--- a/Nominal/Ex/Lambda.thy Wed Apr 14 10:29:56 2010 +0200
+++ b/Nominal/Ex/Lambda.thy Wed Apr 14 13:21:11 2010 +0200
@@ -127,6 +127,16 @@
| t_App[intro]: "\<lbrakk>\<Gamma> \<turnstile> t1 : T1 \<rightarrow> T2 \<or> \<Gamma> \<turnstile> t2 : T1\<rbrakk> \<Longrightarrow> \<Gamma> \<turnstile> App t1 t2 : T2"
| t_Lam[intro]: "\<lbrakk>atom x \<sharp> \<Gamma>; (x, T1) # \<Gamma> \<turnstile> t : T2\<rbrakk> \<Longrightarrow> \<Gamma> \<turnstile> Lam x t : T1 \<rightarrow> T2"
+ML {*
+val inductive_atomize = @{thms induct_atomize};
+
+val atomize_conv =
+ MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE))
+ (HOL_basic_ss addsimps inductive_atomize);
+val atomize_intr = Conv.fconv_rule (Conv.prems_conv ~1 atomize_conv);
+fun atomize_induct ctxt = Conv.fconv_rule (Conv.prems_conv ~1
+ (Conv.params_conv ~1 (K (Conv.prems_conv ~1 atomize_conv)) ctxt));
+*}
ML {*
fun map_term f t =
@@ -186,12 +196,27 @@
ML {*
open Nominal_Permeq
+open Nominal_ThmDecls
+*}
+
+ML {*
+fun mk_perm p trm =
+let
+ val ty = fastype_of trm
+in
+ Const (@{const_name "permute"}, @{typ "perm"} --> ty --> ty) $ p $ trm
+end
+
+fun mk_minus p =
+ Const (@{const_name "uminus"}, @{typ "perm => perm"}) $ p
*}
ML {*
fun single_case_tac ctxt pred_names pi intro =
let
- val rule = Drule.instantiate' [] [SOME pi] @{thm permute_boolE}
+ val thy = ProofContext.theory_of ctxt
+ val cpi = Thm.cterm_of thy (mk_minus pi)
+ val rule = Drule.instantiate' [] [SOME cpi] @{thm permute_boolE}
in
eqvt_strict_tac ctxt [] [] THEN'
SUBPROOF (fn {prems, context as ctxt, ...} =>
@@ -208,130 +233,85 @@
*}
ML {*
-fun eqvt_rel_tac pred_name =
+fun prepare_pred params_no pi pred =
+let
+ val (c, xs) = strip_comb pred;
+ val (xs1, xs2) = chop params_no xs
+in
+ HOLogic.mk_imp
+ (pred, list_comb (c, xs1 @ map (mk_perm pi) xs2))
+end
+*}
+
+ML {*
+fun transp ([] :: _) = []
+ | transp xs = map hd xs :: transp (map tl xs);
+*}
+
+ML {*
+ Local_Theory.note;
+ Local_Theory.notes;
+ fold_map
+*}
+
+ML {*
+fun note_named_thm (name, thm) ctxt =
+let
+ val thm_name = Binding.qualified_name
+ (Long_Name.qualify (Long_Name.base_name name) "eqvt")
+ val attr = Attrib.internal (K eqvt_add)
+in
+ Local_Theory.note ((thm_name, [attr]), [thm]) ctxt
+end
+*}
+
+ML {*
+fun eqvt_rel_tac pred_name ctxt =
let
val thy = ProofContext.theory_of ctxt
val ({names, ...}, {raw_induct, intrs, ...}) =
Inductive.the_inductive ctxt (Sign.intern_const thy pred_name)
- val param_no = length (Inductive.params_of raw_induct)
- val (([raw_concl], [pi]), ctxt') =
+ val raw_induct = atomize_induct ctxt raw_induct;
+ val intros = map atomize_intr intrs;
+ val params_no = length (Inductive.params_of raw_induct)
+ val (([raw_concl], [raw_pi]), ctxt') =
ctxt |> Variable.import_terms false [concl_of raw_induct]
- ||>> Variable.variant_fixes ["pi"];
+ ||>> Variable.variant_fixes ["pi"]
+ val pi = Free (raw_pi, @{typ perm})
val preds = map (fst o HOLogic.dest_imp)
(HOLogic.dest_conj (HOLogic.dest_Trueprop raw_concl));
+ val goal = HOLogic.mk_Trueprop
+ (foldr1 HOLogic.mk_conj (map (prepare_pred params_no pi) preds))
+ val thm = Goal.prove ctxt' [] [] goal (fn {context,...} =>
+ HEADGOAL (EVERY' (rtac raw_induct :: map (single_case_tac context names pi) intros)))
+ |> singleton (ProofContext.export ctxt' ctxt)
+ val thms = map (fn th => zero_var_indexes (th RS mp)) (Datatype_Aux.split_conj_thm thm)
in
-
+ ctxt |> fold_map note_named_thm (names ~~ thms)
+ |> snd
end
*}
-
-lemma [eqvt]:
- assumes a: "valid Gamma"
- shows "valid (p \<bullet> Gamma)"
-using a
-apply(induct)
-apply(tactic {* my_tac @{context} ["Lambda.valid"] @{cterm "- p"} @{thm valid.intros(1)} 1 *})
-apply(tactic {* my_tac @{context }["Lambda.valid"] @{cterm "- p"} @{thm valid.intros(2)} 1 *})
-done
-
-lemma
- shows "Gamma \<turnstile> t : T \<longrightarrow> (p \<bullet> Gamma) \<turnstile> (p \<bullet> t) : (p \<bullet> T)"
-ML_prf {*
-val ({names, ...}, {raw_induct, ...}) =
- Inductive.the_inductive @{context} (Sign.intern_const @{theory} "typing")
-*}
-apply(tactic {* rtac raw_induct 1 *})
-apply(tactic {* my_tac @{context} ["Lambda.typing"] @{cterm "- p"} @{thm typing.intros(1)} 1 *})
-apply(tactic {* my_tac @{context} ["Lambda.typing"] @{cterm "- p"} @{thm typing.intros(2)} 1 *})
-apply(tactic {* my_tac @{context} ["Lambda.typing"] @{cterm "- p"} @{thm typing.intros(3)} 1 *})
-done
+ML {*
+local structure P = OuterParse and K = OuterKeyword in
-lemma uu[eqvt]:
- assumes a: "Gamma \<turnstile> t : T"
- shows "(p \<bullet> Gamma) \<turnstile> (p \<bullet> t) : (p \<bullet> T)"
-using a
-apply(induct)
-apply(tactic {* my_tac @{context} @{thms typing.intros} 1 *})
-apply(perm_strict_simp)
-apply(rule typing.intros)
-apply(rule conj_mono[THEN mp])
-prefer 3
-apply(assumption)
-apply(rule impI)
-prefer 2
-apply(rule impI)
-apply(simp)
-apply(auto)[1]
-apply(simp)
-apply(tactic {* my_tac @{context} @{thms typing.intros} 1 *})
-done
+val _ =
+ OuterSyntax.local_theory "equivariance"
+ "prove equivariance for inductive predicate involving nominal datatypes" K.thy_decl
+ (P.xname >> eqvt_rel_tac);
-(*
-inductive
- typing :: "(name\<times>ty) list \<Rightarrow> lam \<Rightarrow> ty \<Rightarrow> bool" ("_ \<turnstile> _ : _" [60,60,60] 60)
-where
- t_Var[intro]: "\<lbrakk>valid \<Gamma>; (x, T) \<in> set \<Gamma>\<rbrakk> \<Longrightarrow> \<Gamma> \<turnstile> Var x : T"
- | t_App[intro]: "\<lbrakk>\<Gamma> \<turnstile> t1 : T1 \<rightarrow> T2 \<and> \<Gamma> \<turnstile> t2 : T1\<rbrakk> \<Longrightarrow> \<Gamma> \<turnstile> App t1 t2 : T2"
- | t_Lam[intro]: "\<lbrakk>atom x \<sharp> \<Gamma>; (x, T1) # \<Gamma> \<turnstile> t : T2\<rbrakk> \<Longrightarrow> \<Gamma> \<turnstile> Lam x t : T1 \<rightarrow> T2"
-
-lemma uu[eqvt]:
- assumes a: "Gamma \<turnstile> t : T"
- shows "(p \<bullet> Gamma) \<turnstile> (p \<bullet> t) : (p \<bullet> T)"
-using a
-apply(induct)
-apply(tactic {* my_tac @{context} @{thms typing.intros} 1 *})
-apply(tactic {* my_tac @{context} @{thms typing.intros} 1 *})
-apply(tactic {* my_tac @{context} @{thms typing.intros} 1 *})
-done
-*)
-
-ML {*
-val inductive_atomize = @{thms induct_atomize};
-
-val atomize_conv =
- MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE))
- (HOL_basic_ss addsimps inductive_atomize);
-val atomize_intr = Conv.fconv_rule (Conv.prems_conv ~1 atomize_conv);
-fun atomize_induct ctxt = Conv.fconv_rule (Conv.prems_conv ~1
- (Conv.params_conv ~1 (K (Conv.prems_conv ~1 atomize_conv)) ctxt));
+end;
*}
-ML {*
-val ({names, ...}, {raw_induct, intrs, elims, ...}) =
- Inductive.the_inductive @{context} (Sign.intern_const @{theory} "typing")
-*}
-
-ML {* val ind_params = Inductive.params_of raw_induct *}
-ML {* val raw_induct = atomize_induct @{context} raw_induct; *}
-ML {* val elims = map (atomize_induct @{context}) elims; *}
-ML {* val monos = Inductive.get_monos @{context}; *}
+equivariance valid
+equivariance typing
-lemma
- shows "Gamma \<turnstile> t : T \<longrightarrow> (p \<bullet> Gamma) \<turnstile> (p \<bullet> t) : (p \<bullet> T)"
-apply(tactic {* rtac raw_induct 1 *})
-apply(tactic {* my_tac @{context} intrs 1 *})
-apply(perm_strict_simp)
-apply(rule typing.intros)
-oops
-
-
+thm valid.eqvt
+thm typing.eqvt
thm eqvts
thm eqvts_raw
-declare permute_lam_raw.simps[eqvt]
-thm alpha_gen_real_eqvt
-(*declare alpha_gen_real_eqvt[eqvt]*)
-
-lemma
- assumes a: "alpha_lam_raw t1 t2"
- shows "alpha_lam_raw (p \<bullet> t1) (p \<bullet> t2)"
-using a
-apply(induct)
-apply(tactic {* my_tac @{context} @{thms alpha_lam_raw.intros} 1 *})
-oops
-
-thm alpha_lam_raw.intros[no_vars]
inductive
alpha_lam_raw'
@@ -342,18 +322,15 @@
| "\<exists>pi. ({atom name}, lam_raw) \<approx>gen alpha_lam_raw fv_lam_raw pi ({atom namea}, lam_rawa) \<Longrightarrow>
alpha_lam_raw' (Lam_raw name lam_raw) (Lam_raw namea lam_rawa)"
+declare permute_lam_raw.simps[eqvt]
+(*declare alpha_gen_real_eqvt[eqvt]*)
+(*equivariance alpha_lam_raw'*)
+
lemma
assumes a: "alpha_lam_raw' t1 t2"
shows "alpha_lam_raw' (p \<bullet> t1) (p \<bullet> t2)"
using a
apply(induct)
-apply(tactic {* my_tac @{context} @{thms alpha_lam_raw'.intros} 1 *})
-apply(tactic {* my_tac @{context} @{thms alpha_lam_raw'.intros} 1 *})
-apply(perm_strict_simp)
-apply(rule alpha_lam_raw'.intros)
-apply(simp add: alphas)
-apply(rule_tac p="- p" in permute_boolE)
-apply(perm_simp permute_minus_cancel(2))
oops