diff -r f3cbda066c3a -r 35be65791f1d quotient.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/quotient.ML	Thu Oct 08 14:27:50 2009 +0200
@@ -0,0 +1,167 @@
+
+
+
+structure Quotient =
+struct
+
+(* constructs the term lambda (c::rty => bool). EX x. c= rel x *)
+fun typedef_term rel rty lthy =
+let
+  val [x, c] = [("x", rty), ("c", rty --> @{typ bool})]
+               |> Variable.variant_frees lthy [rel]
+               |> map Free
+in
+  lambda c
+    (HOLogic.exists_const rty $
+       lambda x (HOLogic.mk_eq (c, (rel $ x))))
+end
+
+(* makes the new type definitions and proves non-emptyness*)
+fun typedef_make (qty_name, mx, rel, rty) lthy =
+let
+  val typedef_tac =
+     EVERY1 [rewrite_goal_tac @{thms mem_def},
+             rtac @{thm exI},
+             rtac @{thm exI},
+             rtac @{thm refl}]
+  val tfrees = map fst (Term.add_tfreesT rty [])
+in
+  LocalTheory.theory_result
+    (Typedef.add_typedef false NONE
+       (qty_name, tfrees, mx)
+         (typedef_term rel rty lthy)
+           NONE typedef_tac) lthy
+end
+
+(* tactic to prove the QUOT_TYPE theorem for the new type *)
+fun typedef_quot_type_tac equiv_thm (typedef_info: Typedef.info) =
+let
+  val unfold_mem = MetaSimplifier.rewrite_rule @{thms mem_def}
+  val rep_thm = #Rep typedef_info |> unfold_mem
+  val rep_inv = #Rep_inverse typedef_info
+  val abs_inv = #Abs_inverse typedef_info |> unfold_mem
+  val rep_inj = #Rep_inject typedef_info
+in
+  EVERY1 [rtac @{thm QUOT_TYPE.intro},
+          rtac equiv_thm,
+          rtac rep_thm,
+          rtac rep_inv,
+          rtac abs_inv,
+          rtac @{thm exI}, 
+          rtac @{thm refl},
+          rtac rep_inj]
+end
+
+(* proves the QUOT_TYPE theorem *)
+fun typedef_quot_type_thm (rel, abs, rep, equiv_thm, typedef_info) lthy =
+let
+  val quot_type_const = Const (@{const_name "QUOT_TYPE"}, dummyT)
+  val goal = HOLogic.mk_Trueprop (quot_type_const $ rel $ abs $ rep)
+             |> Syntax.check_term lthy
+in
+  Goal.prove lthy [] [] goal
+    (K (typedef_quot_type_tac equiv_thm typedef_info))
+end
+
+(* proves the quotient theorem *)
+fun typedef_quotient_thm (rel, abs, rep, abs_def, rep_def, quot_type_thm) lthy =
+let
+  val quotient_const = Const (@{const_name "QUOTIENT"}, dummyT)
+  val goal = HOLogic.mk_Trueprop (quotient_const $ rel $ abs $ rep)
+             |> Syntax.check_term lthy
+
+  val typedef_quotient_thm_tac =
+    EVERY1 [K (rewrite_goals_tac [abs_def, rep_def]),
+            rtac @{thm QUOT_TYPE.QUOTIENT},
+            rtac quot_type_thm]
+in
+  Goal.prove lthy [] [] goal
+    (K typedef_quotient_thm_tac)
+end
+
+(* two wrappers for define and note *)
+fun make_def (name, mx, rhs) lthy =
+let
+  val ((rhs, (_ , thm)), lthy') =
+     LocalTheory.define Thm.internalK ((name, mx), (Attrib.empty_binding, rhs)) lthy
+in
+  ((rhs, thm), lthy')
+end
+
+fun note_thm (name, thm) lthy =
+let
+  val ((_,[thm']), lthy') = LocalTheory.note Thm.theoremK ((name, []), [thm]) lthy
+in
+  (thm', lthy')
+end
+
+(* main function for constructing the quotient type *)
+fun typedef_main (qty_name, mx, rel, rty, equiv_thm) lthy =
+let
+  (* generates typedef *)
+  val ((_, typedef_info), lthy1) = typedef_make (qty_name, mx, rel, rty) lthy
+
+  (* abs and rep functions *)
+  val abs_ty = #abs_type typedef_info
+  val rep_ty = #rep_type typedef_info
+  val abs_name = #Abs_name typedef_info
+  val rep_name = #Rep_name typedef_info
+  val abs = Const (abs_name, rep_ty --> abs_ty)
+  val rep = Const (rep_name, abs_ty --> rep_ty)
+
+  (* ABS and REP definitions *)
+  val ABS_const = Const (@{const_name "QUOT_TYPE.ABS"}, dummyT )
+  val REP_const = Const (@{const_name "QUOT_TYPE.REP"}, dummyT )
+  val ABS_trm = Syntax.check_term lthy1 (ABS_const $ rel $ abs)
+  val REP_trm = Syntax.check_term lthy1 (REP_const $ rep)
+  val ABS_name = Binding.prefix_name "ABS_" qty_name
+  val REP_name = Binding.prefix_name "REP_" qty_name
+  val (((ABS, ABS_def), (REP, REP_def)), lthy2) =
+         lthy1 |> make_def (ABS_name, NoSyn, ABS_trm)
+               ||>> make_def (REP_name, NoSyn, REP_trm)
+
+  (* quot_type theorem *)
+  val quot_thm = typedef_quot_type_thm (rel, abs, rep, equiv_thm, typedef_info) lthy2
+  val quot_thm_name = Binding.prefix_name "QUOT_TYPE_" qty_name
+
+  (* quotient theorem *)
+  val quotient_thm = typedef_quotient_thm (rel, ABS, REP, ABS_def, REP_def, quot_thm) lthy2
+  val quotient_thm_name = Binding.prefix_name "QUOTIENT_" qty_name
+
+  (* interpretation *)
+  val bindd = ((Binding.make ("", Position.none)), ([]: Attrib.src list))
+  val ((_, [eqn1pre]), lthy3) = Variable.import true [ABS_def] lthy2;
+  val eqn1i = Thm.prop_of (symmetric eqn1pre)
+  val ((_, [eqn2pre]), lthy4) = Variable.import true [REP_def] lthy3;
+  val eqn2i = Thm.prop_of (symmetric eqn2pre)
+
+  val exp_morphism = ProofContext.export_morphism lthy4 (ProofContext.init (ProofContext.theory_of lthy4));
+  val exp_term = Morphism.term exp_morphism;
+  val exp = Morphism.thm exp_morphism;
+
+  val mthd = Method.SIMPLE_METHOD ((rtac quot_thm 1) THEN
+    ALLGOALS (simp_tac (HOL_basic_ss addsimps [(symmetric (exp ABS_def)), (symmetric (exp REP_def))])))
+  val mthdt = Method.Basic (fn _ => mthd)
+  val bymt = Proof.global_terminal_proof (mthdt, NONE)
+  val exp_i = [(@{const_name QUOT_TYPE}, ((("QUOT_TYPE_I_" ^ (Binding.name_of qty_name)), true),
+    Expression.Named [
+     ("R", rel),
+     ("Abs", abs),
+     ("Rep", rep)
+    ]))]
+in
+  lthy4
+  |> note_thm (quot_thm_name, quot_thm)
+  ||>> note_thm (quotient_thm_name, quotient_thm)
+  ||> LocalTheory.theory (fn thy =>
+      let
+        val global_eqns = map exp_term [eqn2i, eqn1i];
+        (* Not sure if the following context should not be used *)
+        val (global_eqns2, lthy5) = Variable.import_terms true global_eqns lthy4;
+        val global_eqns3 = map (fn t => (bindd, t)) global_eqns2;
+      in ProofContext.theory_of (bymt (Expression.interpretation (exp_i, []) global_eqns3 thy)) end)
+end
+
+end;
+
+open Quotient
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