Abstract data types (model, principle of no junk)

I have the following abstract data structure

Now i have to find a model that satisfies the principle of no junk and proof that

Could someone advise me to get to a solution and to understand the whole topic?


1 spec NatSet = Bool and Nat then 2 3 sorts 4 natSet = emptySet | add(natSet, nat) 5 6 ops 7 isEmpty: (natSet) bool, 8 contains: (natSet, nat) bool, 9 union: (natSet, natSet) natSet, 10 intersect: (natSet, natSet) natSet 11 12 vars 13 s,s’: natSet, 14 n,n’: nat 15 16 axioms 17 isEmpty(emptySet) = true 18 isEmpty(add(s, n)) = false 19 20 contains(emptySet, n) = false 21 contains(add(s, n), n) = true 22 n 6= n’ ⇒ contains(add(s, n), n’) = contains(s, n’) 23 24 union(emptySet, s) = s 25 union(add(s, n), s’) = add(union(s,s’), n) 26 27 intersect(emptySet, s’) = emptySet 28 intersect(s, emptySet) = emptySet 29 intersect(add(s, n), add(s’, n)) = add(intersect(s, s’), n) 30 n 6= n’ ⇒ intersect(add(s, n), add(s’, n’)) = 31 union(intersect(s, add(s’, n’)), intersect(add(s, n), s’)) 32 end 

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Names removed from Mac Mail VIP list are sent to Junk

I do not use the VIP list in my Mac Mail (Version 12.2). It’s just not how I organize my mail — not how I roll.

And yet somehow, I accidentally added my wife to the VIP list.

It was very easy to remove her name from the VIP list, and in fact the extraneous “VIP” list is no longer even present in my list of mailboxes. Great.

But now we get to the problem.

When she was removed from the VIP list, she was somehow added to the Junk list. Every email that I receive from her – from either of her three email accounts – is unceremoniously dumped into Junk Mail. This did not happen before the VIP incident, and I can’t seem to “re-approve” her contact as a valid and good email now.

How can I remove my wife from Junk Mail? Please help, and in addition to my sanity, you may save a marriage!

Here are some details:

  • The VIP addition/subtraction was the very clear and distinct moment that this happened
  • POP3
  • I’ve bashed BASH many times, and am not afraid of Terminal
  • In addition to Apple’s junk filters, I use a general rule to send any email that is not in my contacts straight to Junk
  • My wife is in my contacts

Let me know if I can provide any more specific information.

Junk code insertion in Smali

I was trying to obfuscate android by adding junk code in Smali. Understood that by adding nop/goto instruction to it works well. However when I tried to add (const/4 v0, 0x4) my app crash after recompile.

# direct methods .method public constructor <init>()V     .locals 0     const/4 v0, 0x4 <<added at this line     .line 12     invoke-direct {p0}, Landroid/support/v7/app/AppCompatActivity;-><init>()V      return-void .end method 

is it suppose that only nop/goto instruction work as junk code?] Thanks in advance!

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.mht files display as junk text from Jetty server

I have some .mht files which load fine from local files but when loaded from the Jetty web server display as junk text.

What can I do to make them work correctly from my Jetty web server? I know that for Apache server I need to add the below lines of code to .htaccess file. But how do I make similar changes for Jetty? I am using IntelliJ as my IDE.

 <IfModule mod_mime.c>    # MIME HyperText Markup Language (MHTML) markup     AddType text/html .mhtml .mht .maff .maf    AddType message/rfc822 .mhtml .mht    AddType multipart/related .mhtml .mht .maff .maf  </IfModule>