# HG changeset patch
# User wenzelm
# Date 1319295444 -7200
# Node ID 401f91ed8a93b7ece267a1f2661cae6fbb74be82
# Parent  87950f7520996eb718dcaa3b9e3c46af2cb5bb27
discontinued redundant ASCII syntax;

diff -r 87950f752099 -r 401f91ed8a93 src/Cube/Cube.thy
--- a/src/Cube/Cube.thy	Sat Oct 22 16:44:34 2011 +0200
+++ b/src/Cube/Cube.thy	Sat Oct 22 16:57:24 2011 +0200
@@ -21,42 +21,36 @@
   MT_context :: "context" and
   Context :: "[typing, context] => context" and
   star :: "term"  ("*") and
-  box :: "term"  ("[]") and
+  box :: "term"  ("\<box>") and
   app :: "[term, term] => term"  (infixl "^" 20) and
   Has_type :: "[term, term] => typing"
 
-notation (xsymbols)
-  box  ("\<box>")
-
 nonterminal context' and typing'
 
 syntax
-  "_Trueprop" :: "[context', typing'] => prop"  ("(_/ |- _)")
+  "_Trueprop" :: "[context', typing'] => prop"  ("(_/ \<turnstile> _)")
   "_Trueprop1" :: "typing' => prop"  ("(_)")
   "" :: "id => context'"  ("_")
   "" :: "var => context'"  ("_")
   "_MT_context" :: "context'"  ("")
   "_Context" :: "[typing', context'] => context'"  ("_ _")
   "_Has_type" :: "[term, term] => typing'"  ("(_:/ _)" [0, 0] 5)
-  "_Lam" :: "[idt, term, term] => term"  ("(3Lam _:_./ _)" [0, 0, 0] 10)
-  "_Pi" :: "[idt, term, term] => term"  ("(3Pi _:_./ _)" [0, 0] 10)
-  "_arrow" :: "[term, term] => term"  (infixr "->" 10)
+  "_Lam" :: "[idt, term, term] => term"  ("(3\<Lambda> _:_./ _)" [0, 0, 0] 10)
+  "_Pi" :: "[idt, term, term] => term"  ("(3\<Pi> _:_./ _)" [0, 0] 10)
+  "_arrow" :: "[term, term] => term"  (infixr "\<rightarrow>" 10)
 
 translations
   "_Trueprop(G, t)" == "CONST Trueprop(G, t)"
-  ("prop") "x:X" == ("prop") "|- x:X"
+  ("prop") "x:X" == ("prop") "\<turnstile> x:X"
   "_MT_context" == "CONST MT_context"
   "_Context" == "CONST Context"
   "_Has_type" == "CONST Has_type"
-  "Lam x:A. B" == "CONST Abs(A, %x. B)"
-  "Pi x:A. B" => "CONST Prod(A, %x. B)"
-  "A -> B" => "CONST Prod(A, %_. B)"
+  "\<Lambda> x:A. B" == "CONST Abs(A, %x. B)"
+  "\<Pi> x:A. B" => "CONST Prod(A, %x. B)"
+  "A \<rightarrow> B" => "CONST Prod(A, %_. B)"
 
 syntax (xsymbols)
-  "_Trueprop" :: "[context', typing'] => prop"    ("(_/ \<turnstile> _)")
-  "_Lam" :: "[idt, term, term] => term"    ("(3\<Lambda> _:_./ _)" [0, 0, 0] 10)
   "_Pi" :: "[idt, term, term] => term"    ("(3\<Pi> _:_./ _)" [0, 0] 10)
-  "_arrow" :: "[term, term] => term"    (infixr "\<rightarrow>" 10)
 
 print_translation {*
   [(@{const_syntax Prod},
@@ -64,10 +58,10 @@
 *}
 
 axiomatization where
-  s_b: "*: []"  and
+  s_b: "*: \<box>"  and
 
-  strip_s: "[| A:*;  a:A ==> G |- x:X |] ==> a:A G |- x:X" and
-  strip_b: "[| A:[]; a:A ==> G |- x:X |] ==> a:A G |- x:X" and
+  strip_s: "[| A:*;  a:A ==> G \<turnstile> x:X |] ==> a:A G \<turnstile> x:X" and
+  strip_b: "[| A:\<box>; a:A ==> G \<turnstile> x:X |] ==> a:A G \<turnstile> x:X" and
 
   app: "[| F:Prod(A, B); C:A |] ==> F^C: B(C)" and
 
@@ -82,7 +76,7 @@
 lemmas rules = simple
 
 lemma imp_elim:
-  assumes "f:A->B" and "a:A" and "f^a:B ==> PROP P"
+  assumes "f:A\<rightarrow>B" and "a:A" and "f^a:B ==> PROP P"
   shows "PROP P" by (rule app assms)+
 
 lemma pi_elim:
@@ -91,25 +85,31 @@
 
 
 locale L2 =
-  assumes pi_bs: "[| A:[]; !!x. x:A ==> B(x):* |] ==> Prod(A,B):*"
-    and lam_bs: "[| A:[]; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):* |]
+  assumes pi_bs: "[| A:\<box>; !!x. x:A ==> B(x):* |] ==> Prod(A,B):*"
+    and lam_bs: "[| A:\<box>; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):* |]
                    ==> Abs(A,f) : Prod(A,B)"
+begin
 
-lemmas (in L2) rules = simple lam_bs pi_bs
+lemmas rules = simple lam_bs pi_bs
+
+end
 
 
 locale Lomega =
   assumes
-    pi_bb: "[| A:[]; !!x. x:A ==> B(x):[] |] ==> Prod(A,B):[]"
-    and lam_bb: "[| A:[]; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):[] |]
+    pi_bb: "[| A:\<box>; !!x. x:A ==> B(x):\<box> |] ==> Prod(A,B):\<box>"
+    and lam_bb: "[| A:\<box>; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):\<box> |]
                    ==> Abs(A,f) : Prod(A,B)"
+begin
 
-lemmas (in Lomega) rules = simple lam_bb pi_bb
+lemmas rules = simple lam_bb pi_bb
+
+end
 
 
 locale LP =
-  assumes pi_sb: "[| A:*; !!x. x:A ==> B(x):[] |] ==> Prod(A,B):[]"
-    and lam_sb: "[| A:*; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):[] |]
+  assumes pi_sb: "[| A:*; !!x. x:A ==> B(x):\<box> |] ==> Prod(A,B):\<box>"
+    and lam_sb: "[| A:*; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):\<box> |]
                    ==> Abs(A,f) : Prod(A,B)"
 begin
 
diff -r 87950f752099 -r 401f91ed8a93 src/Cube/Example.thy
--- a/src/Cube/Example.thy	Sat Oct 22 16:44:34 2011 +0200
+++ b/src/Cube/Example.thy	Sat Oct 22 16:57:24 2011 +0200
@@ -30,98 +30,98 @@
 
 subsection {* Simple types *}
 
-schematic_lemma "A:* |- A->A : ?T"
+schematic_lemma "A:* \<turnstile> A\<rightarrow>A : ?T"
   by (depth_solve rules)
 
-schematic_lemma "A:* |- Lam a:A. a : ?T"
+schematic_lemma "A:* \<turnstile> \<Lambda> a:A. a : ?T"
   by (depth_solve rules)
 
-schematic_lemma "A:* B:* b:B |- Lam x:A. b : ?T"
+schematic_lemma "A:* B:* b:B \<turnstile> \<Lambda> x:A. b : ?T"
   by (depth_solve rules)
 
-schematic_lemma "A:* b:A |- (Lam a:A. a)^b: ?T"
+schematic_lemma "A:* b:A \<turnstile> (\<Lambda> a:A. a)^b: ?T"
   by (depth_solve rules)
 
-schematic_lemma "A:* B:* c:A b:B |- (Lam x:A. b)^ c: ?T"
+schematic_lemma "A:* B:* c:A b:B \<turnstile> (\<Lambda> x:A. b)^ c: ?T"
   by (depth_solve rules)
 
-schematic_lemma "A:* B:* |- Lam a:A. Lam b:B. a : ?T"
+schematic_lemma "A:* B:* \<turnstile> \<Lambda> a:A. \<Lambda> b:B. a : ?T"
   by (depth_solve rules)
 
 
 subsection {* Second-order types *}
 
-schematic_lemma (in L2) "|- Lam A:*. Lam a:A. a : ?T"
+schematic_lemma (in L2) "\<turnstile> \<Lambda> A:*. \<Lambda> a:A. a : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in L2) "A:* |- (Lam B:*.Lam b:B. b)^A : ?T"
+schematic_lemma (in L2) "A:* \<turnstile> (\<Lambda> B:*.\<Lambda> b:B. b)^A : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in L2) "A:* b:A |- (Lam B:*.Lam b:B. b) ^ A ^ b: ?T"
+schematic_lemma (in L2) "A:* b:A \<turnstile> (\<Lambda> B:*.\<Lambda> b:B. b) ^ A ^ b: ?T"
   by (depth_solve rules)
 
-schematic_lemma (in L2) "|- Lam B:*.Lam a:(Pi A:*.A).a ^ ((Pi A:*.A)->B) ^ a: ?T"
+schematic_lemma (in L2) "\<turnstile> \<Lambda> B:*.\<Lambda> a:(\<Pi> A:*.A).a ^ ((\<Pi> A:*.A)\<rightarrow>B) ^ a: ?T"
   by (depth_solve rules)
 
 
 subsection {* Weakly higher-order propositional logic *}
 
-schematic_lemma (in Lomega) "|- Lam A:*.A->A : ?T"
+schematic_lemma (in Lomega) "\<turnstile> \<Lambda> A:*.A\<rightarrow>A : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in Lomega) "B:* |- (Lam A:*.A->A) ^ B : ?T"
+schematic_lemma (in Lomega) "B:* \<turnstile> (\<Lambda> A:*.A\<rightarrow>A) ^ B : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in Lomega) "B:* b:B |- (Lam y:B. b): ?T"
+schematic_lemma (in Lomega) "B:* b:B \<turnstile> (\<Lambda> y:B. b): ?T"
   by (depth_solve rules)
 
-schematic_lemma (in Lomega) "A:* F:*->* |- F^(F^A): ?T"
+schematic_lemma (in Lomega) "A:* F:*\<rightarrow>* \<turnstile> F^(F^A): ?T"
   by (depth_solve rules)
 
-schematic_lemma (in Lomega) "A:* |- Lam F:*->*.F^(F^A): ?T"
+schematic_lemma (in Lomega) "A:* \<turnstile> \<Lambda> F:*\<rightarrow>*.F^(F^A): ?T"
   by (depth_solve rules)
 
 
 subsection {* LP *}
 
-schematic_lemma (in LP) "A:* |- A -> * : ?T"
+schematic_lemma (in LP) "A:* \<turnstile> A \<rightarrow> * : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP) "A:* P:A->* a:A |- P^a: ?T"
+schematic_lemma (in LP) "A:* P:A\<rightarrow>* a:A \<turnstile> P^a: ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP) "A:* P:A->A->* a:A |- Pi a:A. P^a^a: ?T"
+schematic_lemma (in LP) "A:* P:A\<rightarrow>A\<rightarrow>* a:A \<turnstile> \<Pi> a:A. P^a^a: ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP) "A:* P:A->* Q:A->* |- Pi a:A. P^a -> Q^a: ?T"
+schematic_lemma (in LP) "A:* P:A\<rightarrow>* Q:A\<rightarrow>* \<turnstile> \<Pi> a:A. P^a \<rightarrow> Q^a: ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP) "A:* P:A->* |- Pi a:A. P^a -> P^a: ?T"
+schematic_lemma (in LP) "A:* P:A\<rightarrow>* \<turnstile> \<Pi> a:A. P^a \<rightarrow> P^a: ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP) "A:* P:A->* |- Lam a:A. Lam x:P^a. x: ?T"
+schematic_lemma (in LP) "A:* P:A\<rightarrow>* \<turnstile> \<Lambda> a:A. \<Lambda> x:P^a. x: ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP) "A:* P:A->* Q:* |- (Pi a:A. P^a->Q) -> (Pi a:A. P^a) -> Q : ?T"
+schematic_lemma (in LP) "A:* P:A\<rightarrow>* Q:* \<turnstile> (\<Pi> a:A. P^a\<rightarrow>Q) \<rightarrow> (\<Pi> a:A. P^a) \<rightarrow> Q : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP) "A:* P:A->* Q:* a0:A |-
-        Lam x:Pi a:A. P^a->Q. Lam y:Pi a:A. P^a. x^a0^(y^a0): ?T"
+schematic_lemma (in LP) "A:* P:A\<rightarrow>* Q:* a0:A \<turnstile>
+        \<Lambda> x:\<Pi> a:A. P^a\<rightarrow>Q. \<Lambda> y:\<Pi> a:A. P^a. x^a0^(y^a0): ?T"
   by (depth_solve rules)
 
 
 subsection {* Omega-order types *}
 
-schematic_lemma (in L2) "A:* B:* |- Pi C:*.(A->B->C)->C : ?T"
+schematic_lemma (in L2) "A:* B:* \<turnstile> \<Pi> C:*.(A\<rightarrow>B\<rightarrow>C)\<rightarrow>C : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in Lomega2) "|- Lam A:*.Lam B:*.Pi C:*.(A->B->C)->C : ?T"
+schematic_lemma (in Lomega2) "\<turnstile> \<Lambda> A:*.\<Lambda> B:*.\<Pi> C:*.(A\<rightarrow>B\<rightarrow>C)\<rightarrow>C : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in Lomega2) "|- Lam A:*.Lam B:*.Lam x:A. Lam y:B. x : ?T"
+schematic_lemma (in Lomega2) "\<turnstile> \<Lambda> A:*.\<Lambda> B:*.\<Lambda> x:A. \<Lambda> y:B. x : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in Lomega2) "A:* B:* |- ?p : (A->B) -> ((B->Pi P:*.P)->(A->Pi P:*.P))"
+schematic_lemma (in Lomega2) "A:* B:* \<turnstile> ?p : (A\<rightarrow>B) \<rightarrow> ((B\<rightarrow>\<Pi> P:*.P)\<rightarrow>(A\<rightarrow>\<Pi> P:*.P))"
   apply (strip_asms rules)
   apply (rule lam_ss)
     apply (depth_solve1 rules)
@@ -145,15 +145,15 @@
 
 subsection {* Second-order Predicate Logic *}
 
-schematic_lemma (in LP2) "A:* P:A->* |- Lam a:A. P^a->(Pi A:*.A) : ?T"
+schematic_lemma (in LP2) "A:* P:A\<rightarrow>* \<turnstile> \<Lambda> a:A. P^a\<rightarrow>(\<Pi> A:*.A) : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP2) "A:* P:A->A->* |-
-    (Pi a:A. Pi b:A. P^a^b->P^b^a->Pi P:*.P) -> Pi a:A. P^a^a->Pi P:*.P : ?T"
+schematic_lemma (in LP2) "A:* P:A\<rightarrow>A\<rightarrow>* \<turnstile>
+    (\<Pi> a:A. \<Pi> b:A. P^a^b\<rightarrow>P^b^a\<rightarrow>\<Pi> P:*.P) \<rightarrow> \<Pi> a:A. P^a^a\<rightarrow>\<Pi> P:*.P : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LP2) "A:* P:A->A->* |-
-    ?p: (Pi a:A. Pi b:A. P^a^b->P^b^a->Pi P:*.P) -> Pi a:A. P^a^a->Pi P:*.P"
+schematic_lemma (in LP2) "A:* P:A\<rightarrow>A\<rightarrow>* \<turnstile>
+    ?p: (\<Pi> a:A. \<Pi> b:A. P^a^b\<rightarrow>P^b^a\<rightarrow>\<Pi> P:*.P) \<rightarrow> \<Pi> a:A. P^a^a\<rightarrow>\<Pi> P:*.P"
   -- {* Antisymmetry implies irreflexivity: *}
   apply (strip_asms rules)
   apply (rule lam_ss)
@@ -174,22 +174,22 @@
 
 subsection {* LPomega *}
 
-schematic_lemma (in LPomega) "A:* |- Lam P:A->A->*.Lam a:A. P^a^a : ?T"
+schematic_lemma (in LPomega) "A:* \<turnstile> \<Lambda> P:A\<rightarrow>A\<rightarrow>*.\<Lambda> a:A. P^a^a : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in LPomega) "|- Lam A:*.Lam P:A->A->*.Lam a:A. P^a^a : ?T"
+schematic_lemma (in LPomega) "\<turnstile> \<Lambda> A:*.\<Lambda> P:A\<rightarrow>A\<rightarrow>*.\<Lambda> a:A. P^a^a : ?T"
   by (depth_solve rules)
 
 
 subsection {* Constructions *}
 
-schematic_lemma (in CC) "|- Lam A:*.Lam P:A->*.Lam a:A. P^a->Pi P:*.P: ?T"
+schematic_lemma (in CC) "\<turnstile> \<Lambda> A:*.\<Lambda> P:A\<rightarrow>*.\<Lambda> a:A. P^a\<rightarrow>\<Pi> P:*.P: ?T"
   by (depth_solve rules)
 
-schematic_lemma (in CC) "|- Lam A:*.Lam P:A->*.Pi a:A. P^a: ?T"
+schematic_lemma (in CC) "\<turnstile> \<Lambda> A:*.\<Lambda> P:A\<rightarrow>*.\<Pi> a:A. P^a: ?T"
   by (depth_solve rules)
 
-schematic_lemma (in CC) "A:* P:A->* a:A |- ?p : (Pi a:A. P^a)->P^a"
+schematic_lemma (in CC) "A:* P:A\<rightarrow>* a:A \<turnstile> ?p : (\<Pi> a:A. P^a)\<rightarrow>P^a"
   apply (strip_asms rules)
   apply (rule lam_ss)
     apply (depth_solve1 rules)
@@ -201,23 +201,23 @@
 
 subsection {* Some random examples *}
 
-schematic_lemma (in LP2) "A:* c:A f:A->A |-
-    Lam a:A. Pi P:A->*.P^c -> (Pi x:A. P^x->P^(f^x)) -> P^a : ?T"
+schematic_lemma (in LP2) "A:* c:A f:A\<rightarrow>A \<turnstile>
+    \<Lambda> a:A. \<Pi> P:A\<rightarrow>*.P^c \<rightarrow> (\<Pi> x:A. P^x\<rightarrow>P^(f^x)) \<rightarrow> P^a : ?T"
   by (depth_solve rules)
 
-schematic_lemma (in CC) "Lam A:*.Lam c:A. Lam f:A->A.
-    Lam a:A. Pi P:A->*.P^c -> (Pi x:A. P^x->P^(f^x)) -> P^a : ?T"
+schematic_lemma (in CC) "\<Lambda> A:*.\<Lambda> c:A. \<Lambda> f:A\<rightarrow>A.
+    \<Lambda> a:A. \<Pi> P:A\<rightarrow>*.P^c \<rightarrow> (\<Pi> x:A. P^x\<rightarrow>P^(f^x)) \<rightarrow> P^a : ?T"
   by (depth_solve rules)
 
 schematic_lemma (in LP2)
-  "A:* a:A b:A |- ?p: (Pi P:A->*.P^a->P^b) -> (Pi P:A->*.P^b->P^a)"
+  "A:* a:A b:A \<turnstile> ?p: (\<Pi> P:A\<rightarrow>*.P^a\<rightarrow>P^b) \<rightarrow> (\<Pi> P:A\<rightarrow>*.P^b\<rightarrow>P^a)"
   -- {* Symmetry of Leibnitz equality *}
   apply (strip_asms rules)
   apply (rule lam_ss)
     apply (depth_solve1 rules)
    prefer 2
    apply (depth_solve1 rules)
-  apply (erule_tac a = "Lam x:A. Pi Q:A->*.Q^x->Q^a" in pi_elim)
+  apply (erule_tac a = "\<Lambda> x:A. \<Pi> Q:A\<rightarrow>*.Q^x\<rightarrow>Q^a" in pi_elim)
    apply (depth_solve1 rules)
   apply (unfold beta)
   apply (erule imp_elim)