src/HOL/Code_Evaluation.thy
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(*  Title:      HOL/Code_Evaluation.thy
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    Author:     Florian Haftmann, TU Muenchen
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*)
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header {* Term evaluation using the generic code generator *}
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theory Code_Evaluation
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imports Plain Typerep Code_Numeral
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begin
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subsection {* Term representation *}
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subsubsection {* Terms and class @{text term_of} *}
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datatype "term" = dummy_term
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definition Const :: "String.literal \<Rightarrow> typerep \<Rightarrow> term" where
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  "Const _ _ = dummy_term"
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definition App :: "term \<Rightarrow> term \<Rightarrow> term" where
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  "App _ _ = dummy_term"
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code_datatype Const App
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class term_of = typerep +
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  fixes term_of :: "'a \<Rightarrow> term"
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lemma term_of_anything: "term_of x \<equiv> t"
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  by (rule eq_reflection) (cases "term_of x", cases t, simp)
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definition valapp :: "('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)
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  \<Rightarrow> 'a \<times> (unit \<Rightarrow> term) \<Rightarrow> 'b \<times> (unit \<Rightarrow> term)" where
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  "valapp f x = (fst f (fst x), \<lambda>u. App (snd f ()) (snd x ()))"
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lemma valapp_code [code, code_unfold]:
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  "valapp (f, tf) (x, tx) = (f x, \<lambda>u. App (tf ()) (tx ()))"
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  by (simp only: valapp_def fst_conv snd_conv)
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subsubsection {* @{text term_of} instances *}
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instantiation "fun" :: (typerep, typerep) term_of
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begin
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definition
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  "term_of (f \<Colon> 'a \<Rightarrow> 'b) = Const (STR ''dummy_pattern'') (Typerep.Typerep (STR ''fun'')
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     [Typerep.typerep TYPE('a), Typerep.typerep TYPE('b)])"
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instance ..
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end
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setup {*
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let
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  fun add_term_of tyco raw_vs thy =
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    let
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      val vs = map (fn (v, _) => (v, @{sort typerep})) raw_vs;
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      val ty = Type (tyco, map TFree vs);
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      val lhs = Const (@{const_name term_of}, ty --> @{typ term})
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        $ Free ("x", ty);
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      val rhs = @{term "undefined \<Colon> term"};
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      val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
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      fun triv_name_of t = (fst o dest_Free o fst o strip_comb o fst
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        o HOLogic.dest_eq o HOLogic.dest_Trueprop) t ^ "_triv";
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    in
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      thy
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      |> Theory_Target.instantiation ([tyco], vs, @{sort term_of})
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      |> `(fn lthy => Syntax.check_term lthy eq)
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      |-> (fn eq => Specification.definition (NONE, ((Binding.name (triv_name_of eq), []), eq)))
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      |> snd
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      |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
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    end;
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  fun ensure_term_of (tyco, (raw_vs, _)) thy =
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    let
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      val need_inst = not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of})
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        andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep};
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    in if need_inst then add_term_of tyco raw_vs thy else thy end;
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in
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  Code.datatype_interpretation ensure_term_of
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  #> Code.abstype_interpretation ensure_term_of
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end
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*}
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setup {*
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let
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  fun mk_term_of_eq thy ty vs tyco (c, tys) =
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    let
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      val t = list_comb (Const (c, tys ---> ty),
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        map Free (Name.names Name.context "a" tys));
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      val (arg, rhs) = pairself (Thm.cterm_of thy o map_types Logic.unvarifyT o Logic.varify)
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        (t, (map_aterms (fn t as Free (v, ty) => HOLogic.mk_term_of ty t | t => t) o HOLogic.reflect_term) t)
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      val cty = Thm.ctyp_of thy ty;
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    in
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      @{thm term_of_anything}
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      |> Drule.instantiate' [SOME cty] [SOME arg, SOME rhs]
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      |> Thm.varifyT
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    end;
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  fun add_term_of_code tyco raw_vs raw_cs thy =
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    let
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      val algebra = Sign.classes_of thy;
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      val vs = map (fn (v, sort) =>
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        (v, curry (Sorts.inter_sort algebra) @{sort typerep} sort)) raw_vs;
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      val ty = Type (tyco, map TFree vs);
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      val cs = (map o apsnd o map o map_atyps)
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        (fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_cs;
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      val const = AxClass.param_of_inst thy (@{const_name term_of}, tyco);
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      val eqs = map (mk_term_of_eq thy ty vs tyco) cs;
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   in
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      thy
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      |> Code.del_eqns const
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      |> fold Code.add_eqn eqs
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    end;
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  fun ensure_term_of_code (tyco, (raw_vs, cs)) thy =
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    let
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      val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of};
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    in if has_inst then add_term_of_code tyco raw_vs cs thy else thy end;
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in
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  Code.datatype_interpretation ensure_term_of_code
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end
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*}
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subsubsection {* Code generator setup *}
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lemmas [code del] = term.recs term.cases term.size
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lemma [code, code del]: "eq_class.eq (t1\<Colon>term) t2 \<longleftrightarrow> eq_class.eq t1 t2" ..
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lemma [code, code del]: "(term_of \<Colon> typerep \<Rightarrow> term) = term_of" ..
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lemma [code, code del]: "(term_of \<Colon> term \<Rightarrow> term) = term_of" ..
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lemma [code, code del]: "(term_of \<Colon> String.literal \<Rightarrow> term) = term_of" ..
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lemma [code, code del]:
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  "(Code_Evaluation.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Evaluation.term) = Code_Evaluation.term_of" ..
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lemma [code, code del]:
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  "(Code_Evaluation.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Evaluation.term) = Code_Evaluation.term_of" ..
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lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_nibble_def, code]: "Code_Evaluation.term_of c =
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    (let (n, m) = nibble_pair_of_char c
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  in Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.Const (STR ''String.char.Char'') (TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char)))
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    (Code_Evaluation.term_of n)) (Code_Evaluation.term_of m))"
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  by (subst term_of_anything) rule 
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code_type "term"
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  (Eval "Term.term")
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code_const Const and App
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  (Eval "Term.Const/ ((_), (_))" and "Term.$/ ((_), (_))")
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code_const "term_of \<Colon> String.literal \<Rightarrow> term"
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  (Eval "HOLogic.mk'_literal")
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code_reserved Eval HOLogic
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subsubsection {* Syntax *}
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definition termify :: "'a \<Rightarrow> term" where
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  [code del]: "termify x = dummy_term"
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abbreviation valtermify :: "'a \<Rightarrow> 'a \<times> (unit \<Rightarrow> term)" where
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  "valtermify x \<equiv> (x, \<lambda>u. termify x)"
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setup {*
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let
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  fun map_default f xs =
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    let val ys = map f xs
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    in if exists is_some ys
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      then SOME (map2 the_default xs ys)
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      else NONE
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    end;
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  fun subst_termify_app (Const (@{const_name termify}, T), [t]) =
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        if not (Term.has_abs t)
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        then if fold_aterms (fn Const _ => I | _ => K false) t true
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          then SOME (HOLogic.reflect_term t)
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          else error "Cannot termify expression containing variables"
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        else error "Cannot termify expression containing abstraction"
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    | subst_termify_app (t, ts) = case map_default subst_termify ts
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       of SOME ts' => SOME (list_comb (t, ts'))
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        | NONE => NONE
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  and subst_termify (Abs (v, T, t)) = (case subst_termify t
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       of SOME t' => SOME (Abs (v, T, t'))
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        | NONE => NONE)
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    | subst_termify t = subst_termify_app (strip_comb t) 
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  fun check_termify ts ctxt = map_default subst_termify ts
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    |> Option.map (rpair ctxt)
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in
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  Context.theory_map (Syntax.add_term_check 0 "termify" check_termify)
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end;
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*}
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locale term_syntax
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begin
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notation App (infixl "<\<cdot>>" 70)
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  and valapp (infixl "{\<cdot>}" 70)
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end
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interpretation term_syntax .
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no_notation App (infixl "<\<cdot>>" 70)
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  and valapp (infixl "{\<cdot>}" 70)
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subsection {* Numeric types *}
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definition term_of_num :: "'a\<Colon>{semiring_div} \<Rightarrow> 'a\<Colon>{semiring_div} \<Rightarrow> term" where
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  "term_of_num two = (\<lambda>_. dummy_term)"
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lemma (in term_syntax) term_of_num_code [code]:
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  "term_of_num two k = (if k = 0 then termify Int.Pls
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    else (if k mod two = 0
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      then termify Int.Bit0 <\<cdot>> term_of_num two (k div two)
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      else termify Int.Bit1 <\<cdot>> term_of_num two (k div two)))"
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  by (auto simp add: term_of_anything Const_def App_def term_of_num_def Let_def)
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lemma (in term_syntax) term_of_nat_code [code]:
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  "term_of (n::nat) = termify (number_of :: int \<Rightarrow> nat) <\<cdot>> term_of_num (2::nat) n"
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  by (simp only: term_of_anything)
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lemma (in term_syntax) term_of_int_code [code]:
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  "term_of (k::int) = (if k = 0 then termify (0 :: int)
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    else if k > 0 then termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) k
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      else termify (uminus :: int \<Rightarrow> int) <\<cdot>> (termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) (- k)))"
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  by (simp only: term_of_anything)
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lemma (in term_syntax) term_of_code_numeral_code [code]:
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  "term_of (k::code_numeral) = termify (number_of :: int \<Rightarrow> code_numeral) <\<cdot>> term_of_num (2::code_numeral) k"
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  by (simp only: term_of_anything)
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subsection {* Obfuscate *}
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print_translation {*
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let
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  val term = Const ("<TERM>", dummyT);
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  fun tr1' [_, _] = term;
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  fun tr2' [] = term;
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in
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  [(@{const_syntax Const}, tr1'),
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    (@{const_syntax App}, tr1'),
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    (@{const_syntax dummy_term}, tr2')]
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end
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*}
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hide const dummy_term App valapp
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hide (open) const Const termify valtermify term_of term_of_num
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subsection {* Tracing of generated and evaluated code *}
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definition tracing :: "String.literal => 'a => 'a"
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where
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  [code del]: "tracing s x = x"
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ML {*
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structure Code_Evaluation =
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struct
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fun tracing s x = (Output.tracing s; x)
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end
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*}
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code_const "tracing :: String.literal => 'a => 'a"
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  (Eval "Code'_Evaluation.tracing")
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hide (open) const tracing
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code_reserved Eval Code_Evaluation
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subsection {* Evaluation setup *}
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ML {*
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signature EVAL =
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sig
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  val eval_ref: (unit -> term) option Unsynchronized.ref
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  val eval_term: theory -> term -> term
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end;
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structure Eval : EVAL =
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struct
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val eval_ref = Unsynchronized.ref (NONE : (unit -> term) option);
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fun eval_term thy t =
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  Code_Eval.eval NONE ("Eval.eval_ref", eval_ref) I thy (HOLogic.mk_term_of (fastype_of t) t) [];
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end;
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*}
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setup {*
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  Value.add_evaluator ("code", Eval.eval_term o ProofContext.theory_of)
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*}
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end