src/HOL/Code_Eval.thy

merged

(*  Title:      HOL/Code_Eval.thy
    Author:     Florian Haftmann, TU Muenchen
*)

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

theory Code_Eval
imports Plain Typerep
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)

ML {*
structure Eval =
struct

fun mk_term f g (Const (c, ty)) =
      @{term Const} $ Message_String.mk c $ g ty
  | mk_term f g (t1 $ t2) =
      @{term App} $ mk_term f g t1 $ mk_term f g t2
  | mk_term f g (Free v) = f v
  | mk_term f g (Bound i) = Bound i
  | mk_term f g (Abs (v, _, t)) = Abs (v, @{typ term}, mk_term f g t);

fun mk_term_of ty t = Const (@{const_name term_of}, ty --> @{typ term}) $ t;

end;
*}


subsubsection {* @{text term_of} instances *}

setup {*
let
  fun add_term_of_def ty vs tyco thy =
    let
      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_instance (K (Class.intro_classes_tac []))
      |> LocalTheory.exit_global
    end;
  fun interpretator (tyco, (raw_vs, _)) thy =
    let
      val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of};
      val constrain_sort =
        curry (Sorts.inter_sort (Sign.classes_of thy)) @{sort term_of};
      val vs = (map o apsnd) constrain_sort raw_vs;
      val ty = Type (tyco, map TFree vs);
    in
      thy
      |> Typerep.perhaps_add_def tyco
      |> not has_inst ? add_term_of_def ty vs tyco
    end;
in
  Code.type_interpretation interpretator
end
*}

setup {*
let
  fun mk_term_of_eq ty vs tyco (c, tys) =
    let
      val t = list_comb (Const (c, tys ---> ty),
        map Free (Name.names Name.context "a" tys));
    in (map_aterms (fn Free (v, ty) => Var ((v, 0), ty) | t => t) t, Eval.mk_term
      (fn (v, ty) => Eval.mk_term_of ty (Var ((v, 0), ty)))
      (Typerep.mk (fn (v, sort) => Typerep.typerep (TFree (v, sort)))) t)
    end;
  fun prove_term_of_eq ty eq thy =
    let
      val cty = Thm.ctyp_of thy ty;
      val (arg, rhs) = pairself (Thm.cterm_of thy) eq;
      val thm = @{thm term_of_anything}
        |> Drule.instantiate' [SOME cty] [SOME arg, SOME rhs]
        |> Thm.varifyT;
    in
      thy
      |> Code.add_eqn thm
    end;
  fun interpretator (tyco, (raw_vs, raw_cs)) thy =
    let
      val constrain_sort =
        curry (Sorts.inter_sort (Sign.classes_of thy)) @{sort term_of};
      val vs = (map o apsnd) constrain_sort raw_vs;
      val cs = (map o apsnd o map o map_atyps)
        (fn TFree (v, sort) => TFree (v, constrain_sort sort)) raw_cs;
      val ty = Type (tyco, map TFree vs);
      val eqs = map (mk_term_of_eq ty vs tyco) cs;
      val const = AxClass.param_of_inst thy (@{const_name term_of}, tyco);
    in
      thy
      |> Code.del_eqns const
      |> fold (prove_term_of_eq ty) eqs
    end;
in
  Code.type_interpretation interpretator
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"
  (SML "Term.term")

code_const Const and App
  (SML "Term.Const/ (_, _)" and "Term.$/ (_, _)")

code_const "term_of \<Colon> message_string \<Rightarrow> term"
  (SML "Message'_String.mk")


subsection {* Evaluation setup *}

ML {*
signature EVAL =
sig
  val mk_term: ((string * typ) -> term) -> (typ -> term) -> term -> term
  val eval_ref: (unit -> term) option ref
  val eval_term: theory -> term -> term
end;

structure Eval : EVAL =
struct

open Eval;

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

fun eval_term thy t =
  t 
  |> Eval.mk_term_of (fastype_of t)
  |> (fn t => Code_ML.eval_term ("Eval.eval_ref", eval_ref) thy t [])
  |> Code.postprocess_term thy;

end;
*}

setup {*
  Value.add_evaluator ("code", Eval.eval_term o ProofContext.theory_of)
*}


subsubsection {* Syntax *}

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
hide (open) const Const App
hide (open) const term_of

end