--- a/src/HOL/HOLCF/Fixrec.thy Wed Jan 13 23:02:28 2016 +0100
+++ b/src/HOL/HOLCF/Fixrec.thy Wed Jan 13 23:07:06 2016 +0100
@@ -9,7 +9,7 @@
keywords "fixrec" :: thy_decl
begin
-subsection {* Pattern-match monad *}
+subsection \<open>Pattern-match monad\<close>
default_sort cpo
@@ -46,13 +46,13 @@
"succeed\<cdot>x \<noteq> fail" "fail \<noteq> succeed\<cdot>x"
by (simp_all add: succeed_def fail_def cont_Abs_match Abs_match_inject)
-subsubsection {* Run operator *}
+subsubsection \<open>Run operator\<close>
definition
run :: "'a match \<rightarrow> 'a::pcpo" where
"run = (\<Lambda> m. sscase\<cdot>\<bottom>\<cdot>(fup\<cdot>ID)\<cdot>(Rep_match m))"
-text {* rewrite rules for run *}
+text \<open>rewrite rules for run\<close>
lemma run_strict [simp]: "run\<cdot>\<bottom> = \<bottom>"
unfolding run_def
@@ -66,7 +66,7 @@
unfolding run_def succeed_def
by (simp add: cont_Rep_match cont_Abs_match Abs_match_inverse)
-subsubsection {* Monad plus operator *}
+subsubsection \<open>Monad plus operator\<close>
definition
mplus :: "'a match \<rightarrow> 'a match \<rightarrow> 'a match" where
@@ -76,7 +76,7 @@
mplus_syn :: "['a match, 'a match] \<Rightarrow> 'a match" (infixr "+++" 65) where
"m1 +++ m2 == mplus\<cdot>m1\<cdot>m2"
-text {* rewrite rules for mplus *}
+text \<open>rewrite rules for mplus\<close>
lemma mplus_strict [simp]: "\<bottom> +++ m = \<bottom>"
unfolding mplus_def
@@ -96,7 +96,7 @@
lemma mplus_assoc: "(x +++ y) +++ z = x +++ (y +++ z)"
by (cases x, simp_all)
-subsection {* Match functions for built-in types *}
+subsection \<open>Match functions for built-in types\<close>
default_sort pcpo
@@ -192,12 +192,12 @@
"match_FF\<cdot>\<bottom>\<cdot>k = \<bottom>"
by (simp_all add: match_FF_def)
-subsection {* Mutual recursion *}
+subsection \<open>Mutual recursion\<close>
-text {*
+text \<open>
The following rules are used to prove unfolding theorems from
fixed-point definitions of mutually recursive functions.
-*}
+\<close>
lemma Pair_equalI: "\<lbrakk>x \<equiv> fst p; y \<equiv> snd p\<rbrakk> \<Longrightarrow> (x, y) \<equiv> p"
by simp
@@ -216,22 +216,22 @@
"\<lbrakk>f \<equiv> fix\<cdot>(Abs_cfun F); cont F; adm P; P \<bottom>; \<And>x. P x \<Longrightarrow> P (F x)\<rbrakk> \<Longrightarrow> P f"
by (simp add: fix_ind)
-text {* lemma for proving rewrite rules *}
+text \<open>lemma for proving rewrite rules\<close>
lemma ssubst_lhs: "\<lbrakk>t = s; P s = Q\<rbrakk> \<Longrightarrow> P t = Q"
by simp
-subsection {* Initializing the fixrec package *}
+subsection \<open>Initializing the fixrec package\<close>
ML_file "Tools/holcf_library.ML"
ML_file "Tools/fixrec.ML"
-method_setup fixrec_simp = {*
+method_setup fixrec_simp = \<open>
Scan.succeed (SIMPLE_METHOD' o Fixrec.fixrec_simp_tac)
-*} "pattern prover for fixrec constants"
+\<close> "pattern prover for fixrec constants"
-setup {*
+setup \<open>
Fixrec.add_matchers
[ (@{const_name up}, @{const_name match_up}),
(@{const_name sinl}, @{const_name match_sinl}),
@@ -242,7 +242,7 @@
(@{const_name TT}, @{const_name match_TT}),
(@{const_name FF}, @{const_name match_FF}),
(@{const_name bottom}, @{const_name match_bottom}) ]
-*}
+\<close>
hide_const (open) succeed fail run