# HG changeset patch
# User urbanc
# Date 1162392344 -3600
# Node ID cf9fe3c408b765fe55fac6e5337c7d7772081187
# Parent  de048d4968d9a6c5da1bbb636831992611a654b9
not needed anymore

diff -r de048d4968d9 -r cf9fe3c408b7 src/HOL/Nominal/Examples/Recursion.thy
--- a/src/HOL/Nominal/Examples/Recursion.thy	Wed Nov 01 15:44:31 2006 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,185 +0,0 @@
-(* $Id$ *)
-
-theory Recursion
-imports "Iteration" 
-begin
-
-types 'a f1_ty' = "name\<Rightarrow>('a::pt_name)"
-      'a f2_ty' = "lam\<Rightarrow>lam\<Rightarrow>'a\<Rightarrow>'a\<Rightarrow>('a::pt_name)"
-      'a f3_ty' = "lam\<Rightarrow>name\<Rightarrow>'a\<Rightarrow>('a::pt_name)"
-
-constdefs
-  rfun' :: "'a f1_ty' \<Rightarrow> 'a f2_ty' \<Rightarrow> 'a f3_ty' \<Rightarrow> lam \<Rightarrow> (lam\<times>'a::pt_name)" 
-  "rfun' f1 f2 f3 t \<equiv> 
-      (itfun 
-        (\<lambda>a. (Var a,f1 a)) 
-        (\<lambda>r1 r2. (App (fst r1) (fst r2), f2 (fst r1) (fst r2) (snd r1) (snd r2))) 
-        (\<lambda>a r. (Lam [a].(fst r),f3 (fst r) a (snd r)))
-       t)"
-
-  rfun :: "'a f1_ty' \<Rightarrow> 'a f2_ty' \<Rightarrow> 'a f3_ty' \<Rightarrow> lam \<Rightarrow> 'a::pt_name" 
-  "rfun f1 f2 f3 t \<equiv> snd (rfun' f1 f2 f3 t)"
-
-lemma fcb': 
-  fixes f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)"
-  and     c: "\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>(y::'a::pt_name) t. a\<sharp>f3 t a y)"
-  shows  "\<exists>a.  a \<sharp> (\<lambda>a r. (Lam [a].fst r, f3 (fst r) a (snd r))) \<and>
-               (\<forall>y.  a \<sharp> (Lam [a].fst y, f3 (fst y) a (snd y)))"
-using c f
-apply(auto)
-apply(rule_tac x="a" in exI)
-apply(auto simp add: abs_fresh fresh_prod)
-apply(rule_tac S="supp f3" in supports_fresh)
-apply(supports_simp add: perm_fst perm_snd)
-apply(simp add: supp_prod)
-apply(simp add: fresh_def)
-done
-
-lemma fsupp':
-  fixes f1::"('a::pt_name) f1_ty'"
-  and   f2::"('a::pt_name) f2_ty'"
-  and   f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)"
-  shows "finite((supp
-          (\<lambda>a. (Var a, f1 a),
-           \<lambda>r1 r2. (App (fst r1) (fst r2), f2 (fst r1) (fst r2) (snd r1) (snd r2)),
-           \<lambda>a r. (Lam [a].fst r, f3 (fst r) a (snd r))))::name set)"
-using f by (finite_guess add: perm_fst perm_snd fs_name1 supp_prod)
-
-lemma rfun'_fst:
-  fixes f1::"('a::pt_name) f1_ty'"
-  and   f2::"('a::pt_name) f2_ty'"
-  and   f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)" 
-  and     c: "(\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>(y::'a::pt_name) t. a\<sharp>f3 t a y))"
-  shows "fst (rfun' f1 f2 f3 t) = t"
-apply(rule lam.induct'[of "\<lambda>_. ((supp (f1,f2,f3))::name set)" "\<lambda>_ t. fst (rfun' f1 f2 f3 t) = t"])
-apply(fold fresh_def)
-apply(simp add: f)
-apply(unfold rfun'_def)
-apply(simp only: itfun_Var[OF fsupp'[OF f],OF fcb'[OF f, OF c]])
-apply(simp)
-apply(simp only: itfun_App[OF fsupp'[OF f],OF fcb'[OF f, OF c]])
-apply(simp)
-apply(auto)
-apply(rule trans)
-apply(rule_tac f="fst" in arg_cong)
-apply(rule itfun_Lam[OF fsupp'[OF f],OF fcb'[OF f, OF c]])
-apply(auto simp add: fresh_prod)
-apply(rule_tac S="supp f1" in supports_fresh)
-apply(supports_simp)
-apply(subgoal_tac "finite ((supp (f1,f2,f3))::name set)")
-apply(simp add: supp_prod)
-apply(rule f)
-apply(simp add: fresh_def)
-apply(rule_tac S="supp f2" in supports_fresh)
-apply(supports_simp add: perm_fst perm_snd)
-apply(subgoal_tac "finite ((supp (f1,f2,f3))::name set)")
-apply(simp add: supp_prod)
-apply(rule f)
-apply(simp add: fresh_def)
-apply(rule_tac S="supp f3" in supports_fresh)
-apply(supports_simp add: perm_fst perm_snd)
-apply(subgoal_tac "finite ((supp (f1,f2,f3))::name set)")
-apply(simp add: supp_prod)
-apply(rule f)
-apply(simp add: fresh_def)
-done
-
-lemma rfun'_Var:
-  fixes f1::"('a::pt_name) f1_ty'"
-  and   f2::"('a::pt_name) f2_ty'"
-  and   f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)"
-  and     c: "\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>(y::'a::pt_name) t. a\<sharp>f3 t a y)"
-  shows "rfun' f1 f2 f3 (Var c) = (Var c, f1 c)"
-apply(simp add: rfun'_def)
-apply(simp add: itfun_Var[OF fsupp'[OF f],OF fcb'[OF f, OF c]])
-done
-
-lemma rfun'_App:
-  fixes f1::"('a::pt_name) f1_ty'"
-  and   f2::"('a::pt_name) f2_ty'"
-  and   f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)"
-  and     c: "\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>(y::'a::pt_name) t. a\<sharp>f3 t a y)"
-  shows "rfun' f1 f2 f3 (App t1 t2) = 
-                (App t1 t2, f2 t1 t2 (rfun f1 f2 f3 t1) (rfun f1 f2 f3 t2))"
-apply(simp add: rfun'_def)
-apply(rule trans)
-apply(rule itfun_App[OF fsupp'[OF f],OF fcb'[OF f, OF c]])
-apply(fold rfun'_def)
-apply(simp_all add: rfun'_fst[OF f, OF c])
-apply(simp_all add: rfun_def)
-done
-
-lemma rfun'_Lam:
-  fixes f1::"('a::pt_name) f1_ty'"
-  and   f2::"('a::pt_name) f2_ty'"
-  and   f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)"
-  and     c: "\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>(y::'a::pt_name) t. a\<sharp>f3 t a y)"
-  and     a: "b\<sharp>(f1,f2,f3)"
-  shows "rfun' f1 f2 f3 (Lam [b].t) = (Lam [b].t, f3 t b (rfun f1 f2 f3 t))"
-using a f
-apply(simp add: rfun'_def)
-apply(rule trans)
-apply(rule itfun_Lam[OF fsupp'[OF f],OF fcb'[OF f, OF c]])
-apply(auto simp add: fresh_prod)
-apply(rule_tac S="supp f1" in supports_fresh)
-apply(supports_simp)
-apply(simp add: supp_prod)
-apply(simp add: fresh_def)
-apply(rule_tac S="supp f2" in supports_fresh)
-apply(supports_simp add: perm_fst perm_snd)
-apply(simp add: supp_prod)
-apply(simp add: fresh_def)
-apply(rule_tac S="supp f3" in supports_fresh)
-apply(supports_simp add: perm_snd perm_fst)
-apply(simp add: supp_prod)
-apply(simp add: fresh_def)
-apply(fold rfun'_def)
-apply(simp_all add: rfun'_fst[OF f, OF c])
-apply(simp_all add: rfun_def)
-done
-
-lemma rfun_Var:
-  fixes f1::"('a::pt_name) f1_ty'"
-  and   f2::"('a::pt_name) f2_ty'"
-  and   f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)"
-  and     c: "\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>(y::'a::pt_name) t. a\<sharp>f3 t a y)"
-  shows "rfun f1 f2 f3 (Var c) = f1 c"
-apply(unfold rfun_def)
-apply(simp add: rfun'_Var[OF f, OF c])
-done
-
-lemma rfun_App:
-  fixes f1::"('a::pt_name) f1_ty'"
-  and   f2::"('a::pt_name) f2_ty'"
-  and   f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)"
-  and     c: "\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>(y::'a::pt_name) t. a\<sharp>f3 t a y)"
-  shows "rfun f1 f2 f3 (App t1 t2) = f2 t1 t2 (rfun f1 f2 f3 t1) (rfun f1 f2 f3 t2)"
-apply(unfold rfun_def)
-apply(simp add: rfun'_App[OF f, OF c])
-apply(simp add: rfun_def)
-done
-
-lemma rfun_Lam:
-  fixes f1::"('a::pt_name) f1_ty'"
-  and   f2::"('a::pt_name) f2_ty'"
-  and   f3::"('a::pt_name) f3_ty'"
-  assumes f: "finite ((supp (f1,f2,f3))::name set)"
-  and     c: "\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>(y::'a::pt_name) t. a\<sharp>f3 t a y)"
-  and     a: "b\<sharp>(f1,f2,f3)"
-  shows "rfun f1 f2 f3 (Lam [b].t) = f3 t b (rfun f1 f2 f3 t)"
-using a
-apply(unfold rfun_def)
-apply(simp add: rfun'_Lam[OF f, OF c])
-apply(simp add: rfun_def)
-done
-
-
-end
\ No newline at end of file