT :: _) = binder_types uT;
(*"('v => 'a1) => ('a2 => 'v) => 'n => ('a1 => 'a2) =>
('n => 'v) => ('n => 'v)"*)
in
if member (op aconv) already n then
(case rest already s of
(trm, trm', vars, comps, _) =>
let
val i = length vars;
val kv = (mk_name i n, vT);
val kb = Bound i;
val comps' = append n c cT kb vT d dT comps;
in (upd $ d $ c $ n $ kb $ trm, trm', kv :: vars, comps',true) end)
else
(case rest (n :: already) s of
(trm, trm', vars, comps, b) =>
let
val i = length vars;
val kv = (mk_name i n, vT);
val kb = Bound i;
val comps' = append n c cT kb vT d dT comps;
val ((c', c'T), f', (d', d'T)) = merge_upds n comps';
val vT' = range_type d'T --> domain_type c'T;
val upd' =
Const (\<^const_name>\<open>StateFun.update\<close>,
d'T --> c'T --> nT --> vT' --> sT --> sT);
in
(upd $ d $ c $ n $ kb $ trm, upd' $ d' $ c' $ n $ f' $ trm', kv :: vars,
comps', b)
end)
end
| mk_updterm _ t = init_seed t;
val ctxt0 = Config.put simp_depth_limit 100 ctxt;
val ctxt1 = put_simpset ss' ctxt0;
val ctxt2 = put_simpset (#1 (Data.get (Context.Proof ctxt0))) ctxt0;
in
(case mk_updterm [] (Thm.term_of ct) of
(trm, trm', vars, _, true) =>
let
val eq1 =
Goal.prove ctxt0 [] []
(Logic.list_all (vars, Logic.mk_equals (trm, trm')))
(fn _ => resolve_tac ctxt0 [meta_ext] 1 THEN simp_tac ctxt1 1);
val eq2 = Simplifier.asm_full_rewrite ctxt2 (Thm.dest_equals_rhs (Thm.cprop_of eq1));
in SOME (Thm.transitive eq1 eq2) end
| _ => NONE)
end
| _ => NONE)};
end;
local
val swap_ex_eq = @{thm StateFun.swap_ex_eq};
fun is_selector thy T sel =
let val (flds, more) = Record.get_recT_fields thy T
in member (fn (s, (n, _)) => n = s) (more :: flds) sel end;
in
val ex_lookup_eq_simproc =
Simplifier.make_simproc \<^context> "ex_lookup_eq_simproc"
{lhss = [\<^term>\<open>Ex t\<close>],
proc = fn _ => fn ctxt => fn ct =>
let
val thy = Proof_Context.theory_of ctxt;
val t = Thm.term_of ct;
val ex_lookup_ss = #2 (Data.get (Context.Proof ctxt));
val ctxt' = ctxt |> Config.put simp_depth_limit 100 |> put_simpset ex_lookup_ss;
fun prove prop =
Goal.prove_global thy [] [] prop
(fn _ => Record.split_simp_tac ctxt [] (K ~1) 1 THEN simp_tac ctxt' 1);
fun mkeq (swap, Teq, lT, lo, d, n, x, s) i =
let
val (_ :: nT :: _) = binder_types lT;
(* ('v => 'a) => 'n => ('n => 'v) => 'a *)
val x' = if not (Term.is_dependent x) then Bound 1 else raise TERM ("", [x]);
val n' = if not (Term.is_dependent n) then Bound 2 else raise TERM ("", [n]);
val sel' = lo $ d $ n' $ s;
in (Const (\<^const_name>\<open>HOL.eq\<close>, Teq) $ sel' $ x', hd (binder_types Teq), nT, swap) end;
fun dest_state (s as Bound 0) = s
| dest_state (s as (Const (sel, sT) $ Bound 0)) =
if is_selector thy (domain_type sT) sel then s
else raise TERM ("StateFun.ex_lookup_eq_simproc: not a record slector", [s])
| dest_state s = raise TERM ("StateFun.ex_lookup_eq_simproc: not a record slector", [s]);
fun dest_sel_eq
(Const (\<^const_name>\<open>HOL.eq\<close>, Teq) $
((lo as (Const (\<^const_name>\<open>StateFun.lookup\<close>, lT))) $ d $ n $ s) $ X) =
(false, Teq, lT, lo, d, n, X, dest_state s)
| dest_sel_eq
(Const (\<^const_name>\<open>HOL.eq\<close>, Teq) $ X $
((lo as (Const (\<^const_name>\<open>StateFun.lookup\<close>, lT))) $ d $ n $ s)) =
(true, Teq, lT, lo, d, n, X, dest_state s)
| dest_sel_eq _ = raise TERM ("", []);
in
(case t of
Const (\<^const_name>\<open>Ex\<close>, Tex) $ Abs (s, T, t) =>
(let
val (eq, eT, nT, swap) = mkeq (dest_sel_eq t) 0;
val prop =
Logic.list_all ([("n", nT), ("x", eT)],
Logic.mk_equals (Const (\<^const_name>\<open>Ex\<close>, Tex) $ Abs (s, T, eq), \<^term>\<open>True\<close>));
val thm = Drule.export_without_context (prove prop);
val thm' = if swap then swap_ex_eq OF [thm] else thm
in SOME thm' end handle TERM _ => NONE)
| _ => NONE)
end handle Option.Option => NONE};
end;
val val_sfx = "V";
val val_prfx = "StateFun."
fun deco base_prfx s = val_prfx ^ (base_prfx ^ suffix val_sfx s);
fun mkUpper str =
(case String.explode str of
[] => ""
| c::cs => String.implode (Char.toUpper c :: cs));
fun mkName (Type (T,args)) = implode (map mkName args) ^ mkUpper (Long_Name.base_name T)
| mkName (TFree (x,_)) = mkUpper (Long_Name.base_name x)
| mkName (TVar ((x,_),_)) = mkUpper (Long_Name.base_name x);
fun is_datatype thy = is_some o BNF_LFP_Compat.get_info thy [BNF_LFP_Compat.Keep_Nesting];
fun mk_map \<^type_name>\<open>List.list\<close> = Syntax.const \<^const_name>\<open>List.map\<close>
| mk_map n = Syntax.const ("StateFun.map_" ^ Long_Name.base_name n);
fun gen_constr_destr comp prfx thy (Type (T, [])) =
Syntax.const (deco prfx (mkUpper (Long_Name.base_name T)))
| gen_constr_destr comp prfx thy (T as Type ("fun",_)) =
let val (argTs, rangeT) = strip_type T;
in
comp
(Syntax.const (deco prfx (implode (map mkName argTs) ^ "Fun")))
(fold (fn x => fn y => x $ y)
(replicate (length argTs) (Syntax.const "StateFun.map_fun"))
(gen_constr_destr comp prfx thy rangeT))
end
| gen_constr_destr comp prfx thy (T' as Type (T, argTs)) =
if is_datatype thy T
then (* datatype args are recursively embedded into val *)
(case argTs of
[argT] =>
comp
((Syntax.const (deco prfx (mkUpper (Long_Name.base_name T)))))
((mk_map T $ gen_constr_destr comp prfx thy argT))
| _ => raise (TYPE ("StateFun.gen_constr_destr", [T'], [])))
else (* type args are not recursively embedded into val *)
Syntax.const (deco prfx (implode (map mkName argTs) ^ mkUpper (Long_Name.base_name T)))
| gen_constr_destr thy _ _ T = raise (TYPE ("StateFun.gen_constr_destr", [T], []));
val mk_constr = gen_constr_destr (fn a => fn b => Syntax.const \<^const_name>\<open>Fun.comp\<close> $ a $ b) "";
val mk_destr = gen_constr_destr (fn a => fn b => Syntax.const \<^const_name>\<open>Fun.comp\<close> $ b $ a) "the_";
val _ =
Theory.setup
(Attrib.setup \<^binding>\<open>statefun_simp\<close>
(Scan.succeed (Thm.declaration_attribute (fn thm => fn context =>
let
val ctxt = Context.proof_of context;
val (lookup_ss, ex_lookup_ss, simprocs_active) = Data.get context;
val (lookup_ss', ex_lookup_ss') =
(case Thm.concl_of thm of
(_ $ ((Const (\<^const_name>\<open>Ex\<close>, _) $ _))) =>
(lookup_ss, simpset_map ctxt (Simplifier.add_simp thm) ex_lookup_ss)
| _ =>
(simpset_map ctxt (Simplifier.add_simp thm) lookup_ss, ex_lookup_ss));
val activate_simprocs =
if simprocs_active then I
else Simplifier.map_ss (fn ctxt => ctxt addsimprocs [lookup_simproc, update_simproc]);
in
context
|> activate_simprocs
|> Data.put (lookup_ss', ex_lookup_ss', true)
end)))
"simplification in statespaces");
end;
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