--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/nominal_thmdecls.ML	Sun Nov 14 16:34:47 2010 +0000
@@ -0,0 +1,237 @@
+(*  Title:      nominal_thmdecls.ML
+    Author:     Christian Urban
+
+  Infrastructure for the lemma collection "eqvts".
+
+  Provides the attributes [eqvt] and [eqvt_raw], and the theorem
+  lists eqvts and eqvts_raw. The first attribute will store the 
+  theorem in the eqvts list and also in the eqvts_raw list. For 
+  the latter the theorem is expected to be of the form
+
+    p o (c x1 x2 ...) = c (p o x1) (p o x2) ...    (1)
+
+  or
+
+    c x1 x2 ... ==> c (p o x1) (p o x2) ...        (2)
+
+  and it is stored in the form
+
+    p o c == c
+
+  The [eqvt_raw] attribute just adds the theorem to eqvts_raw.
+
+  TODO: In case of the form in (2) one should also
+        add the equational form to eqvts
+*)
+
+signature NOMINAL_THMDECLS =
+sig
+  val eqvt_add: attribute
+  val eqvt_del: attribute
+  val eqvt_raw_add: attribute
+  val eqvt_raw_del: attribute
+  val setup: theory -> theory
+  val get_eqvts_thms: Proof.context -> thm list
+  val get_eqvts_raw_thms: Proof.context -> thm list
+  val eqvt_transform: Proof.context -> thm -> thm
+  val is_eqvt: Proof.context -> term -> bool
+end;
+
+structure Nominal_ThmDecls: NOMINAL_THMDECLS =
+struct
+
+structure EqvtData = Generic_Data
+( type T = thm Item_Net.T;
+  val empty = Thm.full_rules;
+  val extend = I;
+  val merge = Item_Net.merge);
+
+structure EqvtRawData = Generic_Data
+( type T = thm Termtab.table;
+  val empty = Termtab.empty;
+  val extend = I;
+  val merge = Termtab.merge (K true));
+
+val eqvts = Item_Net.content o EqvtData.get;
+val eqvts_raw = map snd o Termtab.dest o EqvtRawData.get;
+
+val get_eqvts_thms = eqvts o  Context.Proof;
+val get_eqvts_raw_thms = eqvts_raw o Context.Proof;
+
+val add_thm = EqvtData.map o Item_Net.update;
+val del_thm = EqvtData.map o Item_Net.remove;
+
+fun add_raw_thm thm = 
+  case prop_of thm of
+    Const ("==", _) $ _ $ (c as Const _) => EqvtRawData.map (Termtab.update (c, thm)) 
+  | _ => raise THM ("Theorem must be a meta-equality where the right-hand side is a constant.", 0, [thm]) 
+
+fun del_raw_thm thm = 
+  case prop_of thm of
+    Const ("==", _) $ _ $ (c as Const _) => EqvtRawData.map (Termtab.delete c)
+  | _ => raise THM ("Theorem must be a meta-equality where the right-hand side is a constant.", 0, [thm]) 
+
+fun is_eqvt ctxt trm =
+  case trm of 
+    (c as Const _) => Termtab.defined (EqvtRawData.get (Context.Proof ctxt)) c
+  | _ => raise TERM ("Term must be a constsnt.", [trm])
+
+
+
+(** transformation of eqvt lemmas **)
+
+fun get_perms trm =
+  case trm of 
+     Const (@{const_name permute}, _) $ _ $ (Bound _) => 
+       raise TERM ("get_perms called on bound", [trm])
+   | Const (@{const_name permute}, _) $ p $ _ => [p]
+   | t $ u => get_perms t @ get_perms u
+   | Abs (_, _, t) => get_perms t 
+   | _ => []
+
+fun put_perm p trm =
+  case trm of 
+     Bound _ => trm
+   | Const _ => trm
+   | t $ u => put_perm p t $ put_perm p u
+   | Abs (x, ty, t) => Abs (x, ty, put_perm p t)
+   | _ => mk_perm p trm
+
+(* tests whether there is a disagreement between the permutations, 
+   and that there is at least one permutation *)
+fun is_bad_list [] = true
+  | is_bad_list [_] = false
+  | is_bad_list (p::q::ps) = if p = q then is_bad_list (q::ps) else true
+
+
+(* transforms equations into the "p o c == c"-form 
+   from p o (c x1 ...xn) = c (p o x1) ... (p o xn) *)
+
+fun eqvt_transform_eq_tac thm = 
+let
+  val ss_thms = @{thms permute_minus_cancel permute_prod.simps split_paired_all}
+in
+  REPEAT o FIRST' 
+    [CHANGED o simp_tac (HOL_basic_ss addsimps ss_thms),
+     rtac (thm RS @{thm trans}),
+     rtac @{thm trans[OF permute_fun_def]} THEN' rtac @{thm ext}]
+end
+
+fun eqvt_transform_eq ctxt thm = 
+  let
+    val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))
+      handle TERM _ => error "Equivariance lemma must be an equality."
+    val (p, t) = dest_perm lhs 
+      handle TERM _ => error "Equivariance lemma is not of the form p \<bullet> c...  = c..."
+
+    val ps = get_perms rhs handle TERM _ => []  
+    val (c, c') = (head_of t, head_of rhs)
+    val msg = "Equivariance lemma is not of the right form "
+  in
+    if c <> c' 
+      then error (msg ^ "(constants do not agree).")
+    else if is_bad_list (p :: ps)  
+      then error (msg ^ "(permutations do not agree).") 
+    else if not (rhs aconv (put_perm p t))
+      then error (msg ^ "(arguments do not agree).")
+    else if is_Const t 
+      then safe_mk_equiv thm
+    else 
+      let 
+        val goal = HOLogic.mk_Trueprop (HOLogic.mk_eq (mk_perm p c, c))
+        val ([goal', p'], ctxt') = Variable.import_terms false [goal, p] ctxt
+      in
+        Goal.prove ctxt [] [] goal' (fn _ => eqvt_transform_eq_tac thm 1)
+        |> singleton (ProofContext.export ctxt' ctxt)
+        |> safe_mk_equiv
+        |> zero_var_indexes
+      end
+  end
+
+(* transforms equations into the "p o c == c"-form 
+   from R x1 ...xn ==> R (p o x1) ... (p o xn) *)
+
+fun eqvt_transform_imp_tac ctxt p p' thm = 
+  let
+    val thy = ProofContext.theory_of ctxt
+    val cp = Thm.cterm_of thy p
+    val cp' = Thm.cterm_of thy (mk_minus p')
+    val thm' = Drule.cterm_instantiate [(cp, cp')] thm
+    val simp = HOL_basic_ss addsimps @{thms permute_minus_cancel(2)}
+  in
+    EVERY' [rtac @{thm iffI}, dtac @{thm permute_boolE}, rtac thm, atac,
+      rtac @{thm permute_boolI}, dtac thm', full_simp_tac simp]
+  end
+
+fun eqvt_transform_imp ctxt thm =
+  let
+    val (prem, concl) = pairself HOLogic.dest_Trueprop (Logic.dest_implies (prop_of thm))
+    val (c, c') = (head_of prem, head_of concl)
+    val ps = get_perms concl handle TERM _ => []  
+    val p = try hd ps
+    val msg = "Equivariance lemma is not of the right form "
+  in
+    if c <> c' 
+      then error (msg ^ "(constants do not agree).")
+    else if is_bad_list ps  
+      then error (msg ^ "(permutations do not agree).") 
+    else if not (concl aconv (put_perm (the p) prem)) 
+      then error (msg ^ "(arguments do not agree).")
+    else 
+      let
+        val prem' = mk_perm (the p) prem    
+        val goal = HOLogic.mk_Trueprop (HOLogic.mk_eq (prem', concl))
+        val ([goal', p'], ctxt') = Variable.import_terms false [goal, the p] ctxt
+      in
+        Goal.prove ctxt' [] [] goal'
+          (fn _ => eqvt_transform_imp_tac ctxt' (the p) p' thm 1) 
+        |> singleton (ProofContext.export ctxt' ctxt)
+      end
+  end     
+
+fun eqvt_transform ctxt thm = 
+  case (prop_of thm) of
+    @{const "Trueprop"} $ (Const (@{const_name "HOL.eq"}, _) $ 
+      (Const (@{const_name "permute"}, _) $ _ $ _) $ _) => 
+        eqvt_transform_eq ctxt thm
+  | @{const "==>"} $ (@{const "Trueprop"} $ _) $ (@{const "Trueprop"} $ _) => 
+      eqvt_transform_imp ctxt thm |> eqvt_transform_eq ctxt
+  | _ => raise error "Only _ = _ and _ ==> _ cases are implemented."
+ 
+
+(** attributes **)
+
+val eqvt_add = Thm.declaration_attribute 
+  (fn thm => fn context =>
+   let
+     val thm' = eqvt_transform (Context.proof_of context) thm
+   in
+     context |> add_thm thm |> add_raw_thm thm'
+   end)
+
+val eqvt_del = Thm.declaration_attribute
+  (fn thm => fn context =>
+   let
+     val thm' = eqvt_transform (Context.proof_of context) thm
+   in
+     context |> del_thm thm  |> del_raw_thm thm'
+   end)
+
+val eqvt_raw_add = Thm.declaration_attribute add_raw_thm;
+val eqvt_raw_del = Thm.declaration_attribute del_raw_thm;
+
+
+(** setup function **)
+
+val setup =
+  Attrib.setup @{binding "eqvt"} (Attrib.add_del eqvt_add eqvt_del) 
+    (cat_lines ["Declaration of equivariance lemmas - they will automtically be",  
+       "brought into the form p o c == c"]) #>
+  Attrib.setup @{binding "eqvt_raw"} (Attrib.add_del eqvt_raw_add eqvt_raw_del) 
+    (cat_lines ["Declaration of equivariance lemmas - no",
+       "transformation is performed"]) #>
+  Global_Theory.add_thms_dynamic (@{binding "eqvts"}, eqvts) #>
+  Global_Theory.add_thms_dynamic (@{binding "eqvts_raw"}, eqvts_raw);
+
+
+end;