From 7a595893230cddb2a82cffc5be0e5bd93ae10c5b Mon Sep 17 00:00:00 2001
From: Alice <alicevteixeira@gmail.com>
Date: Tue, 14 Nov 2023 11:32:32 +0000
Subject: [PATCH] vault backup: 2023-11-14 11:32:32

---
 .obsidian/core-plugins.json | 20 ----------
 4a1s/MFES/PL - Aula 8.md    | 78 ++++++++++++++++++++++++++++++++++++-
 2 files changed, 77 insertions(+), 21 deletions(-)

diff --git a/.obsidian/core-plugins.json b/.obsidian/core-plugins.json
index 9405bfd..e69de29 100644
--- a/.obsidian/core-plugins.json
+++ b/.obsidian/core-plugins.json
@@ -1,20 +0,0 @@
-[
-  "file-explorer",
-  "global-search",
-  "switcher",
-  "graph",
-  "backlink",
-  "canvas",
-  "outgoing-link",
-  "tag-pane",
-  "page-preview",
-  "daily-notes",
-  "templates",
-  "note-composer",
-  "command-palette",
-  "editor-status",
-  "bookmarks",
-  "outline",
-  "word-count",
-  "file-recovery"
-]
\ No newline at end of file
diff --git a/4a1s/MFES/PL - Aula 8.md b/4a1s/MFES/PL - Aula 8.md
index 1c5f949..8168f5e 100644
--- a/4a1s/MFES/PL - Aula 8.md	
+++ b/4a1s/MFES/PL - Aula 8.md	
@@ -1,5 +1,45 @@
-
+https://why3.lri.fr/try/?name=test.mlw&lang=whyml&code=AN7HpJ4Recall1the4officeyassignment%2F4puzzle2from3Fichaz17r3whereBHz44people1areydistributed%2F0byz35officesl2such2that7vH7s2each4person0is6assignedza4singleVHm2Nuno1and3Pedro0do1not3share0anlHl0If1Ana1hasoo2just1for5herselfV2then0so2doesdHg5Officesyaccomodate%2F0at2most1twouIHHuBuMg0if5running2Why32withXyappropriate%2F1SMT4solverlBH0inuByfollowing%2F1you2will0be2able0to5inspect5counterASA6examplesBH2when6adequate7tBNHHz1s3Modele5problemuI6definingVVypredicate%2FBKuQ5writingza1set0of4axiomsfH0In3orderV5expressc3thirdyrequirement%2F3above7r4defineBHfc7h3alonesyexpressing%2Ful5someoneuMg2onlyBH6occupierXSuVWHEz2s2ShowikTuGuPyinconsistent%2Fu0u3hBKu12goalhHEz3s2Find1outuhfunyproperties%2F4followuDpb7vL7suP3MariaPuKR1One7ruT1sheukukLfu7u7u7u8iTDccuOusuLuMu9lbbXmuSaBL5equally2haveusiiidBMDHz4s5Finallyfyformulate%2Fg3provezau85statingVBLuUuU1onef1mayvG3emptyd1For2thisc3first3writeduvBHuwdVfvAg7nzieAzesuzu%2FvO4anyone7ItBHDz5n5Producefyalternative%2Fyformalization%2F3usingV5insteadvEVVpBLr3logic6functionU3givesvB4uniqueRXXBHuIuIY4Repeat1allk6previous3stepsuXvWVlDN7JoBNNNN4moduleuQNF2typec7yu7781Twos3ThreeHnanu%2Fou%2FsvBsvANHveyhasOffice%2F7nk7orerNH3axiom0A1B7v4forallzprAlV4existszopAjphmoHj0A2BmjorAj7r0o10o2BphhJhln7O3qqm7MzoUqFHfzBBiBfnoqhhiVngqUlgLo7RzqDHVurUbfAZUZbWAoAaap0p1plpJjbikiapkpbngpNFXzCgdPlrWHnzDBnBbk0p20p3ApZRdqXXJakoZqjqqqjqdLnam7XuqqnqsrpNMBvHysanity%2Btest%2Fg3falseuAA3checkuzvk3model3makes3senseAvpHHi0g1BiBZvvvrYv3qHm0g2mPvyrQQ7nhv1nOqvxq7oeBLvvvxAhAhhkvyoiqcqBNDvxvQdzoiif7yazpAoAvxdvQjenijHH3lemmayatMostOneEmpty%2FBjBiXcqBegdoarnXLpbqNN1endBNNNNvnyOffices%2BFn%2FBNDvqinv978vosvoHnTnv%2Bov%2BsOsONHvZhPkSVBpNHvqzBqqjvprhHHv8v4izplAhhcOzooAi7tpvpplpJqfjOlrqrpHFbzCkeWkraNHnzDnBfkvrvqpddoAeAnv8qAqAmqpAqAqgLdnprovprpBpBrnNNDv0vpBhBvpBNHqvxBqnOUv9fXpHlvxBllVkrOkrlprUNHOv27nOiAn7olRzpAoAQQmpUkHHv0v0Blkv0v0qkjeov8rnZLpeqNNv0NNNN
 ```c
+(*
+    Recall the office assignment puzzle from Ficha 1, where 
+    4 people are distributed by 3 offices, such that:
+    - each person is assigned a single office
+    - Nuno and Pedro do not share an office
+    - If Ana has an office just for herself, then so does Pedro
+    - Offices accomodate at most two people
+    
+    Recall that, if running Why3 with an appropriate SMT solver, 
+    in the following you will be able to inspect counter-examples 
+    when adequate. 
+
+    
+    1. Model the problem by defining an appropriate predicate 
+       and writing a set of axioms.
+       In order to express the third requirement above, define 
+       a predicate "alone" expressing that someone is the only 
+       occupier of an office.
+       
+    2. Show that the axioms are not inconsistent by writing an 
+       appropriate goal.
+       
+    3. Find out if the following properties follow from the axioms:
+        - If Maria is assigned office One, then she will be
+            the only occupier of that office.
+        - If Ana and Nuno share an office, then Maria and Pedro will 
+            equally have to share an office. 
+    
+    4. Finally, formulate and prove a goal stating that 
+        at most one office may be empty. For this, first write a predicate 
+        expressing that an office is empty (i.e. not assigned to anyone). 
+        
+    5. Produce an alternative formalization using, instead of a predicate, 
+        a logic function that gives the unique office assigned to 
+        each person. Repeat all the previous steps with this formalization.
+    
+*) 
+
+
+
 module Offices
 
   type office = One | Two | Three
@@ -34,6 +74,42 @@ module Offices
       o1 = o2
 
 end 
+
+
+
+
+
+
+
+module Offices_Fn 
+
+  type office = One | Two | Three
+  type person = Ana | Nuno | Pedro | Maria
+
+  function office (person) : office
+
+  axiom B: office Pedro <> office Nuno
+  
+  predicate alone (p:person) = forall o:office. forall p1:person.
+    p1 <> p -> office p <> office p1
+    
+  axiom C: alone Ana -> alone Pedro
+
+  axiom D: forall p1 p2 p3: person. p1<>p2 /\ p1<>p3 /\ p2<>p3 ->
+      office p1 <> office p2 \/ office p1 <> office p3
+
+
+  goal sanity_test : false 
+
+  goal g1 : office Maria = One -> alone Maria
+  goal g2 : office Ana = office Nuno -> office Maria = office Pedro
+
+  predicate empty (o:office) = forall p:person. office p <> o
+  
+  lemma atMostOneEmpty : forall o1 o2: office. empty o1 /\ empty o2 ->
+      o1 = o2
+
+end
 ```