src/HOL/ex/CodeEval.thy

+(*  ID:         $Id$
+    Author:     Florian Haftmann, TU Muenchen
+*)
+
+header {* A simple embedded term evaluation mechanism *}
+
+theory CodeEval
+imports CodeEmbed
+begin
+
+section {* A simple embedded term evaluation mechanism *}
+
+subsection {* The typ_of class *}
+
+class typ_of =
+  fixes typ_of :: "'a option \<Rightarrow> typ"
+
+ML {*
+structure TypOf =
+struct
+
+local
+  val thy = the_context ();
+  val const_typ_of = Sign.intern_const thy "typ_of";
+  val const_None = Sign.intern_const thy "None";
+  fun typ_option ty = Type (Sign.intern_type (the_context ()) "option", [ty]);
+  fun term_typ_of ty = Const (const_typ_of, typ_option ty --> Embed.typ_typ);
+in
+  val class_typ_of = Sign.intern_class thy "typ_of";
+  fun term_typ_of_None ty =
+    term_typ_of ty $ Const (const_None, typ_option ty);
+  fun mk_typ_of_def ty =
+    let
+      val lhs = term_typ_of ty $ Free ("x", typ_option ty)
+      val rhs = Embed.term_typ (fn v => term_typ_of_None (TFree v)) ty
+    in Logic.mk_equals (lhs, rhs) end;
+end;
+
+end;
+*}
+
+setup {*
+let
+  fun mk _ arities _ =
+    maps (fn ((tyco, asorts), _) => [(("", []), TypOf.mk_typ_of_def
+      (Type (tyco, map TFree (Name.names Name.context "'a" asorts))))]) arities;
+  fun tac _ = ClassPackage.intro_classes_tac [];
+  fun hook specs =
+    DatatypeCodegen.prove_codetypes_arities tac
+      (map (fn (tyco, (is_dt, _)) => (tyco, is_dt)) specs)
+      [TypOf.class_typ_of] mk
+in DatatypeCodegen.add_codetypes_hook_bootstrap hook end
+*}
+
+
+subsection {* term_of class *}
+
+class term_of = typ_of +
+  constrains typ_of :: "'a option \<Rightarrow> typ"
+  fixes term_of :: "'a \<Rightarrow> term"
+
+ML {*
+structure TermOf =
+struct
+
+local
+  val thy = the_context ();
+  val const_term_of = Sign.intern_const thy "term_of";
+  fun term_term_of ty = Const (const_term_of, ty --> Embed.typ_term);
+in
+  val class_term_of = Sign.intern_class thy "term_of";
+  fun mk_terms_of_defs vs (tyco, cs) =
+    let
+      val dty = Type (tyco, map TFree vs);
+      fun mk_eq c =
+        let
+          val lhs : term = term_term_of dty $ c;
+          val rhs : term = Embed.term_term
+            (fn (v, ty) => term_term_of ty $ Free (v, ty))
+            (Embed.term_typ (fn (v, sort) => TypOf.term_typ_of_None (TFree (v, sort)))) c
+        in
+          HOLogic.mk_eq (lhs, rhs)
+        end;
+    in map mk_eq cs end;
+  fun mk_term_of t =
+    term_term_of (Term.fastype_of t) $ t;
+end;
+
+end;
+*}
+
+setup {*
+let
+  fun mk thy arities css =
+    let
+      val vs = (Name.names Name.context "'a" o snd o fst o hd) arities;
+      val raw_defs = map (TermOf.mk_terms_of_defs vs) css;
+      fun mk' thy' = map (apfst (rpair [])) ((PrimrecPackage.mk_combdefs thy' o flat) raw_defs)
+    in ClassPackage.assume_arities_thy thy arities mk' end;
+  fun tac _ = ClassPackage.intro_classes_tac [];
+  fun hook specs =
+    if (fst o hd) specs = (fst o dest_Type) Embed.typ_typ then I
+    else
+      DatatypeCodegen.prove_codetypes_arities tac
+      (map (fn (tyco, (is_dt, _)) => (tyco, is_dt)) specs)
+      [TermOf.class_term_of] mk
+in DatatypeCodegen.add_codetypes_hook_bootstrap hook end
+*}
+
+
+subsection {* Evaluation infrastructure *}
+
+lemma lift_eq_Trueprop:
+  "p == q \<Longrightarrow> Trueprop p == Trueprop q" by auto
+
+ML {*
+signature EVAL =
+sig
+  val eval_term: term -> theory -> term * theory
+  val eval_term' : theory -> term -> term
+  val term: string -> unit
+  val eval_ref: term ref
+  val oracle: string * (theory * exn -> term)
+  val method: Method.src -> Proof.context -> Method.method
+end;
+
+structure Eval : EVAL =
+struct
+
+val eval_ref = ref Logic.protectC;
+
+fun eval_term t =
+  CodegenPackage.eval_term
+    (("Eval.eval_ref", eval_ref), TermOf.mk_term_of t);
+
+fun eval_term' thy t =
+  let
+    val thy' = Theory.copy thy;
+    val (t', _) = eval_term t thy';
+  in t' end;
+
+fun term t =
+  let
+    val thy = the_context ();
+    val t' = eval_term' thy (Sign.read_term thy t);
+  in () end;
+
+val lift_eq_Trueprop = thm "lift_eq_Trueprop";
+
+exception Eval of term;
+
+val oracle = ("Eval", fn (thy, Eval t) =>
+  Logic.mk_equals (t, eval_term' thy t));
+
+val oracle_name = NameSpace.pack [Context.theory_name (the_context ()), fst oracle];
+
+
+fun conv ct =
+  let
+    val {thy, t, ...} = rep_cterm ct;
+    val t' = HOLogic.dest_Trueprop t;
+    val thm' = Thm.invoke_oracle_i thy oracle_name (thy, Eval t');
+  in
+    lift_eq_Trueprop OF [thm']
+  end;
+
+fun tac i = Tactical.PRIMITIVE (Drule.fconv_rule
+  (Drule.goals_conv (equal i) conv));
+
+val method =
+  Method.no_args (Method.METHOD (fn _ =>
+    tac 1 THEN rtac TrueI 1));
+
+end;
+*}
+
+setup {*
+  Theory.add_oracle Eval.oracle
+  #> Method.add_method ("eval", Eval.method, "solve goal by evaluation")
+*}
+
+
+subsection {* Small examples *}
+
+ML {* Eval.term "[]::nat list" *}
+ML {* Eval.term "(Suc 2 + Suc 0) * Suc 3" *}
+ML {* Eval.term "fst ([]::nat list, Suc 0) = []" *}
+
+text {* a fancy datatype *}
+
+datatype ('a, 'b) bair =
+    Bair "'a\<Colon>order" 'b
+  | Shift "('a, 'b) cair"
+  | Dummy unit
+and ('a, 'b) cair =
+    Cair 'a 'b
+
+code_generate term_of
+
+ML {* Eval.term "Shift (Cair (4::nat) [Suc 0])" *}
+
+lemma
+  "Suc 0 = 1" by eval
+
+lemma
+  "rev [0, Suc 0, Suc 0] = [Suc 0, Suc 0, 0]" by eval
+
+lemma
+  "fst (snd (fst ( ((Some (2::nat), (Suc 0, ())), [0::nat]) ))) = Suc 0" by eval
+
+end