Partway through changing function application syntax style.

1 files changed, 17 insertions, 17 deletions

diff --git a/Prod.thy b/Prod.thy
index 8fa73f3..e4e7091 100644
--- a/Prod.thy
+++ b/Prod.thy
@@ -15,7 +15,7 @@ section \<open>Constants and syntax\<close>
 axiomatization
   Prod :: "[Term, Typefam] \<Rightarrow> Term" and
   lambda :: "[Term, Term \<Rightarrow> Term] \<Rightarrow> Term" and
-  appl :: "[Term, Term] \<Rightarrow> Term"  (infixl "`" 60)
+  appl :: "[Term, Term] \<Rightarrow> Term"  ("(1_`_)" [61, 60] 60)
     \<comment> \<open>Application binds tighter than abstraction.\<close>
 
 syntax
@@ -27,48 +27,48 @@ syntax
 text "The translations below bind the variable \<open>x\<close> in the expressions \<open>B\<close> and \<open>b\<close>."
 
 translations
-  "\<Prod>x:A. B" \<rightleftharpoons> "CONST Prod A (\<lambda>x. B)"
-  "\<^bold>\<lambda>x:A. b" \<rightleftharpoons> "CONST lambda A (\<lambda>x. b)"
-  "PROD x:A. B" \<rightharpoonup> "CONST Prod A (\<lambda>x. B)"
-  "%%x:A. b" \<rightharpoonup> "CONST lambda A (\<lambda>x. b)"
+  "\<Prod>x:A. B" \<rightleftharpoons> "CONST Prod(A, \<lambda>x. B)"
+  "\<^bold>\<lambda>x:A. b" \<rightleftharpoons> "CONST lambda(A, \<lambda>x. b)"
+  "PROD x:A. B" \<rightharpoonup> "CONST Prod(A, \<lambda>x. B)"
+  "%%x:A. b" \<rightharpoonup> "CONST lambda(A, \<lambda>x. b)"
 
 text "Nondependent functions are a special case."
 
 abbreviation Function :: "[Term, Term] \<Rightarrow> Term"  (infixr "\<rightarrow>" 40)
-  where "A \<rightarrow> B \<equiv> \<Prod>_:A. B"
+  where "A \<rightarrow> B \<equiv> \<Prod>_: A. B"
 
 
 section \<open>Type rules\<close>
 
 axiomatization where
-  Prod_form: "\<And>i A B. \<lbrakk>A : U(i); B: A \<longrightarrow> U(i)\<rbrakk> \<Longrightarrow> \<Prod>x:A. B x : U(i)"
+  Prod_form: "\<And>i A B. \<lbrakk>A: U(i); B: A \<longrightarrow> U(i)\<rbrakk> \<Longrightarrow> \<Prod>x:A. B(x): U(i)"
 and
-  Prod_intro: "\<And>i A B b. \<lbrakk>A : U(i); \<And>x. x : A \<Longrightarrow> b x : B x\<rbrakk> \<Longrightarrow> \<^bold>\<lambda>x:A. b x : \<Prod>x:A. B x"
+  Prod_intro: "\<And>i A B b. \<lbrakk>A: U(i); B: A \<longrightarrow> U(i); \<And>x. x: A \<Longrightarrow> b(x): B(x)\<rbrakk> \<Longrightarrow> \<^bold>\<lambda>x:A. b(x): \<Prod>x:A. B(x)"
 and
-  Prod_elim: "\<And>A B f a. \<lbrakk>f : \<Prod>x:A. B x; a : A\<rbrakk> \<Longrightarrow> f`a : B a"
+  Prod_elim: "\<And>A B f a. \<lbrakk>f: \<Prod>x:A. B(x); a: A\<rbrakk> \<Longrightarrow> f`a: B(a)"
 and
-  Prod_comp: "\<And>A B b a. \<lbrakk>\<And>x. x : A \<Longrightarrow> b x : B x; a : A\<rbrakk> \<Longrightarrow> (\<^bold>\<lambda>x:A. b x)`a \<equiv> b a"
+  Prod_comp: "\<And>i A B b a. \<lbrakk>A: U(i); B: A \<longrightarrow> U(i); \<And>x. x: A \<Longrightarrow> b(x): B(x); a: A\<rbrakk> \<Longrightarrow> (\<^bold>\<lambda>x:A. b(x))`a \<equiv> b(a)"
 and
-  Prod_uniq: "\<And>A B f. f : \<Prod>x:A. B x \<Longrightarrow> \<^bold>\<lambda>x:A. (f`x) \<equiv> f"
+  Prod_uniq: "\<And>A B f. f : \<Prod>x:A. B(x) \<Longrightarrow> \<^bold>\<lambda>x:A. (f`x) \<equiv> f"
 
 text "
   Note that the syntax \<open>\<^bold>\<lambda>\<close> (bold lambda) used for dependent functions clashes with the proof term syntax (cf. \<section>2.5.2 of the Isabelle/Isar Implementation).
 "
 
 text "
-  In addition to the usual type rules, it is a meta-theorem (*PROVE THIS!*) that whenever \<open>\<Prod>x:A. B x : U(i)\<close> is derivable from some set of premises \<Gamma>, then so are \<open>A : U(i)\<close> and \<open>B: A \<longrightarrow> U(i)\<close>.
+  In addition to the usual type rules, it is a meta-theorem (*PROVE THIS!*) that whenever \<open>\<Prod>x:A. B x: U(i)\<close> is derivable from some set of premises \<Gamma>, then so are \<open>A: U(i)\<close> and \<open>B: A \<longrightarrow> U(i)\<close>.
   
   That is to say, the following inference rules are admissible, and it simplifies proofs greatly to axiomatize them directly.
 "
 
 axiomatization where
-  Prod_form_cond1: "\<And>i A B. (\<Prod>x:A. B x : U(i)) \<Longrightarrow> A : U(i)"
+  Prod_form_cond1: "\<And>i A B. (\<Prod>x:A. B(x): U(i)) \<Longrightarrow> A: U(i)"
 and
-  Prod_form_cond2: "\<And>i A B. (\<Prod>x:A. B x : U(i)) \<Longrightarrow> B: A \<longrightarrow> U(i)"
+  Prod_form_cond2: "\<And>i A B. (\<Prod>x:A. B(x): U(i)) \<Longrightarrow> B: A \<longrightarrow> U(i)"
 
 text "Set up the standard reasoner to use the type rules:"
 
-lemmas Prod_rules [intro] = Prod_form Prod_intro Prod_elim Prod_comp Prod_uniq
+lemmas Prod_rules = Prod_form Prod_intro Prod_elim Prod_comp Prod_uniq
 lemmas Prod_form_conds [intro (*elim, wellform*)] = Prod_form_cond1 Prod_form_cond2
 lemmas Prod_comps [comp] = Prod_comp Prod_uniq
 
@@ -84,9 +84,9 @@ where
 and
   Unit_intro: "\<star> : \<one>"
 and
-  Unit_elim: "\<And>i C c a. \<lbrakk>C: \<one> \<longrightarrow> U(i); c : C \<star>; a : \<one>\<rbrakk> \<Longrightarrow> ind\<^sub>\<one> C c a : C a"
+  Unit_elim: "\<And>i C c a. \<lbrakk>C: \<one> \<longrightarrow> U(i); c : C(\<star>); a : \<one>\<rbrakk> \<Longrightarrow> ind\<^sub>\<one>(C, c, a) : C(a)"
 and
-  Unit_comp: "\<And>i C c. \<lbrakk>C: \<one> \<longrightarrow> U(i); c : C \<star>\<rbrakk> \<Longrightarrow> ind\<^sub>\<one> C c \<star> \<equiv> c"
+  Unit_comp: "\<And>i C c. \<lbrakk>C: \<one> \<longrightarrow> U(i); c : C(\<star>)\<rbrakk> \<Longrightarrow> ind\<^sub>\<one>(C, c, \<star>) \<equiv> c"
 
 lemmas Unit_rules [intro] = Unit_form Unit_intro Unit_elim Unit_comp
 lemmas Unit_comps [comp] = Unit_comp