(*  Title:      HOL/Code_Evaluation.thy

    Author:     Florian Haftmann, TU Muenchen

*)

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

theory Code_Evaluation

imports Plain Typerep Code_Numeral

begin

subsection {* Term representation *}

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

datatype "term" = dummy_term

definition Const :: "String.literal \<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_unfold]:

  "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 *}

instantiation "fun" :: (typerep, typerep) term_of

begin

definition

  "term_of (f \<Colon> 'a \<Rightarrow> 'b) = Const (STR ''dummy_pattern'') (Typerep.Typerep (STR ''fun'')

     [Typerep.typerep TYPE('a), Typerep.typerep TYPE('b)])"

instance ..

end

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 if need_inst then add_term_of tyco raw_vs thy else thy 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 algebra = Sign.classes_of thy;

      val vs = map (fn (v, sort) =>

        (v, curry (Sorts.inter_sort algebra) @{sort typerep} sort)) 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 if has_inst then add_term_of_code tyco raw_vs cs thy else thy 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> String.literal \<Rightarrow> term) = term_of" ..

lemma [code, code del]:

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

lemma [code, code del]:

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

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

    (let (n, m) = nibble_pair_of_char c

  in Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.Const (STR ''String.char.Char'') (TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char)))

    (Code_Evaluation.term_of n)) (Code_Evaluation.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> String.literal \<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_code_numeral_code [code]:

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