--- a/src/HOL/Decision_Procs/approximation.ML Wed Sep 29 18:22:32 2021 +0200
+++ b/src/HOL/Decision_Procs/approximation.ML Wed Sep 29 22:54:38 2021 +0200
@@ -15,12 +15,8 @@
fun reorder_bounds_tac ctxt prems i =
let
- fun variable_of_bound (Const (\<^const_name>\<open>Trueprop\<close>, _) $
- (Const (\<^const_name>\<open>Set.member\<close>, _) $
- Free (name, _) $ _)) = name
- | variable_of_bound (Const (\<^const_name>\<open>Trueprop\<close>, _) $
- (Const (\<^const_name>\<open>HOL.eq\<close>, _) $
- Free (name, _) $ _)) = name
+ fun variable_of_bound \<^Const_>\<open>Trueprop for \<^Const_>\<open>Set.member _ for \<open>Free (name, _)\<close> _\<close>\<close> = name
+ | variable_of_bound \<^Const_>\<open>Trueprop for \<^Const_>\<open>HOL.eq _ for \<open>Free (name, _)\<close> _\<close>\<close> = name
| variable_of_bound t = raise TERM ("variable_of_bound", [t])
val variable_bounds
@@ -43,18 +39,18 @@
end
fun approximate ctxt t = case fastype_of t
- of \<^typ>\<open>bool\<close> =>
+ of \<^Type>\<open>bool\<close> =>
Approximation_Computation.approx_bool ctxt t
- | \<^typ>\<open>(float interval) option\<close> =>
+ | \<^typ>\<open>float interval option\<close> =>
Approximation_Computation.approx_arith ctxt t
- | \<^typ>\<open>(float interval) option list\<close> =>
+ | \<^typ>\<open>float interval option list\<close> =>
Approximation_Computation.approx_form_eval ctxt t
| _ => error ("Bad term: " ^ Syntax.string_of_term ctxt t);
fun rewrite_interpret_form_tac ctxt prec splitting taylor i st = let
fun lookup_splitting (Free (name, _)) =
(case AList.lookup (op =) splitting name
- of SOME s => HOLogic.mk_number \<^typ>\<open>nat\<close> s
+ of SOME s => HOLogic.mk_number \<^Type>\<open>nat\<close> s
| NONE => \<^term>\<open>0 :: nat\<close>)
| lookup_splitting t = raise TERM ("lookup_splitting", [t])
val vs = nth (Thm.prems_of st) (i - 1)
@@ -63,16 +59,16 @@
|> Term.strip_comb |> snd |> List.last
|> HOLogic.dest_list
val p = prec
- |> HOLogic.mk_number \<^typ>\<open>nat\<close>
+ |> HOLogic.mk_number \<^Type>\<open>nat\<close>
|> Thm.cterm_of ctxt
in case taylor
of NONE => let
val n = vs |> length
- |> HOLogic.mk_number \<^typ>\<open>nat\<close>
+ |> HOLogic.mk_number \<^Type>\<open>nat\<close>
|> Thm.cterm_of ctxt
val s = vs
|> map lookup_splitting
- |> HOLogic.mk_list \<^typ>\<open>nat\<close>
+ |> HOLogic.mk_list \<^Type>\<open>nat\<close>
|> Thm.cterm_of ctxt
in
(resolve_tac ctxt [Thm.instantiate (TVars.empty,
@@ -86,7 +82,7 @@
then raise (TERM ("More than one variable used for taylor series expansion", [Thm.prop_of st]))
else let
val t = t
- |> HOLogic.mk_number \<^typ>\<open>nat\<close>
+ |> HOLogic.mk_number \<^Type>\<open>nat\<close>
|> Thm.cterm_of ctxt
val s = vs |> map lookup_splitting |> hd
|> Thm.cterm_of ctxt
@@ -97,42 +93,38 @@
end
end
-fun calculated_subterms (\<^const>\<open>Trueprop\<close> $ t) = calculated_subterms t
- | calculated_subterms (\<^const>\<open>HOL.implies\<close> $ _ $ t) = calculated_subterms t
- | calculated_subterms (\<^term>\<open>(\<le>) :: real \<Rightarrow> real \<Rightarrow> bool\<close> $ t1 $ t2) = [t1, t2]
- | calculated_subterms (\<^term>\<open>(<) :: real \<Rightarrow> real \<Rightarrow> bool\<close> $ t1 $ t2) = [t1, t2]
- | calculated_subterms (\<^term>\<open>(\<in>) :: real \<Rightarrow> real set \<Rightarrow> bool\<close> $ t1 $
- (\<^term>\<open>atLeastAtMost :: real \<Rightarrow> real \<Rightarrow> real set\<close> $ t2 $ t3)) = [t1, t2, t3]
+fun calculated_subterms \<^Const_>\<open>Trueprop for t\<close> = calculated_subterms t
+ | calculated_subterms \<^Const_>\<open>implies for _ t\<close> = calculated_subterms t
+ | calculated_subterms \<^Const_>\<open>less_eq \<^Type>\<open>real\<close> for t1 t2\<close> = [t1, t2]
+ | calculated_subterms \<^Const_>\<open>less \<^Type>\<open>real\<close> for t1 t2\<close> = [t1, t2]
+ | calculated_subterms \<^Const_>\<open>Set.member \<^Type>\<open>real\<close> for
+ t1 \<^Const_>\<open>atLeastAtMost \<^Type>\<open>real\<close> for t2 t3\<close>\<close> = [t1, t2, t3]
| calculated_subterms t = raise TERM ("calculated_subterms", [t])
-fun dest_interpret_form (\<^const>\<open>interpret_form\<close> $ b $ xs) = (b, xs)
+fun dest_interpret_form \<^Const_>\<open>interpret_form for b xs\<close> = (b, xs)
| dest_interpret_form t = raise TERM ("dest_interpret_form", [t])
-fun dest_interpret (\<^const>\<open>interpret_floatarith\<close> $ b $ xs) = (b, xs)
+fun dest_interpret \<^Const_>\<open>interpret_floatarith for b xs\<close> = (b, xs)
| dest_interpret t = raise TERM ("dest_interpret", [t])
-fun dest_interpret_env (\<^const>\<open>interpret_form\<close> $ _ $ xs) = xs
- | dest_interpret_env (\<^const>\<open>interpret_floatarith\<close> $ _ $ xs) = xs
+fun dest_interpret_env \<^Const_>\<open>interpret_form for _ xs\<close> = xs
+ | dest_interpret_env \<^Const_>\<open>interpret_floatarith for _ xs\<close> = xs
| dest_interpret_env t = raise TERM ("dest_interpret_env", [t])
-fun dest_float (\<^const>\<open>Float\<close> $ m $ e) = (snd (HOLogic.dest_number m), snd (HOLogic.dest_number e))
+fun dest_float \<^Const_>\<open>Float for m e\<close> = (snd (HOLogic.dest_number m), snd (HOLogic.dest_number e))
| dest_float t = raise TERM ("dest_float", [t])
-fun dest_ivl
- (Const (\<^const_name>\<open>Some\<close>, _) $
- (Const (\<^const_name>\<open>Interval\<close>, _) $ ((Const (\<^const_name>\<open>Pair\<close>, _) $ u $ l)))) =
+fun dest_ivl \<^Const_>\<open>Some _ for \<^Const_>\<open>Interval _ for \<^Const_>\<open>Pair _ _ for u l\<close>\<close>\<close> =
SOME (dest_float u, dest_float l)
- | dest_ivl (Const (\<^const_name>\<open>None\<close>, _)) = NONE
+ | dest_ivl \<^Const_>\<open>None _\<close> = NONE
| dest_ivl t = raise TERM ("dest_result", [t])
-fun mk_approx' prec t = (\<^const>\<open>approx'\<close>
- $ HOLogic.mk_number \<^typ>\<open>nat\<close> prec
- $ t $ \<^term>\<open>[] :: (float interval) option list\<close>)
+fun mk_approx' prec t =
+ \<^Const>\<open>approx' for \<open>HOLogic.mk_number \<^Type>\<open>nat\<close> prec\<close> t \<^Const>\<open>Nil \<^typ>\<open>float interval option\<close>\<close>\<close>
-fun mk_approx_form_eval prec t xs = (\<^const>\<open>approx_form_eval\<close>
- $ HOLogic.mk_number \<^typ>\<open>nat\<close> prec
- $ t $ xs)
+fun mk_approx_form_eval prec t xs =
+ \<^Const>\<open>approx_form_eval for \<open>HOLogic.mk_number \<^Type>\<open>nat\<close> prec\<close> t xs\<close>
fun float2_float10 prec round_down (m, e) = (
let
@@ -166,21 +158,21 @@
fun mk_result prec (SOME (l, u)) =
(let
fun mk_float10 rnd x = (let val (m, e) = float2_float10 prec rnd x
- in if e = 0 then HOLogic.mk_number \<^typ>\<open>real\<close> m
- else if e = 1 then \<^term>\<open>divide :: real \<Rightarrow> real \<Rightarrow> real\<close> $
- HOLogic.mk_number \<^typ>\<open>real\<close> m $
+ in if e = 0 then HOLogic.mk_number \<^Type>\<open>real\<close> m
+ else if e = 1 then \<^Const>\<open>divide \<^Type>\<open>real\<close>\<close> $
+ HOLogic.mk_number \<^Type>\<open>real\<close> m $
\<^term>\<open>10\<close>
- else \<^term>\<open>divide :: real \<Rightarrow> real \<Rightarrow> real\<close> $
- HOLogic.mk_number \<^typ>\<open>real\<close> m $
+ else \<^Const>\<open>divide \<^Type>\<open>real\<close>\<close> $
+ HOLogic.mk_number \<^Type>\<open>real\<close> m $
(\<^term>\<open>power 10 :: nat \<Rightarrow> real\<close> $
- HOLogic.mk_number \<^typ>\<open>nat\<close> (~e)) end)
- in \<^term>\<open>atLeastAtMost :: real \<Rightarrow> real \<Rightarrow> real set\<close> $ mk_float10 true l $ mk_float10 false u end)
+ HOLogic.mk_number \<^Type>\<open>nat\<close> (~e)) end)
+ in \<^Const>\<open>atLeastAtMost \<^Type>\<open>real\<close> for \<open>mk_float10 true l\<close> \<open>mk_float10 false u\<close>\<close> end)
| mk_result _ NONE = \<^term>\<open>UNIV :: real set\<close>
fun realify t =
let
val t = Logic.varify_global t
- val m = map (fn (name, _) => (name, \<^typ>\<open>real\<close>)) (Term.add_tvars t [])
+ val m = map (fn (name, _) => (name, \<^Type>\<open>real\<close>)) (Term.add_tvars t [])
val t = Term.subst_TVars m t
in t end
@@ -237,12 +229,12 @@
|> HOLogic.dest_Trueprop
|> dest_interpret_form
|> (fn (data, xs) =>
- mk_approx_form_eval prec data (HOLogic.mk_list \<^typ>\<open>(float interval) option\<close>
- (map (fn _ => \<^term>\<open>None :: (float interval) option\<close>) (HOLogic.dest_list xs)))
+ mk_approx_form_eval prec data (HOLogic.mk_list \<^typ>\<open>float interval option\<close>
+ (map (fn _ => \<^Const>\<open>None \<^typ>\<open>float interval option\<close>\<close>) (HOLogic.dest_list xs)))
|> approximate ctxt
|> HOLogic.dest_list
|> curry ListPair.zip (HOLogic.dest_list xs @ calculated_subterms arith_term)
- |> map (fn (elem, s) => \<^term>\<open>(\<in>) :: real \<Rightarrow> real set \<Rightarrow> bool\<close> $ elem $ mk_result prec (dest_ivl s))
+ |> map (fn (elem, s) => \<^Const>\<open>Set.member \<^Type>\<open>real\<close> for elem \<open>mk_result prec (dest_ivl s)\<close>\<close>)
|> foldr1 HOLogic.mk_conj))
fun approx_arith prec ctxt t = realify t
@@ -257,8 +249,8 @@
|> mk_result prec
fun approx prec ctxt t =
- if type_of t = \<^typ>\<open>prop\<close> then approx_form prec ctxt t
- else if type_of t = \<^typ>\<open>bool\<close> then approx_form prec ctxt (\<^const>\<open>Trueprop\<close> $ t)
+ if type_of t = \<^Type>\<open>prop\<close> then approx_form prec ctxt t
+ else if type_of t = \<^Type>\<open>bool\<close> then approx_form prec ctxt \<^Const>\<open>Trueprop for t\<close>
else approx_arith prec ctxt t
fun approximate_cmd modes raw_t state =