src/HOL/Tools/Lifting/lifting_bnf.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Lifting/lifting_bnf.ML	Thu Apr 10 17:48:18 2014 +0200
@@ -0,0 +1,118 @@
+(*  Title:      HOL/Tools/Transfer/transfer_bnf.ML
+    Author:     Ondrej Kuncar, TU Muenchen
+
+Setup for Lifting for types that are BNF.
+*)
+
+signature LIFTING_BNF =
+sig
+end
+
+structure Lifting_BNF : LIFTING_BNF =
+struct
+
+open BNF_Util
+open BNF_Def
+open Transfer_BNF
+
+(* Quotient map theorem *)
+
+fun Quotient_tac bnf ctxt i =
+  let
+    val rel_Grp = rel_Grp_of_bnf bnf
+    fun get_lhs thm = thm |> concl_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> fst
+    val vars = get_lhs rel_Grp |> strip_comb |> snd |> map_filter (try (strip_comb #> snd #> hd))
+    val UNIVs = map (fn var => HOLogic.mk_UNIV (var |> dest_Var |> snd |> dest_Type |> snd |> hd)) vars
+    val inst = map2 (curry(pairself (certify ctxt))) vars UNIVs
+    val rel_Grp_UNIV_sym = rel_Grp |> Drule.instantiate_normalize ([], inst) 
+      |> Local_Defs.unfold ctxt @{thms subset_UNIV[THEN eqTrueI] UNIV_def[symmetric] simp_thms(21)}
+      |> (fn thm => thm RS sym)
+    val rel_mono = rel_mono_of_bnf bnf
+    val rel_conversep_sym = rel_conversep_of_bnf bnf RS sym
+  in
+    EVERY' [SELECT_GOAL (Local_Defs.unfold_tac ctxt [@{thm Quotient_alt_def5}]), 
+      REPEAT_DETERM o (etac conjE), rtac conjI, SELECT_GOAL (Local_Defs.unfold_tac ctxt [rel_Grp_UNIV_sym]),
+      rtac rel_mono THEN_ALL_NEW atac, rtac conjI, SELECT_GOAL (Local_Defs.unfold_tac ctxt
+        [rel_conversep_sym, rel_Grp_UNIV_sym]), rtac rel_mono THEN_ALL_NEW atac,
+      SELECT_GOAL (Local_Defs.unfold_tac ctxt [rel_conversep_sym, rel_OO_of_bnf bnf RS sym]),
+      hyp_subst_tac ctxt, rtac refl] i
+  end
+
+fun mk_Quotient args =
+  let
+    val argTs = map fastype_of args
+  in
+    list_comb (Const (@{const_name Quotient}, argTs ---> HOLogic.boolT), args)
+  end
+
+fun prove_Quotient_map bnf ctxt =
+  let
+    val live = live_of_bnf bnf
+    val old_ctxt = ctxt
+    val (((As, Bs), Ds), ctxt) = ctxt
+      |> mk_TFrees live
+      ||>> mk_TFrees live
+      ||>> mk_TFrees (dead_of_bnf bnf)
+    val argTss = map2 (fn a => fn b => [mk_pred2T a a, a --> b, b --> a,mk_pred2T a b]) As Bs
+    val ((argss, argss'), ctxt) = fold_map2 mk_Frees ["R", "Abs", "Rep", "T"] (transpose argTss) ctxt
+      |>> `transpose
+   
+    val assms = map (mk_Quotient #> HOLogic.mk_Trueprop) argss
+    val R_rel = list_comb (mk_rel_of_bnf Ds As As bnf, nth argss' 0)
+    val Abs_map = list_comb (mk_map_of_bnf Ds As Bs bnf, nth argss' 1)
+    val Rep_map = list_comb (mk_map_of_bnf Ds Bs As bnf, nth argss' 2)
+    val T_rel = list_comb (mk_rel_of_bnf Ds As Bs bnf, nth argss' 3)
+    val concl = mk_Quotient [R_rel, Abs_map, Rep_map, T_rel] |> HOLogic.mk_Trueprop
+    val goal = Logic.list_implies (assms, concl)
+    val thm = Goal.prove ctxt [] [] goal 
+      (fn {context = ctxt, prems = _} => Quotient_tac bnf ctxt 1)
+  in
+    Drule.zero_var_indexes (singleton (Variable.export ctxt old_ctxt) thm)
+  end
+
+
+fun Quotient_map bnf ctxt =
+  let
+    val Quotient = prove_Quotient_map bnf ctxt
+    fun qualify defname suffix = Binding.qualified true suffix defname
+    val Quotient_thm_name = qualify (base_name_of_bnf bnf) "Quotient"
+    val notes = [((Quotient_thm_name, []), [([Quotient], @{attributes [quot_map]})])]
+  in
+    notes
+  end
+
+(* relator_eq_onp  *)
+
+fun relator_eq_onp bnf ctxt =
+  let
+    val pred_data = lookup_defined_pred_data ctxt (type_name_of_bnf bnf)
+  in
+    [((Binding.empty, []), [([Transfer.rel_eq_onp pred_data], @{attributes [relator_eq_onp]})])]    
+  end
+
+(* relator_mono  *)
+
+fun relator_mono bnf =
+  [((Binding.empty, []), [([rel_mono_of_bnf bnf], @{attributes [relator_mono]})])]    
+  
+(* relator_distr  *)
+
+fun relator_distr bnf =
+  [((Binding.empty, []), [([rel_OO_of_bnf bnf RS sym], @{attributes [relator_distr]})])]
+
+(* interpretation *)
+
+fun lifting_bnf_interpretation bnf lthy =
+  if dead_of_bnf bnf > 0 then lthy
+  else
+    let
+      val notes = relator_eq_onp bnf lthy @ Quotient_map bnf lthy @ relator_mono bnf
+        @ relator_distr bnf
+    in
+      snd (Local_Theory.notes notes lthy)
+    end
+
+val _ = Context.>> (Context.map_theory (bnf_interpretation
+  (bnf_only_type_ctr (fn bnf => map_local_theory (lifting_bnf_interpretation bnf)))))
+
+end