1. Rigorous Software Engineering
Assignment 3
（exercise 2, 3.3, 3.5）

2. Exercise 2 abstract sig Student {} sig Graduate extends Student{}
sig Undergraduate extends Student {}
sig ID {}
sig Major {}
sig University {}

3. abstract sig Student {
id: one ID,
major: one Major,
university: lone University,
isLegal: Bool,
classmates: set Student, }

4. Every student has a unique student ID.
Descriptions
Descriptions
A student should register at a university, and only registered students are legal students.
Every student has a unique student ID.
Alloy
Alloy
fact legal_in_university{
all s: Student | (s.university != none) iff (s.isLegal = True) }
fact unique_ids{
all disj s, t: Student | s.id != t.id }
fact no_id_without_student{
all i: ID | one s: Student | s.id = i }

5. Graduates and undergraduates are never classmates.
Descriptions
Students with the same major who are registered at the same university are regarded as classmates.
Graduates and undergraduates are never classmates.
Alloy
fact classmates_have_same_major_and_uni{
all disj s, t: Student | (s.major = t.major and s.university = t.university
and (s in Undergraduate and t in Undergraduate or s in Graduate and t in Graduate)
iff (s in t.classmates) }

6. fact no_self_classmate{ all s: Student | s not in s.classmates }
Descriptions
Descriptions
The classmate relation is not reflexive (a student cannot be his/her own classmate).
Visualize the model for 2 Universities, 3 Majors, 3 Students and 3 IDs.
Alloy
Alloy
fact no_self_classmate{
all s: Student | s not in s.classmates }
pred show{}
run show for 2 University, 3 Major, 3 Student, 3 ID

7. Exercise 3.3 Doris Day’s song
“Everybody loves my baby
but my baby don’t love nobody but me”
David Gries has pointed out that, from a strictly logical point of view, this implies ‘I am my baby’.
Everybody loves my baby (b)
pred my_baby[b: Person] {
(all p: Person | b in p.loves)
and b.loves = Me }
assert song {
all p: Person | my_baby[p] implies Me = p }
My baby don’t love nobody but me

8. Exercise 3.3 Doris Day’s song
“Everybody loves my baby
but my baby don’t love nobody but me”
David Gries has pointed out that, from a strictly logical point of view, this implies ‘I am my baby’.
pred my_baby[b: Person] {
(all p: Person | b in p.loves)
and b.loves = Me }
assert song {
all p: Person | my_baby[p] implies Me = p }
+ b

9. Exercise 3.5 Modeling the Tube
Station: the set of all stations
JubileeStation, CentralStation, CircleStation: for each line, a subset of Station
jubliee, central, circle: binary relations relating stations on each line to one another if they are directly connected
sig Station {}
sig JubileeStation in Station {
jubilee: set JubileeStation }
sig CentralStation in Station {
central: set CentralStation
sig CircleStation in Station {
circle: set CircleStation

10. Exercise 3.5 Modeling the Tube
Stanmore, BakerStreet, Epping: singleton subsets of Station for individual stations
one sig Stanmore, BakerStreet, Epping extends Station {}

11. Exercise 3.5 Modeling the Tube
(a) Named stations are on exactly the lines as shown in graphic
Jubilee line
Central line
Circle line
Stanmore in (JubileeStation - CentralStation) - CircleStation
BakerStreet in (JubileeStation & CircleStation) - CentralStation
Epping in (CentralStation - JubileeStation) - CircleStation

12. Exercise 3.5 Modeling the Tube
(b) No station (including those unnamed) is on all three lines
Jubilee line
Central line
Circle line
no (JubileeStation & CentralStation & CircleStation)

13. Exercise 3.5 Modeling the Tube
(c) The Circle line forms a circle
Jubilee line
Central line
Circle line
^circle: (s1, s2), (s1, s3), …,(s1, sn), …, (sn-1, sn)
all s: CircleStation {
one s.circle
CircleStation in s.^circle }
Every station has one “next” station, including the “last” station.
All stations that can be reached starting from s

14. Exercise 3.5 Modeling the Tube
(d) Jubilee is a straight line starting at Stanmore
Jubilee line
Central line
Circle line
Stanmore is the starting station, other station in Jubilee can be reached from Stanmore
JubileeStation in Stanmore.*jubilee
all s: JubileeStation {
lone s.jubilee
s not in s.^jubilee }
Every station has one or zero “next” station
All stations that can be reached starting from s

15. Exercise 3.5 Modeling the Tube
(e) there’s a station between Stanmore and BakerStreet
Jubilee line
Central line
Circle line
All (A, B) tuples that one can travel from A to B on Jubilee
let reach = ^jubilee | some Stanmore.reach & reach.BakerStreet
All stations that can be reached starting from Stanmore
All stations that can reach BakerStreet

16. Exercise 3.5 Modeling the Tube
(f) It is possible to travel from BakerStreet to Epping
Jubilee line
Central line
Circle line
Epping in BakerStreet.^(jubilee + central + circle)
All (A, B) tuples that one can travel from A to B
All stations that can be reached starting from BakerStreet