# HG changeset patch
# User berghofe
# Date 1229184789 -3600
# Node ID 66fe138979f4977e86df43f65e14caa56e8818a8
# Parent  1b8e021e8c1f324038666d4dd2ab4cea2563aafd# Parent  933145f5a9ba960c869ad9b77490dd996c165dfc
merged

diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/CK_Machine.thy
--- a/src/HOL/Nominal/Examples/CK_Machine.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/CK_Machine.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 theory CK_Machine 
   imports "../Nominal" 
 begin
@@ -41,21 +39,21 @@
 
 section {* Capture-Avoiding Substitution *}
 
-consts subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [100,100,100] 100)
-
 nominal_primrec
+  subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [100,100,100] 100)
+where
   "(VAR x)[y::=s] = (if x=y then s else (VAR x))"
-  "(APP t\<^isub>1 t\<^isub>2)[y::=s] = APP (t\<^isub>1[y::=s]) (t\<^isub>2[y::=s])"
-  "x\<sharp>(y,s) \<Longrightarrow> (LAM [x].t)[y::=s] = LAM [x].(t[y::=s])"
-  "(NUM n)[y::=s] = NUM n"
-  "(t\<^isub>1 -- t\<^isub>2)[y::=s] = (t\<^isub>1[y::=s]) -- (t\<^isub>2[y::=s])"
-  "(t\<^isub>1 ++ t\<^isub>2)[y::=s] = (t\<^isub>1[y::=s]) ++ (t\<^isub>2[y::=s])"
-  "x\<sharp>(y,s) \<Longrightarrow> (FIX [x].t)[y::=s] = FIX [x].(t[y::=s])"
-  "TRUE[y::=s] = TRUE"
-  "FALSE[y::=s] = FALSE"
-  "(IF t1 t2 t3)[y::=s] = IF (t1[y::=s]) (t2[y::=s]) (t3[y::=s])"
-  "(ZET t)[y::=s] = ZET (t[y::=s])"
-  "(EQI t1 t2)[y::=s] = EQI (t1[y::=s]) (t2[y::=s])"
+| "(APP t\<^isub>1 t\<^isub>2)[y::=s] = APP (t\<^isub>1[y::=s]) (t\<^isub>2[y::=s])"
+| "x\<sharp>(y,s) \<Longrightarrow> (LAM [x].t)[y::=s] = LAM [x].(t[y::=s])"
+| "(NUM n)[y::=s] = NUM n"
+| "(t\<^isub>1 -- t\<^isub>2)[y::=s] = (t\<^isub>1[y::=s]) -- (t\<^isub>2[y::=s])"
+| "(t\<^isub>1 ++ t\<^isub>2)[y::=s] = (t\<^isub>1[y::=s]) ++ (t\<^isub>2[y::=s])"
+| "x\<sharp>(y,s) \<Longrightarrow> (FIX [x].t)[y::=s] = FIX [x].(t[y::=s])"
+| "TRUE[y::=s] = TRUE"
+| "FALSE[y::=s] = FALSE"
+| "(IF t1 t2 t3)[y::=s] = IF (t1[y::=s]) (t2[y::=s]) (t3[y::=s])"
+| "(ZET t)[y::=s] = ZET (t[y::=s])"
+| "(EQI t1 t2)[y::=s] = EQI (t1[y::=s]) (t2[y::=s])"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh)+
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/CR_Takahashi.thy
--- a/src/HOL/Nominal/Examples/CR_Takahashi.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/CR_Takahashi.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 (* Authors: Christian Urban and Mathilde Arnaud                   *)
 (*                                                                *)
 (* A formalisation of the Church-Rosser proof by Masako Takahashi.*)
@@ -20,12 +18,12 @@
   | App "lam" "lam"
   | Lam "\<guillemotleft>name\<guillemotright>lam" ("Lam [_]._" [100,100] 100)
 
-consts subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [100,100,100] 100)
-
 nominal_primrec
+  subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [100,100,100] 100)
+where
   "(Var x)[y::=s] = (if x=y then s else (Var x))"
-  "(App t\<^isub>1 t\<^isub>2)[y::=s] = App (t\<^isub>1[y::=s]) (t\<^isub>2[y::=s])"
-  "x\<sharp>(y,s) \<Longrightarrow> (Lam [x].t)[y::=s] = Lam [x].(t[y::=s])"
+| "(App t\<^isub>1 t\<^isub>2)[y::=s] = App (t\<^isub>1[y::=s]) (t\<^isub>2[y::=s])"
+| "x\<sharp>(y,s) \<Longrightarrow> (Lam [x].t)[y::=s] = Lam [x].(t[y::=s])"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh)
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Class.thy
--- a/src/HOL/Nominal/Examples/Class.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Class.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 theory Class
 imports "../Nominal" 
 begin
@@ -17,16 +15,22 @@
   | OR   "ty" "ty"   ("_ OR _" [100,100] 100)
   | IMP  "ty" "ty"   ("_ IMP _" [100,100] 100)
 
-instance ty :: size ..
-
-nominal_primrec
+instantiation ty :: size
+begin
+
+nominal_primrec size_ty
+where
   "size (PR s)     = (1::nat)"
-  "size (NOT T)     = 1 + size T"
-  "size (T1 AND T2) = 1 + size T1 + size T2"
-  "size (T1 OR T2)  = 1 + size T1 + size T2"
-  "size (T1 IMP T2) = 1 + size T1 + size T2"
+| "size (NOT T)     = 1 + size T"
+| "size (T1 AND T2) = 1 + size T1 + size T2"
+| "size (T1 OR T2)  = 1 + size T1 + size T2"
+| "size (T1 IMP T2) = 1 + size T1 + size T2"
 by (rule TrueI)+
 
+instance ..
+
+end
+
 lemma ty_cases:
   fixes T::ty
   shows "(\<exists>s. T=PR s) \<or> (\<exists>T'. T=NOT T') \<or> (\<exists>S U. T=S OR U) \<or> (\<exists>S U. T=S AND U) \<or> (\<exists>S U. T=S IMP U)"
@@ -66,25 +70,23 @@
 
 text {* renaming functions *}
 
-consts
-  nrename :: "trm \<Rightarrow> name \<Rightarrow> name \<Rightarrow> trm"      ("_[_\<turnstile>n>_]" [100,100,100] 100) 
+nominal_primrec (freshness_context: "(d::coname,e::coname)") 
   crename :: "trm \<Rightarrow> coname \<Rightarrow> coname \<Rightarrow> trm"  ("_[_\<turnstile>c>_]" [100,100,100] 100) 
-
-nominal_primrec (freshness_context: "(d::coname,e::coname)") 
+where
   "(Ax x a)[d\<turnstile>c>e] = (if a=d then Ax x e else Ax x a)" 
-  "\<lbrakk>a\<sharp>(d,e,N);x\<sharp>M\<rbrakk> \<Longrightarrow> (Cut <a>.M (x).N)[d\<turnstile>c>e] = Cut <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e])" 
-  "(NotR (x).M a)[d\<turnstile>c>e] = (if a=d then NotR (x).(M[d\<turnstile>c>e]) e else NotR (x).(M[d\<turnstile>c>e]) a)" 
-  "a\<sharp>(d,e) \<Longrightarrow> (NotL <a>.M x)[d\<turnstile>c>e] = (NotL <a>.(M[d\<turnstile>c>e]) x)" 
-  "\<lbrakk>a\<sharp>(d,e,N,c);b\<sharp>(d,e,M,c);b\<noteq>a\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c)[d\<turnstile>c>e] = 
+| "\<lbrakk>a\<sharp>(d,e,N);x\<sharp>M\<rbrakk> \<Longrightarrow> (Cut <a>.M (x).N)[d\<turnstile>c>e] = Cut <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e])" 
+| "(NotR (x).M a)[d\<turnstile>c>e] = (if a=d then NotR (x).(M[d\<turnstile>c>e]) e else NotR (x).(M[d\<turnstile>c>e]) a)" 
+| "a\<sharp>(d,e) \<Longrightarrow> (NotL <a>.M x)[d\<turnstile>c>e] = (NotL <a>.(M[d\<turnstile>c>e]) x)" 
+| "\<lbrakk>a\<sharp>(d,e,N,c);b\<sharp>(d,e,M,c);b\<noteq>a\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c)[d\<turnstile>c>e] = 
           (if c=d then AndR <a>.(M[d\<turnstile>c>e]) <b>.(N[d \<turnstile>c>e]) e else AndR <a>.(M[d\<turnstile>c>e]) <b>.(N[d\<turnstile>c>e]) c)" 
-  "x\<sharp>y \<Longrightarrow> (AndL1 (x).M y)[d\<turnstile>c>e] = AndL1 (x).(M[d\<turnstile>c>e]) y"
-  "x\<sharp>y \<Longrightarrow> (AndL2 (x).M y)[d\<turnstile>c>e] = AndL2 (x).(M[d\<turnstile>c>e]) y"
-  "a\<sharp>(d,e,b) \<Longrightarrow> (OrR1 <a>.M b)[d\<turnstile>c>e] = (if b=d then OrR1 <a>.(M[d\<turnstile>c>e]) e else OrR1 <a>.(M[d\<turnstile>c>e]) b)"
-  "a\<sharp>(d,e,b) \<Longrightarrow> (OrR2 <a>.M b)[d\<turnstile>c>e] = (if b=d then OrR2 <a>.(M[d\<turnstile>c>e]) e else OrR2 <a>.(M[d\<turnstile>c>e]) b)"
-  "\<lbrakk>x\<sharp>(N,z);y\<sharp>(M,z);y\<noteq>x\<rbrakk> \<Longrightarrow> (OrL (x).M (y).N z)[d\<turnstile>c>e] = OrL (x).(M[d\<turnstile>c>e]) (y).(N[d\<turnstile>c>e]) z"
-  "a\<sharp>(d,e,b) \<Longrightarrow> (ImpR (x).<a>.M b)[d\<turnstile>c>e] = 
+| "x\<sharp>y \<Longrightarrow> (AndL1 (x).M y)[d\<turnstile>c>e] = AndL1 (x).(M[d\<turnstile>c>e]) y"
+| "x\<sharp>y \<Longrightarrow> (AndL2 (x).M y)[d\<turnstile>c>e] = AndL2 (x).(M[d\<turnstile>c>e]) y"
+| "a\<sharp>(d,e,b) \<Longrightarrow> (OrR1 <a>.M b)[d\<turnstile>c>e] = (if b=d then OrR1 <a>.(M[d\<turnstile>c>e]) e else OrR1 <a>.(M[d\<turnstile>c>e]) b)"
+| "a\<sharp>(d,e,b) \<Longrightarrow> (OrR2 <a>.M b)[d\<turnstile>c>e] = (if b=d then OrR2 <a>.(M[d\<turnstile>c>e]) e else OrR2 <a>.(M[d\<turnstile>c>e]) b)"
+| "\<lbrakk>x\<sharp>(N,z);y\<sharp>(M,z);y\<noteq>x\<rbrakk> \<Longrightarrow> (OrL (x).M (y).N z)[d\<turnstile>c>e] = OrL (x).(M[d\<turnstile>c>e]) (y).(N[d\<turnstile>c>e]) z"
+| "a\<sharp>(d,e,b) \<Longrightarrow> (ImpR (x).<a>.M b)[d\<turnstile>c>e] = 
        (if b=d then ImpR (x).<a>.(M[d\<turnstile>c>e]) e else ImpR (x).<a>.(M[d\<turnstile>c>e]) b)"
-  "\<lbrakk>a\<sharp>(d,e,N);x\<sharp>(M,y)\<rbrakk> \<Longrightarrow> (ImpL <a>.M (x).N y)[d\<turnstile>c>e] = ImpL <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e]) y"
+| "\<lbrakk>a\<sharp>(d,e,N);x\<sharp>(M,y)\<rbrakk> \<Longrightarrow> (ImpL <a>.M (x).N y)[d\<turnstile>c>e] = ImpL <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e]) y"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh abs_supp fin_supp)+
@@ -92,19 +94,21 @@
 done
 
 nominal_primrec (freshness_context: "(u::name,v::name)") 
+  nrename :: "trm \<Rightarrow> name \<Rightarrow> name \<Rightarrow> trm"      ("_[_\<turnstile>n>_]" [100,100,100] 100) 
+where
   "(Ax x a)[u\<turnstile>n>v] = (if x=u then Ax v a else Ax x a)" 
-  "\<lbrakk>a\<sharp>N;x\<sharp>(u,v,M)\<rbrakk> \<Longrightarrow> (Cut <a>.M (x).N)[u\<turnstile>n>v] = Cut <a>.(M[u\<turnstile>n>v]) (x).(N[u\<turnstile>n>v])" 
-  "x\<sharp>(u,v) \<Longrightarrow> (NotR (x).M a)[u\<turnstile>n>v] = NotR (x).(M[u\<turnstile>n>v]) a" 
-  "(NotL <a>.M x)[u\<turnstile>n>v] = (if x=u then NotL <a>.(M[u\<turnstile>n>v]) v else NotL <a>.(M[u\<turnstile>n>v]) x)" 
-  "\<lbrakk>a\<sharp>(N,c);b\<sharp>(M,c);b\<noteq>a\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c)[u\<turnstile>n>v] = AndR <a>.(M[u\<turnstile>n>v]) <b>.(N[u\<turnstile>n>v]) c" 
-  "x\<sharp>(u,v,y) \<Longrightarrow> (AndL1 (x).M y)[u\<turnstile>n>v] = (if y=u then AndL1 (x).(M[u\<turnstile>n>v]) v else AndL1 (x).(M[u\<turnstile>n>v]) y)"
-  "x\<sharp>(u,v,y) \<Longrightarrow> (AndL2 (x).M y)[u\<turnstile>n>v] = (if y=u then AndL2 (x).(M[u\<turnstile>n>v]) v else AndL2 (x).(M[u\<turnstile>n>v]) y)"
-  "a\<sharp>b \<Longrightarrow> (OrR1 <a>.M b)[u\<turnstile>n>v] = OrR1 <a>.(M[u\<turnstile>n>v]) b"
-  "a\<sharp>b \<Longrightarrow> (OrR2 <a>.M b)[u\<turnstile>n>v] = OrR2 <a>.(M[u\<turnstile>n>v]) b"
-  "\<lbrakk>x\<sharp>(u,v,N,z);y\<sharp>(u,v,M,z);y\<noteq>x\<rbrakk> \<Longrightarrow> (OrL (x).M (y).N z)[u\<turnstile>n>v] = 
+| "\<lbrakk>a\<sharp>N;x\<sharp>(u,v,M)\<rbrakk> \<Longrightarrow> (Cut <a>.M (x).N)[u\<turnstile>n>v] = Cut <a>.(M[u\<turnstile>n>v]) (x).(N[u\<turnstile>n>v])" 
+| "x\<sharp>(u,v) \<Longrightarrow> (NotR (x).M a)[u\<turnstile>n>v] = NotR (x).(M[u\<turnstile>n>v]) a" 
+| "(NotL <a>.M x)[u\<turnstile>n>v] = (if x=u then NotL <a>.(M[u\<turnstile>n>v]) v else NotL <a>.(M[u\<turnstile>n>v]) x)" 
+| "\<lbrakk>a\<sharp>(N,c);b\<sharp>(M,c);b\<noteq>a\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c)[u\<turnstile>n>v] = AndR <a>.(M[u\<turnstile>n>v]) <b>.(N[u\<turnstile>n>v]) c" 
+| "x\<sharp>(u,v,y) \<Longrightarrow> (AndL1 (x).M y)[u\<turnstile>n>v] = (if y=u then AndL1 (x).(M[u\<turnstile>n>v]) v else AndL1 (x).(M[u\<turnstile>n>v]) y)"
+| "x\<sharp>(u,v,y) \<Longrightarrow> (AndL2 (x).M y)[u\<turnstile>n>v] = (if y=u then AndL2 (x).(M[u\<turnstile>n>v]) v else AndL2 (x).(M[u\<turnstile>n>v]) y)"
+| "a\<sharp>b \<Longrightarrow> (OrR1 <a>.M b)[u\<turnstile>n>v] = OrR1 <a>.(M[u\<turnstile>n>v]) b"
+| "a\<sharp>b \<Longrightarrow> (OrR2 <a>.M b)[u\<turnstile>n>v] = OrR2 <a>.(M[u\<turnstile>n>v]) b"
+| "\<lbrakk>x\<sharp>(u,v,N,z);y\<sharp>(u,v,M,z);y\<noteq>x\<rbrakk> \<Longrightarrow> (OrL (x).M (y).N z)[u\<turnstile>n>v] = 
         (if z=u then OrL (x).(M[u\<turnstile>n>v]) (y).(N[u\<turnstile>n>v]) v else OrL (x).(M[u\<turnstile>n>v]) (y).(N[u\<turnstile>n>v]) z)"
-  "\<lbrakk>a\<sharp>b; x\<sharp>(u,v)\<rbrakk> \<Longrightarrow> (ImpR (x).<a>.M b)[u\<turnstile>n>v] = ImpR (x).<a>.(M[u\<turnstile>n>v]) b"
-  "\<lbrakk>a\<sharp>N;x\<sharp>(u,v,M,y)\<rbrakk> \<Longrightarrow> (ImpL <a>.M (x).N y)[u\<turnstile>n>v] = 
+| "\<lbrakk>a\<sharp>b; x\<sharp>(u,v)\<rbrakk> \<Longrightarrow> (ImpR (x).<a>.M b)[u\<turnstile>n>v] = ImpR (x).<a>.(M[u\<turnstile>n>v]) b"
+| "\<lbrakk>a\<sharp>N;x\<sharp>(u,v,M,y)\<rbrakk> \<Longrightarrow> (ImpL <a>.M (x).N y)[u\<turnstile>n>v] = 
         (if y=u then ImpL <a>.(M[u\<turnstile>n>v]) (x).(N[u\<turnstile>n>v]) v else ImpL <a>.(M[u\<turnstile>n>v]) (x).(N[u\<turnstile>n>v]) y)"
 apply(finite_guess)+
 apply(rule TrueI)+
@@ -766,32 +770,30 @@
 apply(simp add: fin_supp)
 done
 
-consts
+nominal_primrec (freshness_context: "(y::name,c::coname,P::trm)")
   substn :: "trm \<Rightarrow> name   \<Rightarrow> coname \<Rightarrow> trm \<Rightarrow> trm" ("_{_:=<_>._}" [100,100,100,100] 100) 
-  substc :: "trm \<Rightarrow> coname \<Rightarrow> name   \<Rightarrow> trm \<Rightarrow> trm" ("_{_:=(_)._}" [100,100,100,100] 100)
-
-nominal_primrec (freshness_context: "(y::name,c::coname,P::trm)")
+where
   "(Ax x a){y:=<c>.P} = (if x=y then Cut <c>.P (y).Ax y a else Ax x a)" 
-  "\<lbrakk>a\<sharp>(c,P,N);x\<sharp>(y,P,M)\<rbrakk> \<Longrightarrow> (Cut <a>.M (x).N){y:=<c>.P} = 
+| "\<lbrakk>a\<sharp>(c,P,N);x\<sharp>(y,P,M)\<rbrakk> \<Longrightarrow> (Cut <a>.M (x).N){y:=<c>.P} = 
   (if M=Ax y a then Cut <c>.P (x).(N{y:=<c>.P}) else Cut <a>.(M{y:=<c>.P}) (x).(N{y:=<c>.P}))" 
-  "x\<sharp>(y,P) \<Longrightarrow> (NotR (x).M a){y:=<c>.P} = NotR (x).(M{y:=<c>.P}) a" 
-  "a\<sharp>(c,P) \<Longrightarrow> (NotL <a>.M x){y:=<c>.P} = 
+| "x\<sharp>(y,P) \<Longrightarrow> (NotR (x).M a){y:=<c>.P} = NotR (x).(M{y:=<c>.P}) a" 
+| "a\<sharp>(c,P) \<Longrightarrow> (NotL <a>.M x){y:=<c>.P} = 
   (if x=y then fresh_fun (\<lambda>x'. Cut <c>.P (x').NotL <a>.(M{y:=<c>.P}) x') else NotL <a>.(M{y:=<c>.P}) x)"
-  "\<lbrakk>a\<sharp>(c,P,N,d);b\<sharp>(c,P,M,d);b\<noteq>a\<rbrakk> \<Longrightarrow> 
+| "\<lbrakk>a\<sharp>(c,P,N,d);b\<sharp>(c,P,M,d);b\<noteq>a\<rbrakk> \<Longrightarrow> 
   (AndR <a>.M <b>.N d){y:=<c>.P} = AndR <a>.(M{y:=<c>.P}) <b>.(N{y:=<c>.P}) d" 
-  "x\<sharp>(y,P,z) \<Longrightarrow> (AndL1 (x).M z){y:=<c>.P} = 
+| "x\<sharp>(y,P,z) \<Longrightarrow> (AndL1 (x).M z){y:=<c>.P} = 
   (if z=y then fresh_fun (\<lambda>z'. Cut <c>.P (z').AndL1 (x).(M{y:=<c>.P}) z') 
    else AndL1 (x).(M{y:=<c>.P}) z)"
-  "x\<sharp>(y,P,z) \<Longrightarrow> (AndL2 (x).M z){y:=<c>.P} = 
+| "x\<sharp>(y,P,z) \<Longrightarrow> (AndL2 (x).M z){y:=<c>.P} = 
   (if z=y then fresh_fun (\<lambda>z'. Cut <c>.P (z').AndL2 (x).(M{y:=<c>.P}) z') 
    else AndL2 (x).(M{y:=<c>.P}) z)"
-  "a\<sharp>(c,P,b) \<Longrightarrow> (OrR1 <a>.M b){y:=<c>.P} = OrR1 <a>.(M{y:=<c>.P}) b"
-  "a\<sharp>(c,P,b) \<Longrightarrow> (OrR2 <a>.M b){y:=<c>.P} = OrR2 <a>.(M{y:=<c>.P}) b"
-  "\<lbrakk>x\<sharp>(y,N,P,z);u\<sharp>(y,M,P,z);x\<noteq>u\<rbrakk> \<Longrightarrow> (OrL (x).M (u).N z){y:=<c>.P} = 
+| "a\<sharp>(c,P,b) \<Longrightarrow> (OrR1 <a>.M b){y:=<c>.P} = OrR1 <a>.(M{y:=<c>.P}) b"
+| "a\<sharp>(c,P,b) \<Longrightarrow> (OrR2 <a>.M b){y:=<c>.P} = OrR2 <a>.(M{y:=<c>.P}) b"
+| "\<lbrakk>x\<sharp>(y,N,P,z);u\<sharp>(y,M,P,z);x\<noteq>u\<rbrakk> \<Longrightarrow> (OrL (x).M (u).N z){y:=<c>.P} = 
   (if z=y then fresh_fun (\<lambda>z'. Cut <c>.P (z').OrL (x).(M{y:=<c>.P}) (u).(N{y:=<c>.P}) z') 
    else OrL (x).(M{y:=<c>.P}) (u).(N{y:=<c>.P}) z)"
-  "\<lbrakk>a\<sharp>(b,c,P); x\<sharp>(y,P)\<rbrakk> \<Longrightarrow> (ImpR (x).<a>.M b){y:=<c>.P} = ImpR (x).<a>.(M{y:=<c>.P}) b"
-  "\<lbrakk>a\<sharp>(N,c,P);x\<sharp>(y,P,M,z)\<rbrakk> \<Longrightarrow> (ImpL <a>.M (x).N z){y:=<c>.P} = 
+| "\<lbrakk>a\<sharp>(b,c,P); x\<sharp>(y,P)\<rbrakk> \<Longrightarrow> (ImpR (x).<a>.M b){y:=<c>.P} = ImpR (x).<a>.(M{y:=<c>.P}) b"
+| "\<lbrakk>a\<sharp>(N,c,P);x\<sharp>(y,P,M,z)\<rbrakk> \<Longrightarrow> (ImpL <a>.M (x).N z){y:=<c>.P} = 
   (if y=z then fresh_fun (\<lambda>z'. Cut <c>.P (z').ImpL <a>.(M{y:=<c>.P}) (x).(N{y:=<c>.P}) z') 
    else ImpL <a>.(M{y:=<c>.P}) (x).(N{y:=<c>.P}) z)"
 apply(finite_guess)+
@@ -842,27 +844,29 @@
 done
 
 nominal_primrec (freshness_context: "(d::name,z::coname,P::trm)")
+  substc :: "trm \<Rightarrow> coname \<Rightarrow> name   \<Rightarrow> trm \<Rightarrow> trm" ("_{_:=(_)._}" [100,100,100,100] 100)
+where
   "(Ax x a){d:=(z).P} = (if d=a then Cut <a>.(Ax x a) (z).P else Ax x a)" 
-  "\<lbrakk>a\<sharp>(d,P,N);x\<sharp>(z,P,M)\<rbrakk> \<Longrightarrow> (Cut <a>.M (x).N){d:=(z).P} = 
+| "\<lbrakk>a\<sharp>(d,P,N);x\<sharp>(z,P,M)\<rbrakk> \<Longrightarrow> (Cut <a>.M (x).N){d:=(z).P} = 
   (if N=Ax x d then Cut <a>.(M{d:=(z).P}) (z).P else Cut <a>.(M{d:=(z).P}) (x).(N{d:=(z).P}))" 
-  "x\<sharp>(z,P) \<Longrightarrow> (NotR (x).M a){d:=(z).P} = 
+| "x\<sharp>(z,P) \<Longrightarrow> (NotR (x).M a){d:=(z).P} = 
   (if d=a then fresh_fun (\<lambda>a'. Cut <a'>.NotR (x).(M{d:=(z).P}) a' (z).P) else NotR (x).(M{d:=(z).P}) a)" 
-  "a\<sharp>(d,P) \<Longrightarrow> (NotL <a>.M x){d:=(z).P} = NotL <a>.(M{d:=(z).P}) x" 
-  "\<lbrakk>a\<sharp>(P,c,N,d);b\<sharp>(P,c,M,d);b\<noteq>a\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c){d:=(z).P} = 
+| "a\<sharp>(d,P) \<Longrightarrow> (NotL <a>.M x){d:=(z).P} = NotL <a>.(M{d:=(z).P}) x" 
+| "\<lbrakk>a\<sharp>(P,c,N,d);b\<sharp>(P,c,M,d);b\<noteq>a\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c){d:=(z).P} = 
   (if d=c then fresh_fun (\<lambda>a'. Cut <a'>.(AndR <a>.(M{d:=(z).P}) <b>.(N{d:=(z).P}) a') (z).P)
    else AndR <a>.(M{d:=(z).P}) <b>.(N{d:=(z).P}) c)" 
-  "x\<sharp>(y,z,P) \<Longrightarrow> (AndL1 (x).M y){d:=(z).P} = AndL1 (x).(M{d:=(z).P}) y"
-  "x\<sharp>(y,P,z) \<Longrightarrow> (AndL2 (x).M y){d:=(z).P} = AndL2 (x).(M{d:=(z).P}) y"
-  "a\<sharp>(d,P,b) \<Longrightarrow> (OrR1 <a>.M b){d:=(z).P} = 
+| "x\<sharp>(y,z,P) \<Longrightarrow> (AndL1 (x).M y){d:=(z).P} = AndL1 (x).(M{d:=(z).P}) y"
+| "x\<sharp>(y,P,z) \<Longrightarrow> (AndL2 (x).M y){d:=(z).P} = AndL2 (x).(M{d:=(z).P}) y"
+| "a\<sharp>(d,P,b) \<Longrightarrow> (OrR1 <a>.M b){d:=(z).P} = 
   (if d=b then fresh_fun (\<lambda>a'. Cut <a'>.OrR1 <a>.(M{d:=(z).P}) a' (z).P) else OrR1 <a>.(M{d:=(z).P}) b)"
-  "a\<sharp>(d,P,b) \<Longrightarrow> (OrR2 <a>.M b){d:=(z).P} = 
+| "a\<sharp>(d,P,b) \<Longrightarrow> (OrR2 <a>.M b){d:=(z).P} = 
   (if d=b then fresh_fun (\<lambda>a'. Cut <a'>.OrR2 <a>.(M{d:=(z).P}) a' (z).P) else OrR2 <a>.(M{d:=(z).P}) b)"
-  "\<lbrakk>x\<sharp>(N,z,P,u);y\<sharp>(M,z,P,u);x\<noteq>y\<rbrakk> \<Longrightarrow> (OrL (x).M (y).N u){d:=(z).P} = 
+| "\<lbrakk>x\<sharp>(N,z,P,u);y\<sharp>(M,z,P,u);x\<noteq>y\<rbrakk> \<Longrightarrow> (OrL (x).M (y).N u){d:=(z).P} = 
   OrL (x).(M{d:=(z).P}) (y).(N{d:=(z).P}) u" 
-  "\<lbrakk>a\<sharp>(b,d,P); x\<sharp>(z,P)\<rbrakk> \<Longrightarrow> (ImpR (x).<a>.M b){d:=(z).P} = 
+| "\<lbrakk>a\<sharp>(b,d,P); x\<sharp>(z,P)\<rbrakk> \<Longrightarrow> (ImpR (x).<a>.M b){d:=(z).P} = 
   (if d=b then fresh_fun (\<lambda>a'. Cut <a'>.ImpR (x).<a>.(M{d:=(z).P}) a' (z).P) 
    else ImpR (x).<a>.(M{d:=(z).P}) b)"
-  "\<lbrakk>a\<sharp>(N,d,P);x\<sharp>(y,z,P,M)\<rbrakk> \<Longrightarrow> (ImpL <a>.M (x).N y){d:=(z).P} = 
+| "\<lbrakk>a\<sharp>(N,d,P);x\<sharp>(y,z,P,M)\<rbrakk> \<Longrightarrow> (ImpL <a>.M (x).N y){d:=(z).P} = 
   ImpL <a>.(M{d:=(z).P}) (x).(N{d:=(z).P}) y"
 apply(finite_guess)+
 apply(rule TrueI)+
@@ -10305,11 +10309,10 @@
 lemma BINDINGc_decreasing:
   shows "X\<subseteq>Y \<Longrightarrow> BINDINGc B Y \<subseteq> BINDINGc B X"
 by (simp add: BINDINGc_def) (blast) 
-
-consts
-  NOTRIGHT::"ty \<Rightarrow> ntrm set \<Rightarrow> ctrm set"
   
 nominal_primrec
+  NOTRIGHT :: "ty \<Rightarrow> ntrm set \<Rightarrow> ctrm set"
+where
  "NOTRIGHT (NOT B) X = { <a>:NotR (x).M a | a x M. fic (NotR (x).M a) a \<and> (x):M \<in> X }"
 apply(rule TrueI)+
 done
@@ -10365,11 +10368,10 @@
 apply(drule pt_bij1[OF pt_coname_inst, OF at_coname_inst])
 apply(simp add: swap_simps)
 done
-
-consts
-  NOTLEFT::"ty \<Rightarrow> ctrm set \<Rightarrow> ntrm set"
   
 nominal_primrec
+  NOTLEFT :: "ty \<Rightarrow> ctrm set \<Rightarrow> ntrm set"
+where
  "NOTLEFT (NOT B) X = { (x):NotL <a>.M x | a x M. fin (NotL <a>.M x) x \<and> <a>:M \<in> X }"
 apply(rule TrueI)+
 done
@@ -10425,11 +10427,10 @@
 apply(drule pt_bij1[OF pt_coname_inst, OF at_coname_inst])
 apply(simp add: swap_simps)
 done
-
-consts
-  ANDRIGHT::"ty \<Rightarrow> ctrm set \<Rightarrow> ctrm set \<Rightarrow> ctrm set"
   
 nominal_primrec
+  ANDRIGHT :: "ty \<Rightarrow> ctrm set \<Rightarrow> ctrm set \<Rightarrow> ctrm set"
+where
  "ANDRIGHT (B AND C) X Y = 
             { <c>:AndR <a>.M <b>.N c | c a b M N. fic (AndR <a>.M <b>.N c) c \<and> <a>:M \<in> X \<and> <b>:N \<in> Y }"
 apply(rule TrueI)+
@@ -10505,10 +10506,9 @@
 apply(simp)
 done
 
-consts
-  ANDLEFT1::"ty \<Rightarrow> ntrm set \<Rightarrow> ntrm set"
-
 nominal_primrec
+  ANDLEFT1 :: "ty \<Rightarrow> ntrm set \<Rightarrow> ntrm set"
+where
  "ANDLEFT1 (B AND C) X = { (y):AndL1 (x).M y | x y M. fin (AndL1 (x).M y) y \<and> (x):M \<in> X }"
 apply(rule TrueI)+
 done
@@ -10565,10 +10565,9 @@
 apply(simp add: swap_simps)
 done
 
-consts
-  ANDLEFT2::"ty \<Rightarrow> ntrm set \<Rightarrow> ntrm set"
-
 nominal_primrec
+  ANDLEFT2 :: "ty \<Rightarrow> ntrm set \<Rightarrow> ntrm set"
+where
  "ANDLEFT2 (B AND C) X = { (y):AndL2 (x).M y | x y M. fin (AndL2 (x).M y) y \<and> (x):M \<in> X }"
 apply(rule TrueI)+
 done
@@ -10625,10 +10624,9 @@
 apply(simp add: swap_simps)
 done
 
-consts
-  ORLEFT::"ty \<Rightarrow> ntrm set \<Rightarrow> ntrm set \<Rightarrow> ntrm set"
-  
 nominal_primrec
+  ORLEFT :: "ty \<Rightarrow> ntrm set \<Rightarrow> ntrm set \<Rightarrow> ntrm set"
+where
  "ORLEFT (B OR C) X Y = 
             { (z):OrL (x).M (y).N z | x y z M N. fin (OrL (x).M (y).N z) z \<and> (x):M \<in> X \<and> (y):N \<in> Y }"
 apply(rule TrueI)+
@@ -10704,10 +10702,9 @@
 apply(simp add: swap_simps)
 done
 
-consts
-  ORRIGHT1::"ty \<Rightarrow> ctrm set \<Rightarrow> ctrm set"
-
 nominal_primrec
+  ORRIGHT1 :: "ty \<Rightarrow> ctrm set \<Rightarrow> ctrm set"
+where
  "ORRIGHT1 (B OR C) X = { <b>:OrR1 <a>.M b | a b M. fic (OrR1 <a>.M b) b \<and> <a>:M \<in> X }"
 apply(rule TrueI)+
 done
@@ -10764,10 +10761,9 @@
 apply(simp)
 done
 
-consts
-  ORRIGHT2::"ty \<Rightarrow> ctrm set \<Rightarrow> ctrm set"
-
 nominal_primrec
+  ORRIGHT2 :: "ty \<Rightarrow> ctrm set \<Rightarrow> ctrm set"
+where
  "ORRIGHT2 (B OR C) X = { <b>:OrR2 <a>.M b | a b M. fic (OrR2 <a>.M b) b \<and> <a>:M \<in> X }"
 apply(rule TrueI)+
 done
@@ -10824,10 +10820,9 @@
 apply(simp)
 done
 
-consts
-  IMPRIGHT::"ty \<Rightarrow> ntrm set \<Rightarrow> ctrm set \<Rightarrow> ntrm set \<Rightarrow> ctrm set \<Rightarrow> ctrm set"
-
 nominal_primrec
+  IMPRIGHT :: "ty \<Rightarrow> ntrm set \<Rightarrow> ctrm set \<Rightarrow> ntrm set \<Rightarrow> ctrm set \<Rightarrow> ctrm set"
+where
  "IMPRIGHT (B IMP C) X Y Z U= 
         { <b>:ImpR (x).<a>.M b | x a b M. fic (ImpR (x).<a>.M b) b 
                                         \<and> (\<forall>z P. x\<sharp>(z,P) \<and> (z):P \<in> Z \<longrightarrow> (x):(M{a:=(z).P}) \<in> X)
@@ -10954,10 +10949,9 @@
 apply(perm_simp add: nsubst_eqvt fresh_right)
 done
 
-consts
-  IMPLEFT::"ty \<Rightarrow> ctrm set \<Rightarrow> ntrm set \<Rightarrow> ntrm set"
-
 nominal_primrec
+  IMPLEFT :: "ty \<Rightarrow> ctrm set \<Rightarrow> ntrm set \<Rightarrow> ntrm set"
+where
  "IMPLEFT (B IMP C) X Y = 
         { (y):ImpL <a>.M (x).N y | x a y M N. fin (ImpL <a>.M (x).N y) y \<and> <a>:M \<in> X \<and> (x):N \<in> Y }"
 apply(rule TrueI)+
@@ -17800,23 +17794,21 @@
 apply(auto)
 done 
 
-consts
+nominal_primrec (freshness_context: "\<theta>n::(name\<times>coname\<times>trm)")
   stn :: "trm\<Rightarrow>(name\<times>coname\<times>trm) list\<Rightarrow>trm" 
-  stc :: "trm\<Rightarrow>(coname\<times>name\<times>trm) list\<Rightarrow>trm" 
-
-nominal_primrec (freshness_context: "\<theta>n::(name\<times>coname\<times>trm)")
+where
   "stn (Ax x a) \<theta>n = lookupc x a \<theta>n"
-  "\<lbrakk>a\<sharp>(N,\<theta>n);x\<sharp>(M,\<theta>n)\<rbrakk> \<Longrightarrow> stn (Cut <a>.M (x).N) \<theta>n = (Cut <a>.M (x).N)" 
-  "x\<sharp>\<theta>n \<Longrightarrow> stn (NotR (x).M a) \<theta>n = (NotR (x).M a)"
-  "a\<sharp>\<theta>n \<Longrightarrow>stn (NotL <a>.M x) \<theta>n = (NotL <a>.M x)"
-  "\<lbrakk>a\<sharp>(N,d,b,\<theta>n);b\<sharp>(M,d,a,\<theta>n)\<rbrakk> \<Longrightarrow> stn (AndR <a>.M <b>.N d) \<theta>n = (AndR <a>.M <b>.N d)"
-  "x\<sharp>(z,\<theta>n) \<Longrightarrow> stn (AndL1 (x).M z) \<theta>n = (AndL1 (x).M z)"
-  "x\<sharp>(z,\<theta>n) \<Longrightarrow> stn (AndL2 (x).M z) \<theta>n = (AndL2 (x).M z)"
-  "a\<sharp>(b,\<theta>n) \<Longrightarrow> stn (OrR1 <a>.M b) \<theta>n = (OrR1 <a>.M b)"
-  "a\<sharp>(b,\<theta>n) \<Longrightarrow> stn (OrR2 <a>.M b) \<theta>n = (OrR2 <a>.M b)"
-  "\<lbrakk>x\<sharp>(N,z,u,\<theta>n);u\<sharp>(M,z,x,\<theta>n)\<rbrakk> \<Longrightarrow> stn (OrL (x).M (u).N z) \<theta>n = (OrL (x).M (u).N z)"
-  "\<lbrakk>a\<sharp>(b,\<theta>n);x\<sharp>\<theta>n\<rbrakk> \<Longrightarrow> stn (ImpR (x).<a>.M b) \<theta>n = (ImpR (x).<a>.M b)"
-  "\<lbrakk>a\<sharp>(N,\<theta>n);x\<sharp>(M,z,\<theta>n)\<rbrakk> \<Longrightarrow> stn (ImpL <a>.M (x).N z) \<theta>n = (ImpL <a>.M (x).N z)"
+| "\<lbrakk>a\<sharp>(N,\<theta>n);x\<sharp>(M,\<theta>n)\<rbrakk> \<Longrightarrow> stn (Cut <a>.M (x).N) \<theta>n = (Cut <a>.M (x).N)" 
+| "x\<sharp>\<theta>n \<Longrightarrow> stn (NotR (x).M a) \<theta>n = (NotR (x).M a)"
+| "a\<sharp>\<theta>n \<Longrightarrow>stn (NotL <a>.M x) \<theta>n = (NotL <a>.M x)"
+| "\<lbrakk>a\<sharp>(N,d,b,\<theta>n);b\<sharp>(M,d,a,\<theta>n)\<rbrakk> \<Longrightarrow> stn (AndR <a>.M <b>.N d) \<theta>n = (AndR <a>.M <b>.N d)"
+| "x\<sharp>(z,\<theta>n) \<Longrightarrow> stn (AndL1 (x).M z) \<theta>n = (AndL1 (x).M z)"
+| "x\<sharp>(z,\<theta>n) \<Longrightarrow> stn (AndL2 (x).M z) \<theta>n = (AndL2 (x).M z)"
+| "a\<sharp>(b,\<theta>n) \<Longrightarrow> stn (OrR1 <a>.M b) \<theta>n = (OrR1 <a>.M b)"
+| "a\<sharp>(b,\<theta>n) \<Longrightarrow> stn (OrR2 <a>.M b) \<theta>n = (OrR2 <a>.M b)"
+| "\<lbrakk>x\<sharp>(N,z,u,\<theta>n);u\<sharp>(M,z,x,\<theta>n)\<rbrakk> \<Longrightarrow> stn (OrL (x).M (u).N z) \<theta>n = (OrL (x).M (u).N z)"
+| "\<lbrakk>a\<sharp>(b,\<theta>n);x\<sharp>\<theta>n\<rbrakk> \<Longrightarrow> stn (ImpR (x).<a>.M b) \<theta>n = (ImpR (x).<a>.M b)"
+| "\<lbrakk>a\<sharp>(N,\<theta>n);x\<sharp>(M,z,\<theta>n)\<rbrakk> \<Longrightarrow> stn (ImpL <a>.M (x).N z) \<theta>n = (ImpL <a>.M (x).N z)"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh abs_supp fin_supp)+
@@ -17824,18 +17816,20 @@
 done
 
 nominal_primrec (freshness_context: "\<theta>c::(coname\<times>name\<times>trm)")
+  stc :: "trm\<Rightarrow>(coname\<times>name\<times>trm) list\<Rightarrow>trm" 
+where
   "stc (Ax x a) \<theta>c = lookupd x a \<theta>c"
-  "\<lbrakk>a\<sharp>(N,\<theta>c);x\<sharp>(M,\<theta>c)\<rbrakk> \<Longrightarrow> stc (Cut <a>.M (x).N) \<theta>c = (Cut <a>.M (x).N)" 
-  "x\<sharp>\<theta>c \<Longrightarrow> stc (NotR (x).M a) \<theta>c = (NotR (x).M a)"
-  "a\<sharp>\<theta>c \<Longrightarrow> stc (NotL <a>.M x) \<theta>c = (NotL <a>.M x)"
-  "\<lbrakk>a\<sharp>(N,d,b,\<theta>c);b\<sharp>(M,d,a,\<theta>c)\<rbrakk> \<Longrightarrow> stc (AndR <a>.M <b>.N d) \<theta>c = (AndR <a>.M <b>.N d)"
-  "x\<sharp>(z,\<theta>c) \<Longrightarrow> stc (AndL1 (x).M z) \<theta>c = (AndL1 (x).M z)"
-  "x\<sharp>(z,\<theta>c) \<Longrightarrow> stc (AndL2 (x).M z) \<theta>c = (AndL2 (x).M z)"
-  "a\<sharp>(b,\<theta>c) \<Longrightarrow> stc (OrR1 <a>.M b) \<theta>c = (OrR1 <a>.M b)"
-  "a\<sharp>(b,\<theta>c) \<Longrightarrow> stc (OrR2 <a>.M b) \<theta>c = (OrR2 <a>.M b)"
-  "\<lbrakk>x\<sharp>(N,z,u,\<theta>c);u\<sharp>(M,z,x,\<theta>c)\<rbrakk> \<Longrightarrow> stc (OrL (x).M (u).N z) \<theta>c = (OrL (x).M (u).N z)"
-  "\<lbrakk>a\<sharp>(b,\<theta>c);x\<sharp>\<theta>c\<rbrakk> \<Longrightarrow> stc (ImpR (x).<a>.M b) \<theta>c = (ImpR (x).<a>.M b)"
-  "\<lbrakk>a\<sharp>(N,\<theta>c);x\<sharp>(M,z,\<theta>c)\<rbrakk> \<Longrightarrow> stc (ImpL <a>.M (x).N z) \<theta>c = (ImpL <a>.M (x).N z)"
+| "\<lbrakk>a\<sharp>(N,\<theta>c);x\<sharp>(M,\<theta>c)\<rbrakk> \<Longrightarrow> stc (Cut <a>.M (x).N) \<theta>c = (Cut <a>.M (x).N)" 
+| "x\<sharp>\<theta>c \<Longrightarrow> stc (NotR (x).M a) \<theta>c = (NotR (x).M a)"
+| "a\<sharp>\<theta>c \<Longrightarrow> stc (NotL <a>.M x) \<theta>c = (NotL <a>.M x)"
+| "\<lbrakk>a\<sharp>(N,d,b,\<theta>c);b\<sharp>(M,d,a,\<theta>c)\<rbrakk> \<Longrightarrow> stc (AndR <a>.M <b>.N d) \<theta>c = (AndR <a>.M <b>.N d)"
+| "x\<sharp>(z,\<theta>c) \<Longrightarrow> stc (AndL1 (x).M z) \<theta>c = (AndL1 (x).M z)"
+| "x\<sharp>(z,\<theta>c) \<Longrightarrow> stc (AndL2 (x).M z) \<theta>c = (AndL2 (x).M z)"
+| "a\<sharp>(b,\<theta>c) \<Longrightarrow> stc (OrR1 <a>.M b) \<theta>c = (OrR1 <a>.M b)"
+| "a\<sharp>(b,\<theta>c) \<Longrightarrow> stc (OrR2 <a>.M b) \<theta>c = (OrR2 <a>.M b)"
+| "\<lbrakk>x\<sharp>(N,z,u,\<theta>c);u\<sharp>(M,z,x,\<theta>c)\<rbrakk> \<Longrightarrow> stc (OrL (x).M (u).N z) \<theta>c = (OrL (x).M (u).N z)"
+| "\<lbrakk>a\<sharp>(b,\<theta>c);x\<sharp>\<theta>c\<rbrakk> \<Longrightarrow> stc (ImpR (x).<a>.M b) \<theta>c = (ImpR (x).<a>.M b)"
+| "\<lbrakk>a\<sharp>(N,\<theta>c);x\<sharp>(M,z,\<theta>c)\<rbrakk> \<Longrightarrow> stc (ImpL <a>.M (x).N z) \<theta>c = (ImpL <a>.M (x).N z)"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh abs_supp fin_supp)+
@@ -17926,51 +17920,50 @@
 apply(perm_simp)
 done
 
-consts
+nominal_primrec (freshness_context: "(\<theta>n::(name\<times>coname\<times>trm) list,\<theta>c::(coname\<times>name\<times>trm) list)")
   psubst :: "(name\<times>coname\<times>trm) list\<Rightarrow>(coname\<times>name\<times>trm) list\<Rightarrow>trm\<Rightarrow>trm" ("_,_<_>" [100,100,100] 100) 
-
-nominal_primrec (freshness_context: "(\<theta>n::(name\<times>coname\<times>trm) list,\<theta>c::(coname\<times>name\<times>trm) list)")
+where
   "\<theta>n,\<theta>c<Ax x a> = lookup x a \<theta>n \<theta>c" 
-  "\<lbrakk>a\<sharp>(N,\<theta>n,\<theta>c);x\<sharp>(M,\<theta>n,\<theta>c)\<rbrakk> \<Longrightarrow> \<theta>n,\<theta>c<Cut <a>.M (x).N> = 
+| "\<lbrakk>a\<sharp>(N,\<theta>n,\<theta>c);x\<sharp>(M,\<theta>n,\<theta>c)\<rbrakk> \<Longrightarrow> \<theta>n,\<theta>c<Cut <a>.M (x).N> = 
    Cut <a>.(if \<exists>x. M=Ax x a then stn M \<theta>n else \<theta>n,\<theta>c<M>) 
        (x).(if \<exists>a. N=Ax x a then stc N \<theta>c else \<theta>n,\<theta>c<N>)" 
-  "x\<sharp>(\<theta>n,\<theta>c) \<Longrightarrow> \<theta>n,\<theta>c<NotR (x).M a> = 
+| "x\<sharp>(\<theta>n,\<theta>c) \<Longrightarrow> \<theta>n,\<theta>c<NotR (x).M a> = 
   (case (findc \<theta>c a) of 
        Some (u,P) \<Rightarrow> fresh_fun (\<lambda>a'. Cut <a'>.NotR (x).(\<theta>n,\<theta>c<M>) a' (u).P) 
      | None \<Rightarrow> NotR (x).(\<theta>n,\<theta>c<M>) a)"
-  "a\<sharp>(\<theta>n,\<theta>c) \<Longrightarrow> \<theta>n,\<theta>c<NotL <a>.M x> = 
+| "a\<sharp>(\<theta>n,\<theta>c) \<Longrightarrow> \<theta>n,\<theta>c<NotL <a>.M x> = 
   (case (findn \<theta>n x) of 
        Some (c,P) \<Rightarrow> fresh_fun (\<lambda>x'. Cut <c>.P (x').(NotL <a>.(\<theta>n,\<theta>c<M>) x')) 
      | None \<Rightarrow> NotL <a>.(\<theta>n,\<theta>c<M>) x)"
-  "\<lbrakk>a\<sharp>(N,c,\<theta>n,\<theta>c);b\<sharp>(M,c,\<theta>n,\<theta>c);b\<noteq>a\<rbrakk> \<Longrightarrow> (\<theta>n,\<theta>c<AndR <a>.M <b>.N c>) = 
+| "\<lbrakk>a\<sharp>(N,c,\<theta>n,\<theta>c);b\<sharp>(M,c,\<theta>n,\<theta>c);b\<noteq>a\<rbrakk> \<Longrightarrow> (\<theta>n,\<theta>c<AndR <a>.M <b>.N c>) = 
   (case (findc \<theta>c c) of 
        Some (x,P) \<Rightarrow> fresh_fun (\<lambda>a'. Cut <a'>.(AndR <a>.(\<theta>n,\<theta>c<M>) <b>.(\<theta>n,\<theta>c<N>) a') (x).P)
      | None \<Rightarrow> AndR <a>.(\<theta>n,\<theta>c<M>) <b>.(\<theta>n,\<theta>c<N>) c)"
-  "x\<sharp>(z,\<theta>n,\<theta>c) \<Longrightarrow> (\<theta>n,\<theta>c<AndL1 (x).M z>) = 
+| "x\<sharp>(z,\<theta>n,\<theta>c) \<Longrightarrow> (\<theta>n,\<theta>c<AndL1 (x).M z>) = 
   (case (findn \<theta>n z) of 
        Some (c,P) \<Rightarrow> fresh_fun (\<lambda>z'. Cut <c>.P (z').AndL1 (x).(\<theta>n,\<theta>c<M>) z') 
      | None \<Rightarrow> AndL1 (x).(\<theta>n,\<theta>c<M>) z)"
-  "x\<sharp>(z,\<theta>n,\<theta>c) \<Longrightarrow> (\<theta>n,\<theta>c<AndL2 (x).M z>) = 
+| "x\<sharp>(z,\<theta>n,\<theta>c) \<Longrightarrow> (\<theta>n,\<theta>c<AndL2 (x).M z>) = 
   (case (findn \<theta>n z) of 
        Some (c,P) \<Rightarrow> fresh_fun (\<lambda>z'. Cut <c>.P (z').AndL2 (x).(\<theta>n,\<theta>c<M>) z') 
      | None \<Rightarrow> AndL2 (x).(\<theta>n,\<theta>c<M>) z)"
-  "\<lbrakk>x\<sharp>(N,z,\<theta>n,\<theta>c);u\<sharp>(M,z,\<theta>n,\<theta>c);x\<noteq>u\<rbrakk> \<Longrightarrow> (\<theta>n,\<theta>c<OrL (x).M (u).N z>) =
+| "\<lbrakk>x\<sharp>(N,z,\<theta>n,\<theta>c);u\<sharp>(M,z,\<theta>n,\<theta>c);x\<noteq>u\<rbrakk> \<Longrightarrow> (\<theta>n,\<theta>c<OrL (x).M (u).N z>) =
   (case (findn \<theta>n z) of  
        Some (c,P) \<Rightarrow> fresh_fun (\<lambda>z'. Cut <c>.P (z').OrL (x).(\<theta>n,\<theta>c<M>) (u).(\<theta>n,\<theta>c<N>) z') 
      | None \<Rightarrow> OrL (x).(\<theta>n,\<theta>c<M>) (u).(\<theta>n,\<theta>c<N>) z)"
-  "a\<sharp>(b,\<theta>n,\<theta>c) \<Longrightarrow> (\<theta>n,\<theta>c<OrR1 <a>.M b>) = 
+| "a\<sharp>(b,\<theta>n,\<theta>c) \<Longrightarrow> (\<theta>n,\<theta>c<OrR1 <a>.M b>) = 
   (case (findc \<theta>c b) of
        Some (x,P) \<Rightarrow> fresh_fun (\<lambda>a'. Cut <a'>.OrR1 <a>.(\<theta>n,\<theta>c<M>) a' (x).P) 
      | None \<Rightarrow> OrR1 <a>.(\<theta>n,\<theta>c<M>) b)"
-  "a\<sharp>(b,\<theta>n,\<theta>c) \<Longrightarrow> (\<theta>n,\<theta>c<OrR2 <a>.M b>) = 
+| "a\<sharp>(b,\<theta>n,\<theta>c) \<Longrightarrow> (\<theta>n,\<theta>c<OrR2 <a>.M b>) = 
   (case (findc \<theta>c b) of
        Some (x,P) \<Rightarrow> fresh_fun (\<lambda>a'. Cut <a'>.OrR2 <a>.(\<theta>n,\<theta>c<M>) a' (x).P) 
      | None \<Rightarrow> OrR2 <a>.(\<theta>n,\<theta>c<M>) b)"
-  "\<lbrakk>a\<sharp>(b,\<theta>n,\<theta>c); x\<sharp>(\<theta>n,\<theta>c)\<rbrakk> \<Longrightarrow> (\<theta>n,\<theta>c<ImpR (x).<a>.M b>) = 
+| "\<lbrakk>a\<sharp>(b,\<theta>n,\<theta>c); x\<sharp>(\<theta>n,\<theta>c)\<rbrakk> \<Longrightarrow> (\<theta>n,\<theta>c<ImpR (x).<a>.M b>) = 
   (case (findc \<theta>c b) of
        Some (z,P) \<Rightarrow> fresh_fun (\<lambda>a'. Cut <a'>.ImpR (x).<a>.(\<theta>n,\<theta>c<M>) a' (z).P)
      | None \<Rightarrow> ImpR (x).<a>.(\<theta>n,\<theta>c<M>) b)"
-  "\<lbrakk>a\<sharp>(N,\<theta>n,\<theta>c); x\<sharp>(z,M,\<theta>n,\<theta>c)\<rbrakk> \<Longrightarrow> (\<theta>n,\<theta>c<ImpL <a>.M (x).N z>) = 
+| "\<lbrakk>a\<sharp>(N,\<theta>n,\<theta>c); x\<sharp>(z,M,\<theta>n,\<theta>c)\<rbrakk> \<Longrightarrow> (\<theta>n,\<theta>c<ImpL <a>.M (x).N z>) = 
   (case (findn \<theta>n z) of
        Some (c,P) \<Rightarrow> fresh_fun (\<lambda>z'. Cut <c>.P (z').ImpL <a>.(\<theta>n,\<theta>c<M>) (x).(\<theta>n,\<theta>c<N>) z') 
      | None \<Rightarrow> ImpL <a>.(\<theta>n,\<theta>c<M>) (x).(\<theta>n,\<theta>c<N>) z)"
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Compile.thy
--- a/src/HOL/Nominal/Examples/Compile.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Compile.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 (* The definitions for a challenge suggested by Adam Chlipala *)
 
 theory Compile
@@ -92,20 +90,24 @@
 
 text {* capture-avoiding substitution *}
 
-consts
-  subst :: "'a \<Rightarrow> name \<Rightarrow> 'a \<Rightarrow> 'a"  ("_[_::=_]" [100,100,100] 100)
+class subst =
+  fixes subst :: "'a \<Rightarrow> name \<Rightarrow> 'a \<Rightarrow> 'a"  ("_[_::=_]" [100,100,100] 100)
 
-nominal_primrec
+instantiation trm :: subst
+begin
+
+nominal_primrec subst_trm
+where
   "(Var x)[y::=t'] = (if x=y then t' else (Var x))"
-  "(App t1 t2)[y::=t'] = App (t1[y::=t']) (t2[y::=t'])"
-  "\<lbrakk>x\<sharp>y; x\<sharp>t'\<rbrakk> \<Longrightarrow> (Lam [x].t)[y::=t'] = Lam [x].(t[y::=t'])"
-  "(Const n)[y::=t'] = Const n"
-  "(Pr e1 e2)[y::=t'] = Pr (e1[y::=t']) (e2[y::=t'])"
-  "(Fst e)[y::=t'] = Fst (e[y::=t'])"
-  "(Snd e)[y::=t'] = Snd (e[y::=t'])"
-  "(InL e)[y::=t'] = InL (e[y::=t'])"
-  "(InR e)[y::=t'] = InR (e[y::=t'])"
-  "\<lbrakk>z\<noteq>x; x\<sharp>y; x\<sharp>e; x\<sharp>e2; z\<sharp>y; z\<sharp>e; z\<sharp>e1; x\<sharp>t'; z\<sharp>t'\<rbrakk> \<Longrightarrow>
+| "(App t1 t2)[y::=t'] = App (t1[y::=t']) (t2[y::=t'])"
+| "\<lbrakk>x\<sharp>y; x\<sharp>t'\<rbrakk> \<Longrightarrow> (Lam [x].t)[y::=t'] = Lam [x].(t[y::=t'])"
+| "(Const n)[y::=t'] = Const n"
+| "(Pr e1 e2)[y::=t'] = Pr (e1[y::=t']) (e2[y::=t'])"
+| "(Fst e)[y::=t'] = Fst (e[y::=t'])"
+| "(Snd e)[y::=t'] = Snd (e[y::=t'])"
+| "(InL e)[y::=t'] = InL (e[y::=t'])"
+| "(InR e)[y::=t'] = InR (e[y::=t'])"
+| "\<lbrakk>z\<noteq>x; x\<sharp>y; x\<sharp>e; x\<sharp>e2; z\<sharp>y; z\<sharp>e; z\<sharp>e1; x\<sharp>t'; z\<sharp>t'\<rbrakk> \<Longrightarrow>
      (Case e of inl x \<rightarrow> e1 | inr z \<rightarrow> e2)[y::=t'] =
        (Case (e[y::=t']) of inl x \<rightarrow> (e1[y::=t']) | inr z \<rightarrow> (e2[y::=t']))"
   apply(finite_guess)+
@@ -114,23 +116,35 @@
   apply(fresh_guess)+
   done
 
-nominal_primrec (Isubst)
+instance ..
+
+end
+
+instantiation trmI :: subst
+begin
+
+nominal_primrec subst_trmI
+where
   "(IVar x)[y::=t'] = (if x=y then t' else (IVar x))"
-  "(IApp t1 t2)[y::=t'] = IApp (t1[y::=t']) (t2[y::=t'])"
-  "\<lbrakk>x\<sharp>y; x\<sharp>t'\<rbrakk> \<Longrightarrow> (ILam [x].t)[y::=t'] = ILam [x].(t[y::=t'])"
-  "(INat n)[y::=t'] = INat n"
-  "(IUnit)[y::=t'] = IUnit"
-  "(ISucc e)[y::=t'] = ISucc (e[y::=t'])"
-  "(IAss e1 e2)[y::=t'] = IAss (e1[y::=t']) (e2[y::=t'])"
-  "(IRef e)[y::=t'] = IRef (e[y::=t'])"
-  "(ISeq e1 e2)[y::=t'] = ISeq (e1[y::=t']) (e2[y::=t'])"
-  "(Iif e e1 e2)[y::=t'] = Iif (e[y::=t']) (e1[y::=t']) (e2[y::=t'])"
+| "(IApp t1 t2)[y::=t'] = IApp (t1[y::=t']) (t2[y::=t'])"
+| "\<lbrakk>x\<sharp>y; x\<sharp>t'\<rbrakk> \<Longrightarrow> (ILam [x].t)[y::=t'] = ILam [x].(t[y::=t'])"
+| "(INat n)[y::=t'] = INat n"
+| "(IUnit)[y::=t'] = IUnit"
+| "(ISucc e)[y::=t'] = ISucc (e[y::=t'])"
+| "(IAss e1 e2)[y::=t'] = IAss (e1[y::=t']) (e2[y::=t'])"
+| "(IRef e)[y::=t'] = IRef (e[y::=t'])"
+| "(ISeq e1 e2)[y::=t'] = ISeq (e1[y::=t']) (e2[y::=t'])"
+| "(Iif e e1 e2)[y::=t'] = Iif (e[y::=t']) (e1[y::=t']) (e2[y::=t'])"
   apply(finite_guess)+
   apply(rule TrueI)+
   apply(simp add: abs_fresh)+
   apply(fresh_guess)+
   done
 
+instance ..
+
+end
+
 lemma Isubst_eqvt[eqvt]:
   fixes pi::"name prm"
   and   t1::"trmI"
@@ -138,7 +152,7 @@
   and   x::"name"
   shows "pi\<bullet>(t1[x::=t2]) = ((pi\<bullet>t1)[(pi\<bullet>x)::=(pi\<bullet>t2)])"
   apply (nominal_induct t1 avoiding: x t2 rule: trmI.strong_induct)
-  apply (simp_all add: Isubst.simps eqvts fresh_bij)
+  apply (simp_all add: subst_trmI.simps eqvts fresh_bij)
   done
 
 lemma Isubst_supp:
@@ -147,7 +161,7 @@
   and   x::"name"
   shows "((supp (t1[x::=t2]))::name set) \<subseteq> (supp t2)\<union>((supp t1)-{x})"
   apply (nominal_induct t1 avoiding: x t2 rule: trmI.strong_induct)
-  apply (auto simp add: Isubst.simps trmI.supp supp_atm abs_supp supp_nat)
+  apply (auto simp add: subst_trmI.simps trmI.supp supp_atm abs_supp supp_nat)
   apply blast+
   done
 
@@ -198,29 +212,29 @@
 
 text {* Translation functions *}
 
-consts trans :: "trm \<Rightarrow> trmI" 
-
 nominal_primrec
+  trans :: "trm \<Rightarrow> trmI"
+where
   "trans (Var x) = (IVar x)"
-  "trans (App e1 e2) = IApp (trans e1) (trans e2)"
-  "trans (Lam [x].e) = ILam [x].(trans e)"
-  "trans (Const n) = INat n"
-  "trans (Pr e1 e2) = 
+| "trans (App e1 e2) = IApp (trans e1) (trans e2)"
+| "trans (Lam [x].e) = ILam [x].(trans e)"
+| "trans (Const n) = INat n"
+| "trans (Pr e1 e2) = 
        (let limit = IRef(INat 0) in 
         let v1 = (trans e1) in 
         let v2 = (trans e2) in 
         (((ISucc limit)\<mapsto>v1);;(ISucc(ISucc limit)\<mapsto>v2));;(INat 0 \<mapsto> ISucc(ISucc(limit))))"
-  "trans (Fst e) = IRef (ISucc (trans e))"
-  "trans (Snd e) = IRef (ISucc (ISucc (trans e)))"
-  "trans (InL e) = 
+| "trans (Fst e) = IRef (ISucc (trans e))"
+| "trans (Snd e) = IRef (ISucc (ISucc (trans e)))"
+| "trans (InL e) = 
         (let limit = IRef(INat 0) in 
          let v = (trans e) in 
          (((ISucc limit)\<mapsto>INat(0));;(ISucc(ISucc limit)\<mapsto>v));;(INat 0 \<mapsto> ISucc(ISucc(limit))))"
-  "trans (InR e) = 
+| "trans (InR e) = 
         (let limit = IRef(INat 0) in 
          let v = (trans e) in 
          (((ISucc limit)\<mapsto>INat(1));;(ISucc(ISucc limit)\<mapsto>v));;(INat 0 \<mapsto> ISucc(ISucc(limit))))"
-  "\<lbrakk>x2\<noteq>x1; x1\<sharp>e; x1\<sharp>e2; x2\<sharp>e; x2\<sharp>e1\<rbrakk> \<Longrightarrow> 
+| "\<lbrakk>x2\<noteq>x1; x1\<sharp>e; x1\<sharp>e2; x2\<sharp>e; x2\<sharp>e1\<rbrakk> \<Longrightarrow> 
    trans (Case e of inl x1 \<rightarrow> e1 | inr x2 \<rightarrow> e2) =
        (let v = (trans e) in
         let v1 = (trans e1) in
@@ -232,11 +246,11 @@
   apply(fresh_guess add: Let_def)+
   done
 
-consts trans_type :: "ty \<Rightarrow> tyI"
-
 nominal_primrec
+  trans_type :: "ty \<Rightarrow> tyI"
+where
   "trans_type (Data \<sigma>) = DataI(NatI)"
-  "trans_type (\<tau>1\<rightarrow>\<tau>2) = (trans_type \<tau>1)\<rightarrow>(trans_type \<tau>2)"
+| "trans_type (\<tau>1\<rightarrow>\<tau>2) = (trans_type \<tau>1)\<rightarrow>(trans_type \<tau>2)"
   by (rule TrueI)+
 
 end
\ No newline at end of file
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Contexts.thy
--- a/src/HOL/Nominal/Examples/Contexts.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Contexts.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 theory Contexts
 imports "../Nominal"
 begin
@@ -42,12 +40,12 @@
 
 text {* Capture-Avoiding Substitution *}
 
-consts subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [100,100,100] 100)
-
 nominal_primrec
+  subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [100,100,100] 100)
+where
   "(Var x)[y::=s] = (if x=y then s else (Var x))"
-  "(App t\<^isub>1 t\<^isub>2)[y::=s] = App (t\<^isub>1[y::=s]) (t\<^isub>2[y::=s])"
-  "x\<sharp>(y,s) \<Longrightarrow> (Lam [x].t)[y::=s] = Lam [x].(t[y::=s])"
+| "(App t\<^isub>1 t\<^isub>2)[y::=s] = App (t\<^isub>1[y::=s]) (t\<^isub>2[y::=s])"
+| "x\<sharp>(y,s) \<Longrightarrow> (Lam [x].t)[y::=s] = Lam [x].(t[y::=s])"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh)
@@ -59,14 +57,13 @@
   This operation is possibly capturing.
 *}
 
-consts 
+nominal_primrec
   filling :: "ctx \<Rightarrow> lam \<Rightarrow> lam" ("_\<lbrakk>_\<rbrakk>" [100,100] 100)
-
-nominal_primrec
+where
   "\<box>\<lbrakk>t\<rbrakk> = t"
-  "(CAppL E t')\<lbrakk>t\<rbrakk> = App (E\<lbrakk>t\<rbrakk>) t'"
-  "(CAppR t' E)\<lbrakk>t\<rbrakk> = App t' (E\<lbrakk>t\<rbrakk>)"
-  "(CLam [x].E)\<lbrakk>t\<rbrakk> = Lam [x].(E\<lbrakk>t\<rbrakk>)" 
+| "(CAppL E t')\<lbrakk>t\<rbrakk> = App (E\<lbrakk>t\<rbrakk>) t'"
+| "(CAppR t' E)\<lbrakk>t\<rbrakk> = App t' (E\<lbrakk>t\<rbrakk>)"
+| "(CLam [x].E)\<lbrakk>t\<rbrakk> = Lam [x].(E\<lbrakk>t\<rbrakk>)" 
 by (rule TrueI)+
 
 text {* 
@@ -81,14 +78,13 @@
 
 text {* The composition of two contexts. *}
 
-consts 
+nominal_primrec
  ctx_compose :: "ctx \<Rightarrow> ctx \<Rightarrow> ctx" ("_ \<circ> _" [100,100] 100)
-
-nominal_primrec
+where
   "\<box> \<circ> E' = E'"
-  "(CAppL E t') \<circ> E' = CAppL (E \<circ> E') t'"
-  "(CAppR t' E) \<circ> E' = CAppR t' (E \<circ> E')"
-  "(CLam [x].E) \<circ> E' = CLam [x].(E \<circ> E')"
+| "(CAppL E t') \<circ> E' = CAppL (E \<circ> E') t'"
+| "(CAppR t' E) \<circ> E' = CAppR t' (E \<circ> E')"
+| "(CLam [x].E) \<circ> E' = CLam [x].(E \<circ> E')"
 by (rule TrueI)+
   
 lemma ctx_compose:
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Crary.thy
--- a/src/HOL/Nominal/Examples/Crary.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Crary.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,4 +1,3 @@
-(* "$Id$" *)
 (*                                                    *)
 (* Formalisation of the chapter on Logical Relations  *)
 (* and a Case Study in Equivalence Checking           *)
@@ -47,14 +46,20 @@
   shows "(\<exists> T\<^isub>1 T\<^isub>2. T=T\<^isub>1\<rightarrow>T\<^isub>2) \<or> T=TUnit \<or> T=TBase"
 by (induct T rule:ty.induct) (auto)
 
-instance ty :: size ..
+instantiation ty :: size
+begin
 
-nominal_primrec
+nominal_primrec size_ty
+where
   "size (TBase) = 1"
-  "size (TUnit) = 1"
-  "size (T\<^isub>1\<rightarrow>T\<^isub>2) = size T\<^isub>1 + size T\<^isub>2"
+| "size (TUnit) = 1"
+| "size (T\<^isub>1\<rightarrow>T\<^isub>2) = size T\<^isub>1 + size T\<^isub>2"
 by (rule TrueI)+
 
+instance ..
+
+end
+
 lemma ty_size_greater_zero[simp]:
   fixes T::"ty"
   shows "size T > 0"
@@ -87,16 +92,15 @@
 using a
 by (induct rule: lookup.induct)
    (auto simp add: fresh_list_cons fresh_prod fresh_atm)
-
-consts
-  psubst :: "Subst \<Rightarrow> trm \<Rightarrow> trm"  ("_<_>" [100,100] 130)
  
 nominal_primrec
+  psubst :: "Subst \<Rightarrow> trm \<Rightarrow> trm"  ("_<_>" [100,100] 130)
+where
   "\<theta><(Var x)> = (lookup \<theta> x)"
-  "\<theta><(App t\<^isub>1 t\<^isub>2)> = App \<theta><t\<^isub>1> \<theta><t\<^isub>2>"
-  "x\<sharp>\<theta> \<Longrightarrow> \<theta><(Lam [x].t)> = Lam [x].(\<theta><t>)"
-  "\<theta><(Const n)> = Const n"
-  "\<theta><(Unit)> = Unit"
+| "\<theta><(App t\<^isub>1 t\<^isub>2)> = App \<theta><t\<^isub>1> \<theta><t\<^isub>2>"
+| "x\<sharp>\<theta> \<Longrightarrow> \<theta><(Lam [x].t)> = Lam [x].(\<theta><t>)"
+| "\<theta><(Const n)> = Const n"
+| "\<theta><(Unit)> = Unit"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh)+
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Fsub.thy
--- a/src/HOL/Nominal/Examples/Fsub.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Fsub.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 (*<*)
 theory Fsub
 imports "../Nominal" 
@@ -229,32 +227,26 @@
 
 section {* Size and Capture-Avoiding Substitution for Types *}
 
-consts size_ty :: "ty \<Rightarrow> nat"
-
 nominal_primrec
+  size_ty :: "ty \<Rightarrow> nat"
+where
   "size_ty (Tvar X) = 1"
-  "size_ty (Top) = 1"
-  "size_ty (T1 \<rightarrow> T2) = (size_ty T1) + (size_ty T2) + 1"
-  "X\<sharp>T1 \<Longrightarrow> size_ty (\<forall>[X<:T1].T2) = (size_ty T1) + (size_ty T2) + 1"
+| "size_ty (Top) = 1"
+| "size_ty (T1 \<rightarrow> T2) = (size_ty T1) + (size_ty T2) + 1"
+| "X\<sharp>T1 \<Longrightarrow> size_ty (\<forall>[X<:T1].T2) = (size_ty T1) + (size_ty T2) + 1"
   apply (finite_guess)+
   apply (rule TrueI)+
   apply (simp add: fresh_nat)
   apply (fresh_guess)+
   done
 
-consts subst_ty :: "tyvrs \<Rightarrow> ty \<Rightarrow> ty \<Rightarrow> ty"
-
-syntax 
- subst_ty_syn :: "ty \<Rightarrow> tyvrs \<Rightarrow> ty \<Rightarrow> ty" ("_[_:=_]\<^isub>t\<^isub>y" [100,100,100] 100)
-
-translations 
-  "T1[Y:=T2]\<^isub>t\<^isub>y" \<rightleftharpoons> "subst_ty Y T2 T1"
-
 nominal_primrec
+  subst_ty :: "ty \<Rightarrow> tyvrs \<Rightarrow> ty \<Rightarrow> ty" ("_[_:=_]\<^isub>t\<^isub>y" [100,100,100] 100)
+where
   "(Tvar X)[Y:=T]\<^isub>t\<^isub>y= (if X=Y then T else (Tvar X))"
-  "(Top)[Y:=T]\<^isub>t\<^isub>y = Top"
-  "(T\<^isub>1 \<rightarrow> T\<^isub>2)[Y:=T]\<^isub>t\<^isub>y = (T\<^isub>1[Y:=T]\<^isub>t\<^isub>y) \<rightarrow> (T\<^isub>2[Y:=T]\<^isub>t\<^isub>y)"
-  "\<lbrakk>X\<sharp>(Y,T); X\<sharp>T\<^isub>1\<rbrakk> \<Longrightarrow> (\<forall>[X<:T\<^isub>1].T\<^isub>2)[Y:=T]\<^isub>t\<^isub>y = (\<forall>[X<:(T\<^isub>1[Y:=T]\<^isub>t\<^isub>y)].(T\<^isub>2[Y:=T]\<^isub>t\<^isub>y))"
+| "(Top)[Y:=T]\<^isub>t\<^isub>y = Top"
+| "(T\<^isub>1 \<rightarrow> T\<^isub>2)[Y:=T]\<^isub>t\<^isub>y = (T\<^isub>1[Y:=T]\<^isub>t\<^isub>y) \<rightarrow> (T\<^isub>2[Y:=T]\<^isub>t\<^isub>y)"
+| "\<lbrakk>X\<sharp>(Y,T); X\<sharp>T\<^isub>1\<rbrakk> \<Longrightarrow> (\<forall>[X<:T\<^isub>1].T\<^isub>2)[Y:=T]\<^isub>t\<^isub>y = (\<forall>[X<:(T\<^isub>1[Y:=T]\<^isub>t\<^isub>y)].(T\<^isub>2[Y:=T]\<^isub>t\<^isub>y))"
   apply (finite_guess)+
   apply (rule TrueI)+
   apply (simp add: abs_fresh)
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Height.thy
--- a/src/HOL/Nominal/Examples/Height.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Height.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 theory Height
   imports "../Nominal"
 begin
@@ -17,13 +15,13 @@
   | Lam "\<guillemotleft>name\<guillemotright>lam" ("Lam [_]._" [100,100] 100)
 
 text {* Definition of the height-function on lambda-terms. *} 
-consts 
-  height :: "lam \<Rightarrow> int"
 
 nominal_primrec
+  height :: "lam \<Rightarrow> int"
+where
   "height (Var x) = 1"
-  "height (App t1 t2) = (max (height t1) (height t2)) + 1"
-  "height (Lam [a].t) = (height t) + 1"
+| "height (App t1 t2) = (max (height t1) (height t2)) + 1"
+| "height (Lam [a].t) = (height t) + 1"
   apply(finite_guess add: perm_int_def)+
   apply(rule TrueI)+
   apply(simp add: fresh_int)
@@ -32,13 +30,12 @@
 
 text {* Definition of capture-avoiding substitution. *}
 
-consts
+nominal_primrec
   subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [100,100,100] 100)
-
-nominal_primrec
+where
   "(Var x)[y::=t'] = (if x=y then t' else (Var x))"
-  "(App t1 t2)[y::=t'] = App (t1[y::=t']) (t2[y::=t'])"
-  "\<lbrakk>x\<sharp>y; x\<sharp>t'\<rbrakk> \<Longrightarrow> (Lam [x].t)[y::=t'] = Lam [x].(t[y::=t'])"
+| "(App t1 t2)[y::=t'] = App (t1[y::=t']) (t2[y::=t'])"
+| "\<lbrakk>x\<sharp>y; x\<sharp>t'\<rbrakk> \<Longrightarrow> (Lam [x].t)[y::=t'] = Lam [x].(t[y::=t'])"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh)
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Lam_Funs.thy
--- a/src/HOL/Nominal/Examples/Lam_Funs.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Lam_Funs.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 theory Lam_Funs
   imports "../Nominal"
 begin
@@ -18,13 +16,12 @@
 
 text {* The depth of a lambda-term. *}
 
-consts 
+nominal_primrec
   depth :: "lam \<Rightarrow> nat"
-
-nominal_primrec
+where
   "depth (Var x) = 1"
-  "depth (App t1 t2) = (max (depth t1) (depth t2)) + 1"
-  "depth (Lam [a].t) = (depth t) + 1"
+| "depth (App t1 t2) = (max (depth t1) (depth t2)) + 1"
+| "depth (Lam [a].t) = (depth t) + 1"
   apply(finite_guess)+
   apply(rule TrueI)+
   apply(simp add: fresh_nat)
@@ -38,13 +35,12 @@
   the invariant that frees always returns a finite set of names. 
 *}
 
-consts 
+nominal_primrec (invariant: "\<lambda>s::name set. finite s")
   frees :: "lam \<Rightarrow> name set"
-
-nominal_primrec (invariant: "\<lambda>s::name set. finite s")
+where
   "frees (Var a) = {a}"
-  "frees (App t1 t2) = (frees t1) \<union> (frees t2)"
-  "frees (Lam [a].t) = (frees t) - {a}"
+| "frees (App t1 t2) = (frees t1) \<union> (frees t2)"
+| "frees (Lam [a].t) = (frees t) - {a}"
 apply(finite_guess)+
 apply(simp)+ 
 apply(simp add: fresh_def)
@@ -78,14 +74,13 @@
   and   X::"name"
   shows "pi\<bullet>(lookup \<theta> X) = lookup (pi\<bullet>\<theta>) (pi\<bullet>X)"
 by (induct \<theta>) (auto simp add: eqvts)
-
-consts
-  psubst :: "(name\<times>lam) list \<Rightarrow> lam \<Rightarrow> lam"  ("_<_>" [95,95] 105)
  
 nominal_primrec
+  psubst :: "(name\<times>lam) list \<Rightarrow> lam \<Rightarrow> lam"  ("_<_>" [95,95] 105)
+where
   "\<theta><(Var x)> = (lookup \<theta> x)"
-  "\<theta><(App e\<^isub>1 e\<^isub>2)> = App (\<theta><e\<^isub>1>) (\<theta><e\<^isub>2>)"
-  "x\<sharp>\<theta> \<Longrightarrow> \<theta><(Lam [x].e)> = Lam [x].(\<theta><e>)"
+| "\<theta><(App e\<^isub>1 e\<^isub>2)> = App (\<theta><e\<^isub>1>) (\<theta><e\<^isub>2>)"
+| "x\<sharp>\<theta> \<Longrightarrow> \<theta><(Lam [x].e)> = Lam [x].(\<theta><e>)"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh)+
@@ -130,26 +125,24 @@
 
 text {* Filling a lambda-term into a context. *}
 
-consts 
+nominal_primrec
   filling :: "clam \<Rightarrow> lam \<Rightarrow> lam" ("_\<lbrakk>_\<rbrakk>" [100,100] 100)
-
-nominal_primrec
+where
   "\<box>\<lbrakk>t\<rbrakk> = t"
-  "(CAppL E t')\<lbrakk>t\<rbrakk> = App (E\<lbrakk>t\<rbrakk>) t'"
-  "(CAppR t' E)\<lbrakk>t\<rbrakk> = App t' (E\<lbrakk>t\<rbrakk>)"
-  "(CLam [x].E)\<lbrakk>t\<rbrakk> = Lam [x].(E\<lbrakk>t\<rbrakk>)" 
+| "(CAppL E t')\<lbrakk>t\<rbrakk> = App (E\<lbrakk>t\<rbrakk>) t'"
+| "(CAppR t' E)\<lbrakk>t\<rbrakk> = App t' (E\<lbrakk>t\<rbrakk>)"
+| "(CLam [x].E)\<lbrakk>t\<rbrakk> = Lam [x].(E\<lbrakk>t\<rbrakk>)" 
 by (rule TrueI)+
 
 text {* Composition od two contexts *}
 
-consts 
+nominal_primrec
  clam_compose :: "clam \<Rightarrow> clam \<Rightarrow> clam" ("_ \<circ> _" [100,100] 100)
-
-nominal_primrec
+where
   "\<box> \<circ> E' = E'"
-  "(CAppL E t') \<circ> E' = CAppL (E \<circ> E') t'"
-  "(CAppR t' E) \<circ> E' = CAppR t' (E \<circ> E')"
-  "(CLam [x].E) \<circ> E' = CLam [x].(E \<circ> E')"
+| "(CAppL E t') \<circ> E' = CAppL (E \<circ> E') t'"
+| "(CAppR t' E) \<circ> E' = CAppR t' (E \<circ> E')"
+| "(CLam [x].E) \<circ> E' = CLam [x].(E \<circ> E')"
 by (rule TrueI)+
   
 lemma clam_compose:
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/LocalWeakening.thy
--- a/src/HOL/Nominal/Examples/LocalWeakening.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/LocalWeakening.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 (* Formalisation of weakening using locally nameless    *)
 (* terms; the nominal infrastructure can also derive    *)
 (* strong induction principles for such representations *)
@@ -29,13 +27,13 @@
 by (induct t rule: llam.induct)
    (auto simp add: llam.inject)
 
-consts llam_size :: "llam \<Rightarrow> nat"
-
 nominal_primrec
- "llam_size (lPar a) = 1"
- "llam_size (lVar n) = 1"
- "llam_size (lApp t1 t2) = 1 + (llam_size t1) + (llam_size t2)"
- "llam_size (lLam t) = 1 + (llam_size t)"
+  llam_size :: "llam \<Rightarrow> nat"
+where
+  "llam_size (lPar a) = 1"
+| "llam_size (lVar n) = 1"
+| "llam_size (lApp t1 t2) = 1 + (llam_size t1) + (llam_size t2)"
+| "llam_size (lLam t) = 1 + (llam_size t)"
 by (rule TrueI)+
 
 function  
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/SN.thy
--- a/src/HOL/Nominal/Examples/SN.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/SN.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 theory SN
   imports Lam_Funs
 begin
@@ -228,12 +226,11 @@
 
 section {* Candidates *}
 
-consts
+nominal_primrec
   RED :: "ty \<Rightarrow> lam set"
-
-nominal_primrec
+where
   "RED (TVar X) = {t. SN(t)}"
-  "RED (\<tau>\<rightarrow>\<sigma>) =   {t. \<forall>u. (u\<in>RED \<tau> \<longrightarrow> (App t u)\<in>RED \<sigma>)}"
+| "RED (\<tau>\<rightarrow>\<sigma>) =   {t. \<forall>u. (u\<in>RED \<tau> \<longrightarrow> (App t u)\<in>RED \<sigma>)}"
 by (rule TrueI)+
 
 text {* neutral terms *}
@@ -248,13 +245,12 @@
 where
   fst[intro!]:  "(App t s) \<guillemotright> t"
 
-consts
+nominal_primrec
   fst_app_aux::"lam\<Rightarrow>lam option"
-
-nominal_primrec
+where
   "fst_app_aux (Var a)     = None"
-  "fst_app_aux (App t1 t2) = Some t1"
-  "fst_app_aux (Lam [x].t) = None"
+| "fst_app_aux (App t1 t2) = Some t1"
+| "fst_app_aux (Lam [x].t) = None"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: fresh_none)
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/SOS.thy
--- a/src/HOL/Nominal/Examples/SOS.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/SOS.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,4 +1,3 @@
-(* "$Id$" *)
 (*                                                        *)
 (* Formalisation of some typical SOS-proofs.              *)
 (*                                                        *) 
@@ -62,13 +61,12 @@
 
 (* parallel substitution *)
 
-consts
+nominal_primrec
   psubst :: "(name\<times>trm) list \<Rightarrow> trm \<Rightarrow> trm"  ("_<_>" [95,95] 105)
- 
-nominal_primrec
+where
   "\<theta><(Var x)> = (lookup \<theta> x)"
-  "\<theta><(App e\<^isub>1 e\<^isub>2)> = App (\<theta><e\<^isub>1>) (\<theta><e\<^isub>2>)"
-  "x\<sharp>\<theta> \<Longrightarrow> \<theta><(Lam [x].e)> = Lam [x].(\<theta><e>)"
+| "\<theta><(App e\<^isub>1 e\<^isub>2)> = App (\<theta><e\<^isub>1>) (\<theta><e\<^isub>2>)"
+| "x\<sharp>\<theta> \<Longrightarrow> \<theta><(Lam [x].e)> = Lam [x].(\<theta><e>)"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh)+
@@ -349,12 +347,12 @@
 using h by (induct) (auto)
 
 (* Valuation *)
-consts
-  V :: "ty \<Rightarrow> trm set" 
 
 nominal_primrec
+  V :: "ty \<Rightarrow> trm set" 
+where
   "V (TVar x) = {e. val e}"
-  "V (T\<^isub>1 \<rightarrow> T\<^isub>2) = {Lam [x].e | x e. \<forall> v \<in> (V T\<^isub>1). \<exists> v'. e[x::=v] \<Down> v' \<and> v' \<in> V T\<^isub>2}"
+| "V (T\<^isub>1 \<rightarrow> T\<^isub>2) = {Lam [x].e | x e. \<forall> v \<in> (V T\<^isub>1). \<exists> v'. e[x::=v] \<Down> v' \<and> v' \<in> V T\<^isub>2}"
   by (rule TrueI)+ 
 
 lemma V_eqvt:
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Standardization.thy
--- a/src/HOL/Nominal/Examples/Standardization.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Standardization.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,4 @@
 (*  Title:      HOL/Nominal/Examples/Standardization.thy
-    ID:         $Id$
     Author:     Stefan Berghofer and Tobias Nipkow
     Copyright   2005, 2008 TU Muenchen
 *)
@@ -24,24 +23,30 @@
 | App "lam" "lam" (infixl "\<degree>" 200)
 | Lam "\<guillemotleft>name\<guillemotright>lam" ("Lam [_]._" [0, 10] 10)
 
-instance lam :: size ..
+instantiation lam :: size
+begin
 
-nominal_primrec
+nominal_primrec size_lam
+where
   "size (Var n) = 0"
-  "size (t \<degree> u) = size t + size u + 1"
-  "size (Lam [x].t) = size t + 1"
+| "size (t \<degree> u) = size t + size u + 1"
+| "size (Lam [x].t) = size t + 1"
   apply finite_guess+
   apply (rule TrueI)+
   apply (simp add: fresh_nat)
   apply fresh_guess+
   done
 
-consts subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [300, 0, 0] 300)
+instance ..
+
+end
 
 nominal_primrec
+  subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]" [300, 0, 0] 300)
+where
   subst_Var: "(Var x)[y::=s] = (if x=y then s else (Var x))"
-  subst_App: "(t\<^isub>1 \<degree> t\<^isub>2)[y::=s] = t\<^isub>1[y::=s] \<degree> t\<^isub>2[y::=s]"
-  subst_Lam: "x \<sharp> (y, s) \<Longrightarrow> (Lam [x].t)[y::=s] = (Lam [x].(t[y::=s]))"
+| subst_App: "(t\<^isub>1 \<degree> t\<^isub>2)[y::=s] = t\<^isub>1[y::=s] \<degree> t\<^isub>2[y::=s]"
+| subst_Lam: "x \<sharp> (y, s) \<Longrightarrow> (Lam [x].t)[y::=s] = (Lam [x].(t[y::=s]))"
   apply(finite_guess)+
   apply(rule TrueI)+
   apply(simp add: abs_fresh)
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/Type_Preservation.thy
--- a/src/HOL/Nominal/Examples/Type_Preservation.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/Type_Preservation.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* $Id$ *)
-
 theory Type_Preservation
   imports Nominal
 begin
@@ -21,13 +19,12 @@
 
 text {* Capture-Avoiding Substitution *}
 
-consts 
+nominal_primrec
   subst :: "lam \<Rightarrow> name \<Rightarrow> lam \<Rightarrow> lam"  ("_[_::=_]")
-
-nominal_primrec
+where
   "(Var x)[y::=s] = (if x=y then s else (Var x))"
-  "(App t\<^isub>1 t\<^isub>2)[y::=s] = App (t\<^isub>1[y::=s]) (t\<^isub>2[y::=s])"
-  "x\<sharp>(y,s) \<Longrightarrow> (Lam [x].t)[y::=s] = Lam [x].(t[y::=s])"
+| "(App t\<^isub>1 t\<^isub>2)[y::=s] = App (t\<^isub>1[y::=s]) (t\<^isub>2[y::=s])"
+| "x\<sharp>(y,s) \<Longrightarrow> (Lam [x].t)[y::=s] = Lam [x].(t[y::=s])"
 apply(finite_guess)+
 apply(rule TrueI)+
 apply(simp add: abs_fresh)
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/Examples/W.thy
--- a/src/HOL/Nominal/Examples/W.thy	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/Examples/W.thy	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,3 @@
-(* "$Id$" *)
-
 theory W
 imports Nominal
 begin
@@ -50,26 +48,68 @@
   Ctxt  = "(var\<times>tyS) list" 
 
 text {* free type variables *}
-consts
-  ftv    :: "'a \<Rightarrow> tvar list"
+
+class ftv = type +
+  fixes ftv :: "'a \<Rightarrow> tvar list"
+
+instantiation * :: (ftv, ftv) ftv
+begin
+
+primrec ftv_prod
+where
+ "ftv (x::'a::ftv, y::'b::ftv) = (ftv x)@(ftv y)"
+
+instance ..
+
+end
 
-primrec (ftv_of_prod)
- "ftv (x,y) = (ftv x)@(ftv y)"
+instantiation tvar :: ftv
+begin
+
+definition
+  ftv_of_tvar[simp]:  "ftv X \<equiv> [(X::tvar)]"
 
-defs (overloaded)
-  ftv_of_tvar[simp]:  "ftv X \<equiv> [(X::tvar)]"
+instance ..
+
+end
+
+instantiation var :: ftv
+begin
+
+definition
   ftv_of_var[simp]:   "ftv (x::var) \<equiv> []" 
 
-primrec (ftv_of_list)
+instance ..
+
+end
+
+instantiation list :: (ftv) ftv
+begin
+
+primrec ftv_list
+where
   "ftv [] = []"
-  "ftv (x#xs) = (ftv x)@(ftv xs)"
+| "ftv (x#xs) = (ftv x)@(ftv xs)"
+
+instance ..
+
+end
 
 (* free type-variables of types *)
-nominal_primrec (ftv_ty)
+
+instantiation ty :: ftv
+begin
+
+nominal_primrec ftv_ty
+where
   "ftv (TVar X) = [X]"
-  "ftv (T\<^isub>1\<rightarrow>T\<^isub>2) = (ftv T\<^isub>1)@(ftv T\<^isub>2)"
+| "ftv (T\<^isub>1\<rightarrow>T\<^isub>2) = (ftv T\<^isub>1)@(ftv T\<^isub>2)"
 by (rule TrueI)+
 
+instance ..
+
+end
+
 lemma ftv_ty_eqvt[eqvt]:
   fixes pi::"tvar prm"
   and   T::"ty"
@@ -77,9 +117,13 @@
 by (nominal_induct T rule: ty.strong_induct)
    (perm_simp add: append_eqvt)+
 
-nominal_primrec (ftv_tyS)
+instantiation tyS :: ftv
+begin
+
+nominal_primrec ftv_tyS
+where
   "ftv (Ty T)    = ftv T"
-  "ftv (\<forall>[X].S) = (ftv S) - [X]"
+| "ftv (\<forall>[X].S) = (ftv S) - [X]"
 apply(finite_guess add: ftv_ty_eqvt fs_tvar1)+
 apply(rule TrueI)+
 apply(rule difference_fresh)
@@ -87,6 +131,10 @@
 apply(fresh_guess add: ftv_ty_eqvt fs_tvar1)+
 done
 
+instance ..
+
+end
+
 lemma ftv_tyS_eqvt[eqvt]:
   fixes pi::"tvar prm"
   and   S::"tyS"
@@ -140,11 +188,11 @@
 
 types Subst = "(tvar\<times>ty) list"
 
-consts
- psubst :: "Subst \<Rightarrow> 'a \<Rightarrow> 'a"       ("_<_>" [100,60] 120)
+class psubst =
+  fixes psubst :: "Subst \<Rightarrow> 'a \<Rightarrow> 'a"       ("_<_>" [100,60] 120)
 
 abbreviation 
-  subst :: "'a \<Rightarrow> tvar \<Rightarrow> ty \<Rightarrow> 'a"  ("_[_::=_]" [100,100,100] 100)
+  subst :: "'a::psubst \<Rightarrow> tvar \<Rightarrow> ty \<Rightarrow> 'a"  ("_[_::=_]" [100,100,100] 100)
 where
   "smth[X::=T] \<equiv> ([(X,T)])<smth>" 
 
@@ -159,11 +207,19 @@
   shows "pi\<bullet>(lookup \<theta> X) = lookup (pi\<bullet>\<theta>) (pi\<bullet>X)"
 by (induct \<theta>) (auto simp add: eqvts)
 
-nominal_primrec (psubst_ty)
+instantiation ty :: psubst
+begin
+
+nominal_primrec psubst_ty
+where
   "\<theta><TVar X>   = lookup \<theta> X"
-  "\<theta><T\<^isub>1 \<rightarrow> T\<^isub>2> = (\<theta><T\<^isub>1>) \<rightarrow> (\<theta><T\<^isub>2>)"
+| "\<theta><T\<^isub>1 \<rightarrow> T\<^isub>2> = (\<theta><T\<^isub>1>) \<rightarrow> (\<theta><T\<^isub>2>)"
 by (rule TrueI)+
 
+instance ..
+
+end
+
 lemma psubst_ty_eqvt[eqvt]:
   fixes pi1::"tvar prm"
   and   \<theta>::"Subst"
diff -r 1b8e021e8c1f -r 66fe138979f4 src/HOL/Nominal/nominal_primrec.ML
--- a/src/HOL/Nominal/nominal_primrec.ML	Sat Dec 13 15:35:29 2008 +0100
+++ b/src/HOL/Nominal/nominal_primrec.ML	Sat Dec 13 17:13:09 2008 +0100
@@ -1,5 +1,4 @@
 (*  Title:      HOL/Nominal/nominal_primrec.ML
-    ID:         $Id$
     Author:     Stefan Berghofer, TU Muenchen and Norbert Voelker, FernUni Hagen
 
 Package for defining functions on nominal datatypes by primitive recursion.
@@ -8,14 +7,10 @@
 
 signature NOMINAL_PRIMREC =
 sig
-  val add_primrec: string -> string list option -> string option ->
-    ((Binding.T * string) * Attrib.src list) list -> theory -> Proof.state
-  val add_primrec_unchecked: string -> string list option -> string option ->
-    ((Binding.T * string) * Attrib.src list) list -> theory -> Proof.state
-  val add_primrec_i: string -> term list option -> term option ->
-    ((Binding.T * term) * attribute list) list -> theory -> Proof.state
-  val add_primrec_unchecked_i: string -> term list option -> term option ->
-    ((Binding.T * term) * attribute list) list -> theory -> Proof.state
+  val add_primrec: term list option -> term option ->
+    (Binding.T * typ option * mixfix) list ->
+    (Binding.T * typ option * mixfix) list ->
+    (Attrib.binding * term) list -> local_theory -> Proof.state
 end;
 
 structure NominalPrimrec : NOMINAL_PRIMREC =
@@ -26,23 +21,31 @@
 exception RecError of string;
 
 fun primrec_err s = error ("Nominal primrec definition error:\n" ^ s);
-fun primrec_eq_err thy s eq =
-  primrec_err (s ^ "\nin\n" ^ quote (Syntax.string_of_term_global thy eq));
+fun primrec_eq_err lthy s eq =
+  primrec_err (s ^ "\nin\n" ^ quote (Syntax.string_of_term lthy eq));
 
 
 (* preprocessing of equations *)
 
-fun process_eqn thy eq rec_fns = 
+fun unquantify t =
   let
+    val (vs, Ts) = split_list (strip_qnt_vars "all" t);
+    val body = strip_qnt_body "all" t;
+    val (vs', _) = Name.variants vs (Name.make_context (fold_aterms
+      (fn Free (v, _) => insert (op =) v | _ => I) body []))
+  in (curry subst_bounds (map2 (curry Free) vs' Ts |> rev) body) end;
+
+fun process_eqn lthy is_fixed spec rec_fns = 
+  let
+    val eq = unquantify spec;
     val (lhs, rhs) = 
-      if null (term_vars eq) then
-        HOLogic.dest_eq (HOLogic.dest_Trueprop (Logic.strip_imp_concl eq))
-        handle TERM _ => raise RecError "not a proper equation"
-      else raise RecError "illegal schematic variable(s)";
+      HOLogic.dest_eq (HOLogic.dest_Trueprop (Logic.strip_imp_concl eq))
+      handle TERM _ => raise RecError "not a proper equation";
 
     val (recfun, args) = strip_comb lhs;
-    val fnameT = dest_Const recfun handle TERM _ => 
-      raise RecError "function is not declared as constant in theory";
+    val fname = case recfun of Free (v, _) => if is_fixed v then v
+          else raise RecError "illegal head of function equation"
+      | _ => raise RecError "illegal head of function equation";
 
     val (ls', rest)  = take_prefix is_Free args;
     val (middle, rs') = take_suffix is_Free rest;
@@ -68,26 +71,28 @@
     else
      (check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees);
       check_vars "extra variables on rhs: "
-        (map dest_Free (term_frees rhs) \\ lfrees);
-      case AList.lookup (op =) rec_fns fnameT of
+        (map dest_Free (term_frees rhs) |> subtract (op =) lfrees
+          |> filter_out (is_fixed o fst));
+      case AList.lookup (op =) rec_fns fname of
         NONE =>
-          (fnameT, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns
+          (fname, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns
       | SOME (_, rpos', eqns) =>
           if AList.defined (op =) eqns cname then
             raise RecError "constructor already occurred as pattern"
           else if rpos <> rpos' then
             raise RecError "position of recursive argument inconsistent"
           else
-            AList.update (op =) (fnameT, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns))
+            AList.update (op =)
+              (fname, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns))
               rec_fns)
   end
-  handle RecError s => primrec_eq_err thy s eq;
+  handle RecError s => primrec_eq_err lthy s spec;
 
 val param_err = "Parameters must be the same for all recursive functions";
 
-fun process_fun thy descr rec_eqns (i, fnameT as (fname, _)) (fnameTs, fnss) =
+fun process_fun lthy descr eqns (i, fname) (fnames, fnss) =
   let
-    val (_, (tname, _, constrs)) = List.nth (descr, i);
+    val (_, (tname, _, constrs)) = nth descr i;
 
     (* substitute "fname ls x rs" by "y" for (x, (_, y)) in subs *)
 
@@ -100,16 +105,17 @@
           let
             val (f, ts) = strip_comb t;
           in
-            if is_Const f andalso dest_Const f mem map fst rec_eqns then
+            if is_Free f
+              andalso member (fn ((v, _), (w, _)) => v = w) eqns (dest_Free f) then
               let
-                val fnameT' as (fname', _) = dest_Const f;
-                val (_, rpos, eqns) = the (AList.lookup (op =) rec_eqns fnameT');
-                val ls = Library.take (rpos, ts);
-                val rest = Library.drop (rpos, ts);
-                val (x', rs) = (hd rest, tl rest)
-                  handle Empty => raise RecError ("not enough arguments\
-                   \ in recursive application\nof function " ^ quote fname' ^ " on rhs");
-                val rs' = (case eqns of
+                val (fname', _) = dest_Free f;
+                val (_, rpos, eqns') = the (AList.lookup (op =) eqns fname');
+                val (ls, rs'') = chop rpos ts
+                val (x', rs) = case rs'' of
+                    x' :: rs => (x', rs)
+                  | [] => raise RecError ("not enough arguments in recursive application\n"
+                      ^ "of function " ^ quote fname' ^ " on rhs");
+                val rs' = (case eqns' of
                     (_, (ls', _, rs', _, _)) :: _ =>
                       let val (rs1, rs2) = chop (length rs') rs
                       in
@@ -126,7 +132,7 @@
                 | SOME (i', y) =>
                     fs
                     |> fold_map (subst subs) (xs @ rs')
-                    ||> process_fun thy descr rec_eqns (i', fnameT')
+                    ||> process_fun lthy descr eqns (i', fname')
                     |-> (fn ts' => pair (list_comb (y, ts')))
               end
             else
@@ -138,41 +144,39 @@
 
     (* translate rec equations into function arguments suitable for rec comb *)
 
-    fun trans eqns (cname, cargs) (fnameTs', fnss', fns) =
+    fun trans eqns (cname, cargs) (fnames', fnss', fns) =
       (case AList.lookup (op =) eqns cname of
           NONE => (warning ("No equation for constructor " ^ quote cname ^
             "\nin definition of function " ^ quote fname);
-              (fnameTs', fnss', (Const (@{const_name undefined}, dummyT))::fns))
+              (fnames', fnss', (Const (@{const_name undefined}, dummyT))::fns))
         | SOME (ls, cargs', rs, rhs, eq) =>
             let
               val recs = filter (is_rec_type o snd) (cargs' ~~ cargs);
               val rargs = map fst recs;
-              val subs = map (rpair dummyT o fst) 
+              val subs = map (rpair dummyT o fst)
                 (rev (rename_wrt_term rhs rargs));
-              val (rhs', (fnameTs'', fnss'')) = 
-                  (subst (map (fn ((x, y), z) =>
-                               (Free x, (body_index y, Free z)))
-                          (recs ~~ subs)) rhs (fnameTs', fnss'))
-                  handle RecError s => primrec_eq_err thy s eq
-            in (fnameTs'', fnss'', 
+              val (rhs', (fnames'', fnss'')) = subst (map2 (fn (x, y) => fn z =>
+                (Free x, (body_index y, Free z))) recs subs) rhs (fnames', fnss')
+                  handle RecError s => primrec_eq_err lthy s eq
+            in (fnames'', fnss'', 
                 (list_abs_free (cargs' @ subs, rhs'))::fns)
             end)
 
-  in (case AList.lookup (op =) fnameTs i of
+  in (case AList.lookup (op =) fnames i of
       NONE =>
-        if exists (equal fnameT o snd) fnameTs then
+        if exists (fn (_, v) => fname = v) fnames then
           raise RecError ("inconsistent functions for datatype " ^ quote tname)
         else
           let
-            val SOME (_, _, eqns as (_, (ls, _, rs, _, _)) :: _) =
-              AList.lookup (op =) rec_eqns fnameT;
-            val (fnameTs', fnss', fns) = fold_rev (trans eqns) constrs
-              ((i, fnameT)::fnameTs, fnss, []) 
+            val SOME (_, _, eqns' as (_, (ls, _, rs, _, _)) :: _) =
+              AList.lookup (op =) eqns fname;
+            val (fnames', fnss', fns) = fold_rev (trans eqns') constrs
+              ((i, fname)::fnames, fnss, []) 
           in
-            (fnameTs', (i, (fname, ls, rs, fns))::fnss')
+            (fnames', (i, (fname, ls, rs, fns))::fnss')
           end
-    | SOME fnameT' =>
-        if fnameT = fnameT' then (fnameTs, fnss)
+    | SOME fname' =>
+        if fname = fname' then (fnames, fnss)
         else raise RecError ("inconsistent functions for datatype " ^ quote tname))
   end;
 
@@ -195,18 +199,21 @@
 
 (* make definition *)
 
-fun make_def thy fs (fname, ls, rs, rec_name, tname) =
+fun make_def ctxt fixes fs (fname, ls, rs, rec_name, tname) =
   let
     val used = map fst (fold Term.add_frees fs []);
     val x = (Name.variant used "x", dummyT);
     val frees = ls @ x :: rs;
-    val rhs = list_abs_free (frees,
+    val raw_rhs = list_abs_free (frees,
       list_comb (Const (rec_name, dummyT), fs @ [Free x]))
-    val def_name = Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def";
-    val def_prop as _ $ _ $ t =
-      singleton (Syntax.check_terms (ProofContext.init thy))
-        (Logic.mk_equals (Const (fname, dummyT), rhs));
-  in ((def_name, def_prop), subst_bounds (rev (map Free frees), strip_abs_body t)) end;
+    val def_name = Thm.def_name (Sign.base_name fname);
+    val rhs = singleton (Syntax.check_terms ctxt) raw_rhs;
+    val SOME var = get_first (fn ((b, _), mx) =>
+      if Binding.base_name b = fname then SOME (b, mx) else NONE) fixes;
+  in
+    ((var, ((Binding.name def_name, []), rhs)),
+     subst_bounds (rev (map Free frees), strip_abs_body rhs))
+  end;
 
 
 (* find datatypes which contain all datatypes in tnames' *)
@@ -227,27 +234,36 @@
 
 local
 
-fun gen_primrec_i note def alt_name invs fctxt eqns_atts thy =
+fun prepare_spec prep_spec ctxt raw_fixes raw_spec =
+  let
+    val ((fixes, spec), _) = prep_spec
+      raw_fixes (map (single o apsnd single) raw_spec) ctxt
+  in (fixes, map (apsnd the_single) spec) end;
+
+fun gen_primrec set_group prep_spec prep_term invs fctxt raw_fixes raw_params raw_spec lthy =
   let
-    val (raw_eqns, atts) = split_list eqns_atts;
-    val eqns = map (apfst Binding.base_name) raw_eqns;
-    val dt_info = NominalPackage.get_nominal_datatypes thy;
-    val rec_eqns = fold_rev (process_eqn thy o snd) eqns [];
+    val (fixes', spec) = prepare_spec prep_spec lthy (raw_fixes @ raw_params) raw_spec;
+    val fixes = List.take (fixes', length raw_fixes);
+    val (names_atts, spec') = split_list spec;
+    val eqns' = map unquantify spec'
+    val eqns = fold_rev (process_eqn lthy (fn v => Variable.is_fixed lthy v
+      orelse exists (fn ((w, _), _) => v = Binding.base_name w) fixes)) spec' [];
+    val dt_info = NominalPackage.get_nominal_datatypes (ProofContext.theory_of lthy);
     val lsrs :: lsrss = maps (fn (_, (_, _, eqns)) =>
-      map (fn (_, (ls, _, rs, _, _)) => ls @ rs) eqns) rec_eqns
+      map (fn (_, (ls, _, rs, _, _)) => ls @ rs) eqns) eqns
     val _ =
       (if forall (curry eq_set lsrs) lsrss andalso forall
          (fn (_, (_, _, (_, (ls, _, rs, _, _)) :: eqns)) =>
                forall (fn (_, (ls', _, rs', _, _)) =>
                  ls = ls' andalso rs = rs') eqns
-           | _ => true) rec_eqns
+           | _ => true) eqns
        then () else primrec_err param_err);
-    val tnames = distinct (op =) (map (#1 o snd) rec_eqns);
+    val tnames = distinct (op =) (map (#1 o snd) eqns);
     val dts = find_dts dt_info tnames tnames;
     val main_fns = 
       map (fn (tname, {index, ...}) =>
         (index, 
-          (fst o the o find_first (fn f => (#1 o snd) f = tname)) rec_eqns))
+          (fst o the o find_first (fn (_, x) => #1 x = tname)) eqns))
       dts;
     val {descr, rec_names, rec_rewrites, ...} = 
       if null dts then
@@ -256,32 +272,32 @@
     val descr = map (fn (i, (tname, args, constrs)) => (i, (tname, args,
       map (fn (cname, cargs) => (cname, fold (fn (dTs, dT) => fn dTs' =>
         dTs' @ dTs @ [dT]) cargs [])) constrs))) descr;
-    val (fnameTs, fnss) =
-      fold_rev (process_fun thy descr rec_eqns) main_fns ([], []);
+    val (fnames, fnss) = fold_rev (process_fun lthy descr eqns) main_fns ([], []);
     val (fs, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
-    val defs' = map (make_def thy fs) defs;
-    val nameTs1 = map snd fnameTs;
-    val nameTs2 = map fst rec_eqns;
-    val _ = if gen_eq_set (op =) (nameTs1, nameTs2) then ()
-            else primrec_err ("functions " ^ commas_quote (map fst nameTs2) ^
-              "\nare not mutually recursive");
-    val primrec_name =
-      if alt_name = "" then (space_implode "_" (map (Sign.base_name o #1) defs)) else alt_name;
-    val (defs_thms', thy') =
-      thy
-      |> Sign.add_path primrec_name
-      |> fold_map def (map (fn ((name, t), _) => ((name, []), t)) defs');
-    val cert = cterm_of thy';
+    val defs' = map (make_def lthy fixes fs) defs;
+    val names1 = map snd fnames;
+    val names2 = map fst eqns;
+    val _ = if gen_eq_set (op =) (names1, names2) then ()
+      else primrec_err ("functions " ^ commas_quote names2 ^
+        "\nare not mutually recursive");
+    val (defs_thms, lthy') = lthy |>
+      set_group ? LocalTheory.set_group (serial_string ()) |>
+      fold_map (apfst (snd o snd) oo
+        LocalTheory.define Thm.definitionK o fst) defs';
+    val qualify = Binding.qualify
+      (space_implode "_" (map (Sign.base_name o #1) defs));
+    val names_atts' = map (apfst qualify) names_atts;
+    val cert = cterm_of (ProofContext.theory_of lthy');
 
     fun mk_idx eq =
       let
-        val Const c = head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop
+        val Free (name, _) = head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop
           (Logic.strip_imp_concl eq))));
-        val SOME i = AList.lookup op = (map swap fnameTs) c;
+        val SOME i = AList.lookup op = (map swap fnames) name;
         val SOME (_, _, constrs) = AList.lookup op = descr i;
-        val SOME (_, _, eqns) = AList.lookup op = rec_eqns c;
+        val SOME (_, _, eqns'') = AList.lookup op = eqns name;
         val SOME (cname, (_, cargs, _, _, _)) = find_first
-          (fn (_, (_, _, _, _, eq')) => eq = eq') eqns
+          (fn (_, (_, _, _, _, eq')) => eq = eq') eqns''
       in (i, find_index (fn (cname', _) => cname = cname') constrs, cargs) end;
 
     val rec_rewritess =
@@ -296,19 +312,15 @@
       curry (List.take o swap) (length fvars) |> map cert;
     val invs' = (case invs of
         NONE => map (fn (i, _) =>
-          let
-            val SOME (_, T) = AList.lookup op = fnameTs i
-            val (Ts, U) = strip_type T
-          in
-            Abs ("x", List.drop (Ts, length lsrs + 1) ---> U, HOLogic.true_const)
-          end) descr
-      | SOME invs' => invs');
+          Abs ("x", fastype_of (snd (nth defs' i)), HOLogic.true_const)) descr
+      | SOME invs' => map (prep_term lthy') invs');
     val inst = (map cert fvars ~~ cfs) @
       (map (cert o Var) pvars ~~ map cert invs') @
       (case ctxtvars of
-         [ctxtvar] => [(cert (Var ctxtvar), cert (the_default HOLogic.unit fctxt))]
+         [ctxtvar] => [(cert (Var ctxtvar),
+           cert (the_default HOLogic.unit (Option.map (prep_term lthy') fctxt)))]
        | _ => []);
-    val rec_rewrites' = map (fn (_, eq) =>
+    val rec_rewrites' = map (fn eq =>
       let
         val (i, j, cargs) = mk_idx eq
         val th = nth (nth rec_rewritess i) j;
@@ -317,8 +329,8 @@
           strip_comb |> snd
       in (cargs, Logic.strip_imp_prems eq,
         Drule.cterm_instantiate (inst @
-          (map (cterm_of thy') cargs' ~~ map (cterm_of thy' o Free) cargs)) th)
-      end) eqns;
+          (map cert cargs' ~~ map (cert o Free) cargs)) th)
+      end) eqns';
 
     val prems = foldr1 (common_prefix op aconv) (map (prems_of o #3) rec_rewrites');
     val cprems = map cert prems;
@@ -346,64 +358,37 @@
     val rule = implies_intr_list rule_prems
       (Conjunction.intr_balanced (map mk_eqn (rec_rewrites' ~~ asmss)));
 
-    val goals = map (fn ((cargs, _, _), (_, eqn)) =>
-      (list_all_free (cargs, eqn), [])) (rec_rewrites' ~~ eqns);
+    val goals = map (fn ((cargs, _, _), eqn) =>
+      (list_all_free (cargs, eqn), [])) (rec_rewrites' ~~ eqns');
 
   in
-    thy' |>
-    ProofContext.init |>
+    lthy' |>
+    Variable.add_fixes (map fst lsrs) |> snd |>
     Proof.theorem_i NONE
-      (fn thss => ProofContext.theory (fn thy =>
+      (fn thss => fn goal_ctxt =>
          let
-           val simps = map standard (flat thss);
-           val (simps', thy') =
-             fold_map note ((map fst eqns ~~ atts) ~~ map single simps) thy;
-           val simps'' = maps snd simps'
+           val simps = ProofContext.export goal_ctxt lthy' (flat thss);
+           val (simps', lthy'') = fold_map (LocalTheory.note Thm.theoremK)
+             (names_atts' ~~ map single simps) lthy'
          in
-           thy'
-           |> note (("simps", [Simplifier.simp_add]), simps'')
+           lthy''
+           |> LocalTheory.note Thm.theoremK ((qualify (Binding.name "simps"),
+             [Attrib.internal (K Simplifier.simp_add)]), maps snd simps')
            |> snd
-           |> Sign.parent_path
-         end))
+         end)
       [goals] |>
     Proof.apply (Method.Basic (fn _ => Method.RAW_METHOD (fn _ =>
-      rewrite_goals_tac (map snd defs_thms') THEN
+      rewrite_goals_tac defs_thms THEN
       compose_tac (false, rule, length rule_prems) 1), Position.none)) |>
     Seq.hd
   end;
 
-fun gen_primrec note def alt_name invs fctxt eqns thy =
-  let
-    val ((names, strings), srcss) = apfst split_list (split_list eqns);
-    val atts = map (map (Attrib.attribute thy)) srcss;
-    val eqn_ts = map (fn s => Syntax.read_prop_global thy s
-      handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s)) strings;
-    val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq
-      (HOLogic.dest_Trueprop (Logic.strip_imp_concl eq))))
-      handle TERM _ => primrec_eq_err thy "not a proper equation" eq) eqn_ts;
-    val (_, eqn_ts') = OldPrimrecPackage.unify_consts thy rec_ts eqn_ts
-  in
-    gen_primrec_i note def alt_name
-      (Option.map (map (Syntax.read_term_global thy)) invs)
-      (Option.map (Syntax.read_term_global thy) fctxt)
-      (names ~~ eqn_ts' ~~ atts) thy
-  end;
-
-fun thy_note ((name, atts), thms) =
-  PureThy.add_thmss [((name, thms), atts)] #-> (fn [thms] => pair (name, thms));
-fun thy_def false ((name, atts), t) =
-      PureThy.add_defs false [((name, t), atts)] #-> (fn [thm] => pair (name, thm))
-  | thy_def true ((name, atts), t) =
-      PureThy.add_defs_unchecked false [((name, t), atts)] #-> (fn [thm] => pair (name, thm));
-
 in
 
-val add_primrec = gen_primrec thy_note (thy_def false);
-val add_primrec_unchecked = gen_primrec thy_note (thy_def true);
-val add_primrec_i = gen_primrec_i thy_note (thy_def false);
-val add_primrec_unchecked_i = gen_primrec_i thy_note (thy_def true);
+val add_primrec = gen_primrec false Specification.check_specification (K I);
+val add_primrec_cmd = gen_primrec true Specification.read_specification Syntax.read_term;
 
-end; (*local*)
+end;
 
 
 (* outer syntax *)
@@ -419,25 +404,26 @@
 val parser2 = (invariant -- P.$$$ ":") |--
     (Scan.repeat1 (unless_flag P.term) >> SOME) -- Scan.optional parser1 NONE ||
   (parser1 >> pair NONE);
-val parser3 =
-  unless_flag P.name -- Scan.optional parser2 (NONE, NONE) ||
-  (parser2 >> pair "");
-val parser4 =
-  (P.$$$ "unchecked" >> K true) -- Scan.optional parser3 ("", (NONE, NONE)) ||
-  (parser3 >> pair false);
 val options =
   Scan.optional (P.$$$ "(" |-- P.!!!
-    (parser4 --| P.$$$ ")")) (false, ("", (NONE, NONE)));
+    (parser2 --| P.$$$ ")")) (NONE, NONE);
+
+fun pipe_error t = P.!!! (Scan.fail_with (K
+  (cat_lines ["Equations must be separated by " ^ quote "|", quote t])));
 
-val primrec_decl =
-  options -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop);
+val statement = SpecParse.opt_thm_name ":" -- P.prop --| Scan.ahead
+  ((P.term :-- pipe_error) || Scan.succeed ("",""));
+
+val statements = P.enum1 "|" statement;
+
+val primrec_decl = P.opt_target -- options --
+  P.fixes -- P.for_fixes --| P.$$$ "where" -- statements;
 
 val _ =
   OuterSyntax.command "nominal_primrec" "define primitive recursive functions on nominal datatypes" K.thy_goal
-    (primrec_decl >> (fn ((unchecked, (alt_name, (invs, fctxt))), eqns) =>
-      Toplevel.print o Toplevel.theory_to_proof
-        ((if unchecked then add_primrec_unchecked else add_primrec) alt_name invs fctxt
-          (map P.triple_swap eqns))));
+    (primrec_decl >> (fn ((((opt_target, (invs, fctxt)), raw_fixes), raw_params), raw_spec) =>
+      Toplevel.print o Toplevel.local_theory_to_proof opt_target
+        (add_primrec_cmd invs fctxt raw_fixes raw_params raw_spec)));
 
 end;