(*  Title:      HOL/Code_Eval.thy

     Author:     Florian Haftmann, TU Muenchen

 *)

 header {* Term evaluation using the generic code generator *}

 theory Code_Eval

 imports Plain Typerep Code_Index

 begin

 subsection {* Term representation *}

 subsubsection {* Terms and class @{text term_of} *}

 datatype "term" = dummy_term

 definition Const :: "message_string \<Rightarrow> typerep \<Rightarrow> term" where

   "Const _ _ = dummy_term"

 definition App :: "term \<Rightarrow> term \<Rightarrow> term" where

   "App _ _ = dummy_term"

 code_datatype Const App

 class term_of = typerep +

   fixes term_of :: "'a \<Rightarrow> term"

 lemma term_of_anything: "term_of x \<equiv> t"

   by (rule eq_reflection) (cases "term_of x", cases t, simp)

 definition valapp :: "('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)

   \<Rightarrow> 'a \<times> (unit \<Rightarrow> term) \<Rightarrow> 'b \<times> (unit \<Rightarrow> term)" where

   "valapp f x = (fst f (fst x), \<lambda>u. App (snd f ()) (snd x ()))"

 lemma valapp_code [code, code inline]:

   "valapp (f, tf) (x, tx) = (f x, \<lambda>u. App (tf ()) (tx ()))"

   by (simp only: valapp_def fst_conv snd_conv)

 subsubsection {* @{text term_of} instances *}

 setup {*

 let

   fun add_term_of tyco raw_vs thy =

     let

       val vs = map (fn (v, _) => (v, @{sort typerep})) raw_vs;

       val ty = Type (tyco, map TFree vs);

       val lhs = Const (@{const_name term_of}, ty --> @{typ term})

         $ Free ("x", ty);

       val rhs = @{term "undefined \<Colon> term"};

       val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));

       fun triv_name_of t = (fst o dest_Free o fst o strip_comb o fst

         o HOLogic.dest_eq o HOLogic.dest_Trueprop) t ^ "_triv";

     in

       thy

       |> TheoryTarget.instantiation ([tyco], vs, @{sort term_of})

       |> `(fn lthy => Syntax.check_term lthy eq)

       |-> (fn eq => Specification.definition (NONE, ((Binding.name (triv_name_of eq), []), eq)))

       |> snd

       |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))

     end;

   fun ensure_term_of (tyco, (raw_vs, _)) thy =

     let

       val need_inst = not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of})

         andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep};

     in

       thy

       |> need_inst ? add_term_of tyco raw_vs

     end;

 in

   Code.type_interpretation ensure_term_of

 end

 *}

 setup {*

 let

   fun mk_term_of_eq thy ty vs tyco (c, tys) =

     let

       val t = list_comb (Const (c, tys ---> ty),

         map Free (Name.names Name.context "a" tys));

       val (arg, rhs) = pairself (Thm.cterm_of thy o map_types Logic.unvarifyT o Logic.varify)

         (t, (map_aterms (fn t as Free (v, ty) => HOLogic.mk_term_of ty t | t => t) o HOLogic.reflect_term) t)

       val cty = Thm.ctyp_of thy ty;

     in

       @{thm term_of_anything}

       |> Drule.instantiate' [SOME cty] [SOME arg, SOME rhs]

       |> Thm.varifyT

     end;

   fun add_term_of_code tyco raw_vs raw_cs thy =

     let

       val vs = map (fn (v, _) => (v, @{sort typerep})) raw_vs;

       val ty = Type (tyco, map TFree vs);

       val cs = (map o apsnd o map o map_atyps)

         (fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_cs;

       val const = AxClass.param_of_inst thy (@{const_name term_of}, tyco);

       val eqs = map (mk_term_of_eq thy ty vs tyco) cs;

    in

       thy

       |> Code.del_eqns const

       |> fold Code.add_eqn eqs

     end;

   fun ensure_term_of_code (tyco, (raw_vs, cs)) thy =

     let

       val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of};

     in

       thy

       |> has_inst ? add_term_of_code tyco raw_vs cs

     end;

 in

   Code.type_interpretation ensure_term_of_code

 end

 *}

 subsubsection {* Code generator setup *}

 lemmas [code del] = term.recs term.cases term.size

 lemma [code, code del]: "eq_class.eq (t1\<Colon>term) t2 \<longleftrightarrow> eq_class.eq t1 t2" ..

 lemma [code, code del]: "(term_of \<Colon> typerep \<Rightarrow> term) = term_of" ..

 lemma [code, code del]: "(term_of \<Colon> term \<Rightarrow> term) = term_of" ..

 lemma [code, code del]: "(term_of \<Colon> message_string \<Rightarrow> term) = term_of" ..

 lemma [code, code del]:

   "(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..

 lemma [code, code del]:

   "(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..

 lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_nibble_def, code]: "Code_Eval.term_of c =

     (let (n, m) = nibble_pair_of_char c

   in Code_Eval.App (Code_Eval.App (Code_Eval.Const (STR ''Pair'') (TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char)))

     (Code_Eval.term_of n)) (Code_Eval.term_of m))"

   by (subst term_of_anything) rule 

 code_type "term"

   (Eval "Term.term")

 code_const Const and App

   (Eval "Term.Const/ (_, _)" and "Term.$/ (_, _)")

 code_const "term_of \<Colon> message_string \<Rightarrow> term"

   (Eval "HOLogic.mk'_message'_string")

 code_reserved Eval HOLogic

 subsubsection {* Syntax *}

 definition termify :: "'a \<Rightarrow> term" where

   [code del]: "termify x = dummy_term"

 abbreviation valtermify :: "'a \<Rightarrow> 'a \<times> (unit \<Rightarrow> term)" where

   "valtermify x \<equiv> (x, \<lambda>u. termify x)"

 setup {*

 let

   fun map_default f xs =

     let val ys = map f xs

     in if exists is_some ys

       then SOME (map2 the_default xs ys)

       else NONE

     end;

   fun subst_termify_app (Const (@{const_name termify}, T), [t]) =

         if not (Term.has_abs t)

         then if fold_aterms (fn Const _ => I | _ => K false) t true

           then SOME (HOLogic.reflect_term t)

           else error "Cannot termify expression containing variables"

         else error "Cannot termify expression containing abstraction"

     | subst_termify_app (t, ts) = case map_default subst_termify ts

        of SOME ts' => SOME (list_comb (t, ts'))

         | NONE => NONE

   and subst_termify (Abs (v, T, t)) = (case subst_termify t

        of SOME t' => SOME (Abs (v, T, t'))

         | NONE => NONE)

     | subst_termify t = subst_termify_app (strip_comb t) 

   fun check_termify ts ctxt = map_default subst_termify ts

     |> Option.map (rpair ctxt)

 in

   Context.theory_map (Syntax.add_term_check 0 "termify" check_termify)

 end;

 *}

 locale term_syntax

 begin

 notation App (infixl "<\<cdot>>" 70)

   and valapp (infixl "{\<cdot>}" 70)

 end

 interpretation term_syntax .

 no_notation App (infixl "<\<cdot>>" 70)

   and valapp (infixl "{\<cdot>}" 70)

 subsection {* Numeric types *}

 definition term_of_num :: "'a\<Colon>{semiring_div} \<Rightarrow> 'a\<Colon>{semiring_div} \<Rightarrow> term" where

   "term_of_num two = (\<lambda>_. dummy_term)"

 lemma (in term_syntax) term_of_num_code [code]:

   "term_of_num two k = (if k = 0 then termify Int.Pls

     else (if k mod two = 0

       then termify Int.Bit0 <\<cdot>> term_of_num two (k div two)

       else termify Int.Bit1 <\<cdot>> term_of_num two (k div two)))"

   by (auto simp add: term_of_anything Const_def App_def term_of_num_def Let_def)

 lemma (in term_syntax) term_of_nat_code [code]:

   "term_of (n::nat) = termify (number_of :: int \<Rightarrow> nat) <\<cdot>> term_of_num (2::nat) n"

   by (simp only: term_of_anything)

 lemma (in term_syntax) term_of_int_code [code]:

   "term_of (k::int) = (if k = 0 then termify (0 :: int)

     else if k > 0 then termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) k

       else termify (uminus :: int \<Rightarrow> int) <\<cdot>> (termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) (- k)))"

   by (simp only: term_of_anything)

 lemma (in term_syntax) term_of_index_code [code]:

   "term_of (k::index) = termify (number_of :: int \<Rightarrow> index) <\<cdot>> term_of_num (2::index) k"

   by (simp only: term_of_anything)

 subsection {* Obfuscate *}

 print_translation {*

 let

   val term = Const ("<TERM>", dummyT);

   fun tr1' [_, _] = term;

   fun tr2' [] = term;

 in

   [(@{const_syntax Const}, tr1'),

     (@{const_syntax App}, tr1'),

     (@{const_syntax dummy_term}, tr2')]

 end

 *}

 hide const dummy_term App valapp

 hide (open) const Const termify valtermify term_of term_of_num

 subsection {* Evaluation setup *}

 ML {*

 signature EVAL =

 sig

   val eval_ref: (unit -> term) option ref

   val eval_term: theory -> term -> term

 end;

 structure Eval : EVAL =

 struct

 val eval_ref = ref (NONE : (unit -> term) option);

 fun eval_term thy t =

   Code_ML.eval NONE ("Eval.eval_ref", eval_ref) I thy (HOLogic.mk_term_of (fastype_of t) t) [];

 end;

 *}

 setup {*

   Value.add_evaluator ("code", Eval.eval_term o ProofContext.theory_of)

 *}

 end