From: matitaweb <claudio.sacerdoticoen@unibo.it>
Date: Tue, 8 Nov 2011 16:54:31 +0000 (+0000)
Subject: commit by user andrea
X-Git-Tag: make_still_working~2128
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=5f6f12fa3806e9bfe4fa79a5555912b68dcd0f00;p=helm.git

commit by user andrea
---

diff --git a/weblib/tutorial/chapter4.ma b/weblib/tutorial/chapter4.ma
index 9bfb3891c..79b6bafff 100644
--- a/weblib/tutorial/chapter4.ma
+++ b/weblib/tutorial/chapter4.ma
@@ -45,7 +45,7 @@ interpretation "atom" 'atom a = (char ? a).
 notation "ϵ" non associative with precedence 90 for @{ 'epsilon }.
 interpretation "epsilon" 'epsilon = (epsilon ?).
 
-notation "∅" non associative with precedence 90 for @{ 'empty }.
+notation "∅" (* slash emptyv *) non associative with precedence 90 for @{ 'empty }.
 interpretation "empty" 'empty = (zero ?).
 
 let rec flatten (S : a href="cic:/matita/tutorial/chapter4/Alpha.ind(1,0,0)"Alpha/a) (l : a href="cic:/matita/tutorial/chapter3/list.ind(1,0,1)"list/a (a href="cic:/matita/tutorial/chapter4/word.def(3)"word/a S)) on l : a href="cic:/matita/tutorial/chapter4/word.def(3)"word/a S ≝ 
@@ -67,76 +67,75 @@ interpretation "union lang" 'union a b = (union ? a b).
 
 definition cat : ∀S,l1,l2,w.Prop ≝ 
   λS.λl1,l2.λw:a href="cic:/matita/tutorial/chapter4/word.def(3)"word/a S.a title="exists" href="cic:/fakeuri.def(1)"∃/aw1,w2.w1 a title="append" href="cic:/fakeuri.def(1)"@/a w2 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a w a title="logical and" href="cic:/fakeuri.def(1)"∧/a l1 w1 a title="logical and" href="cic:/fakeuri.def(1)"∧/a l2 w2.
-interpretation "cat lang" 'pc a b = (cat ? a b).
+interpretation "cat lang" 'concat a b = (cat ? a b).
 
 definition star ≝ λS.λl.λw:a href="cic:/matita/tutorial/chapter4/word.def(3)"word/a S.a title="exists" href="cic:/fakeuri.def(1)"∃/alw. a href="cic:/matita/tutorial/chapter4/flatten.fix(0,1,4)"flatten/a ? lw a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a w a title="logical and" href="cic:/fakeuri.def(1)"∧/a a href="cic:/matita/tutorial/chapter4/conjunct.fix(0,1,4)"conjunct/a ? lw l. 
 interpretation "star lang" 'kstar l = (star ? l).
 
-notation > "𝐋 term 70 E" non associative with precedence 75 for @{in_l ? $E}.
+notation "ℓ term 70 E" non associative with precedence 75 for @{in_l ? $E}.
 
 let rec in_l (S : a href="cic:/matita/tutorial/chapter4/Alpha.ind(1,0,0)"Alpha/a) (r : a href="cic:/matita/tutorial/chapter4/re.ind(1,0,1)"re/a S) on r : a href="cic:/matita/tutorial/chapter4/word.def(3)"word/a S → Prop ≝ 
 match r with
- [ zero ⇒ a title="empty lang" href="cic:/fakeuri.def(1)"∅/a
+ [ zero ⇒ a title="empty lang" href="cic:/fakeuri.def(1)"∅/a 
  | epsilon ⇒ a title="sing lang" href="cic:/fakeuri.def(1)"{/a: a title="nil" href="cic:/fakeuri.def(1)"[/a] }
- | char x ⇒ a title="sing lang" href="cic:/fakeuri.def(1)"{/a: a title="cons" href="cic:/fakeuri.def(1)"[/ax]span style="text-decoration: underline;"/span}
- | _ ⇒ a title="empty lang" href="cic:/fakeuri.def(1)"∅/a
+ |  char x ⇒ a title="sing lang" href="cic:/fakeuri.def(1)"{/a: xa title="cons" href="cic:/fakeuri.def(1)":/a:a title="nil" href="cic:/fakeuri.def(1)"[/a] }
+ | concat r1 r2 ⇒ ℓ r1 a title="cat lang" href="cic:/fakeuri.def(1)"·/a ℓ r2 
+ | or r1 r2 ⇒ ℓ r1 a title="union lang" href="cic:/fakeuri.def(1)"∪/a ℓ r2 
+ | star r1 ⇒ (ℓ r1)a title="star lang" href="cic:/fakeuri.def(1)"^/a* 
  ].
 
-
-(*
- | concat r1 r2 ⇒ 𝐋 r1 · 𝐋 r2
- | or r1 r2 ⇒  𝐋 r1 ∪ 𝐋 r2
- | star r1 ⇒ (𝐋 r1) ^*
- ].
-
-*)
-
- notation "𝐋 term 70 E" non associative with precedence 75 for @{'in_l $E}.
+notation "ℓ term 70 E" non associative with precedence 75 for @{'in_l $E}.
 interpretation "in_l" 'in_l E = (in_l ? E).
 interpretation "in_l mem" 'mem w l = (in_l ? l w).
 
-notation "a || b" left associative with precedence 30 for @{'orb $a $b}.
+notation "a ∨ b" left associative with precedence 30 for @{'orb $a $b}.
 interpretation "orb" 'orb a b = (orb a b).
 
-ndefinition if_then_else ≝ λT:Type[0].λe,t,f.match e return λ_.T with [ true ⇒ t | false ⇒ f].
+(* ndefinition if_then_else ≝ λT:Type[0].λe,t,f.match e return λ_.T with [ true ⇒ t | false ⇒ f].
 notation > "'if' term 19 e 'then' term 19 t 'else' term 19 f" non associative with precedence 19 for @{ 'if_then_else $e $t $f }.
 notation < "'if' \nbsp term 19 e \nbsp 'then' \nbsp term 19 t \nbsp 'else' \nbsp term 90 f \nbsp" non associative with precedence 19 for @{ 'if_then_else $e $t $f }.
-interpretation "if_then_else" 'if_then_else e t f = (if_then_else ? e t f).
-
-ninductive pitem (S: Alpha) : Type[0] ≝
-   pz: pitem S
- | pe: pitem S
- | ps: S → pitem S
- | pp: S → pitem S
- | pc: pitem S → pitem S → pitem S
- | po: pitem S → pitem S → pitem S
- | pk: pitem S → pitem S.
+interpretation "if_then_else" 'if_then_else e t f = (if_then_else ? e t f). *)
+
+inductive pitem (S: a href="cic:/matita/tutorial/chapter4/Alpha.ind(1,0,0)"Alpha/a) : Type[0] ≝
+ | pzero: pitem S
+ | pepsilon: pitem S
+ | pchar: S → pitem S
+ | ppoint: S → pitem S
+ | pconcat: pitem S → pitem S → pitem S
+ | por: pitem S → pitem S → pitem S
+ | pstar: pitem S → pitem S.
  
-ndefinition pre ≝ λS.pitem S × bool.
-
-interpretation "pstar" 'pk a = (pk ? a).
-interpretation "por" 'plus a b = (po ? a b).
-interpretation "pcat" 'pc a b = (pc ? a b).
-notation < ".a" non associative with precedence 90 for @{ 'pp $a}.
-notation > "`. term 90 a" non associative with precedence 90 for @{ 'pp $a}.
-interpretation "ppatom" 'pp a = (pp ? a).
-(* to get rid of \middot *)
-ncoercion pc : ∀S.∀p:pitem S. pitem S → pitem S  ≝ pc on _p : pitem ? to ∀_:?.?.
-interpretation "patom" 'ps a = (ps ? a).
-interpretation "pepsilon" 'epsilon = (pe ?).
-interpretation "pempty" 'empty = (pz ?).
-
-notation > "|term 19 e|" non associative with precedence 70 for @{forget ? $e}.
-nlet rec forget (S: Alpha) (l : pitem S) on l: re S ≝
+definition pre ≝ λS.a href="cic:/matita/tutorial/chapter4/pitem.ind(1,0,1)"pitem/a S a title="Product" href="cic:/fakeuri.def(1)"×/a a href="cic:/matita/basics/bool/bool.ind(1,0,0)" title="null"bool/a.
+
+interpretation "pstar" 'kstar a = (pstar ? a).
+interpretation "por" 'plus a b = (por ? a b).
+interpretation "pcat" 'concat a b = (pconcat ? a b).
+
+notation "• a" non associative with precedence 90 for @{ 'ppoint $a}.
+(* notation > "`. term 90 a" non associative with precedence 90 for @{ 'pp $a}. *)
+
+interpretation "ppatom" 'ppoint a = (ppoint ? a).
+(* to get rid of \middot 
+ncoercion pc : ∀S.∀p:pitem S. pitem S → pitem S  ≝ pc on _p : pitem ? to ∀_:?.?. *)
+interpretation "patom" 'pchar a = (pchar ? a).
+interpretation "pepsilon" 'epsilon = (pepsilon ?).
+interpretation "pempty" 'empty = (pzero ?).
+
+notation "\boxv term 19 e \boxv" (* slash boxv *) non associative with precedence 70 for @{forget ? $e}.
+
+let rec forget (S: a href="cic:/matita/tutorial/chapter4/Alpha.ind(1,0,0)"Alpha/a) (l : a href="cic:/matita/tutorial/chapter4/pitem.ind(1,0,1)"pitem/a S) on l: a href="cic:/matita/tutorial/chapter4/re.ind(1,0,1)"re/a S ≝
  match l with
-  [ pz ⇒ ∅
-  | pe ⇒ ϵ
-  | ps x ⇒ `x
-  | pp x ⇒ `x
-  | pc E1 E2 ⇒ (|E1| · |E2|)
-  | po E1 E2 ⇒ (|E1| + |E2|)
-  | pk E ⇒ |E|^* ].
+  [ pzero ⇒ a title="empty" href="cic:/fakeuri.def(1)"∅/a
+  | pepsilon ⇒ a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a
+  | pchar x ⇒ a href="cic:/matita/tutorial/chapter4/re.con(0,3,1)"char/a ? x 
+  | ppoint x ⇒ a href="cic:/matita/tutorial/chapter4/re.con(0,3,1)"char/a ? x  
+  | pconcat e1 e2 ⇒ │e1│ a title="cat" href="cic:/fakeuri.def(1)"·/a │e2│
+  | por e1 e2 ⇒ │e1│  a title="or" href="cic:/fakeuri.def(1)"+/a │e2│
+  | pstar e ⇒ │e│a title="star" href="cic:/fakeuri.def(1)"^/a* 
+  ].
+
 notation < "|term 19 e|" non associative with precedence 70 for @{'forget $e}.
 interpretation "forget" 'forget a = (forget ? a).
 
-notation "\fst term 90 x" non associative with precedence 90 for @{'fst $x}.
\ No newline at end of file
+
+notation "\fst term 90 x" non associative with precedence 90 for @{'fst $x}.