| author | berghofe |
| Sat, 13 Dec 2008 13:24:45 +0100 | |
| changeset 29097 | 68245155eb58 |
| parent 29088 | 95a239a5e055 |
| child 29098 | 6b23a58cc67c |
| child 29099 | bebd671c6055 |
--- a/src/HOL/Nominal/Examples/CK_Machine.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/CK_Machine.thy Sat Dec 13 13:24:45 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)+
--- a/src/HOL/Nominal/Examples/CR_Takahashi.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/CR_Takahashi.thy Sat Dec 13 13:24:45 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)
--- a/src/HOL/Nominal/Examples/Compile.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/Compile.thy Sat Dec 13 13:24:45 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
--- a/src/HOL/Nominal/Examples/Contexts.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/Contexts.thy Sat Dec 13 13:24:45 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:
--- a/src/HOL/Nominal/Examples/Crary.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/Crary.thy Sat Dec 13 13:24:45 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)+
--- a/src/HOL/Nominal/Examples/Fsub.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/Fsub.thy Sat Dec 13 13:24:45 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)
--- a/src/HOL/Nominal/Examples/Height.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/Height.thy Sat Dec 13 13:24:45 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)
--- a/src/HOL/Nominal/Examples/Lam_Funs.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/Lam_Funs.thy Sat Dec 13 13:24:45 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:
--- a/src/HOL/Nominal/Examples/LocalWeakening.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/LocalWeakening.thy Sat Dec 13 13:24:45 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
--- a/src/HOL/Nominal/Examples/SN.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/SN.thy Sat Dec 13 13:24:45 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)
--- a/src/HOL/Nominal/Examples/SOS.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/SOS.thy Sat Dec 13 13:24:45 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:
--- a/src/HOL/Nominal/Examples/Standardization.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/Standardization.thy Sat Dec 13 13:24:45 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)
--- a/src/HOL/Nominal/Examples/Type_Preservation.thy Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/Examples/Type_Preservation.thy Sat Dec 13 13:24:45 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)
--- a/src/HOL/Nominal/nominal_primrec.ML Fri Dec 12 12:14:02 2008 +0100 +++ b/src/HOL/Nominal/nominal_primrec.ML Sat Dec 13 13:24:45 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;