Desktop model Roger L. Costello March 24, 2018 Desktop0 Desktop1 cut paste icon1 icon3 icon2 icon3 icon3 Roger L. Costello March 24, 2018

It’s time to model software In the previous examples there was just one or a small number of solutions (instances) satisfying the constraints. With software there are usually many solutions.

Model a desktop and two operations In this example we model software that allows users to add and remove icons from a desktop. A cut operation removes one icon from the desktop. A paste operation adds one icon to the desktop.

Problem Statement Model a desktop, its icons, and cut and paste operations. We will create two versions of the model: Version #1: Hardcode the icons. Version #2: Arbitrary set of icons.

Version #1: Simple Model Let’s model a desktop that has just two icons named A and B, and a cut operation that removes B. Desktop (first) Desktop (second) cut A B A

A set of Desktops, each with a set of icons sig Desktop { icons: set Icon } The set keyword means that icons maps each Desktop to a set of Icon (an Icon is either A or B). icons Desktop0 A Desktop0 is mapped to this set: {A, B} Desktop0 B Desktop1 A Desktop1 is mapped to this (singleton) set: {A}

Order the Desktops -- there is a first Desktop, a second Desktop, etc. open util/ordering[Desktop] “first” denotes the first Desktop. “first.icons” denotes the icons on the first Desktop. “prev” denotes the previous Desktop. Suppose d denotes one of the Desktops, then d.prev.icons denotes the icons on the previous Desktop. “last” denotes the last Desktop. “next” denotes the next Desktop.

There are two icons, A and B abstract sig Icon {} one sig A extends Icon {} one sig B extends Icon {} Alternatively: enum Icon { A, B }

Constrain the first desktop to contain both icons, the second desktop to contain just A fact { first.icons = A + B first.next.icons = A }

Specify in the run command that the instance is to contain 2 Desktops. run {} for 3 but 2 Desktop

open util/ordering[Desktop] sig Desktop { icons: set Icon } enum Icon { A, B } fact { first.icons = A + B first.next.icons = A } run {} for 3 but 2 Desktop

Version #2: Arbitrary icons, cut/paste operations We want the model to represent any set of icons on the first Desktop. Let d = the first Desktop and i = an icon on the first Desktop. The second Desktop = d - i, or The second Desktop = d + j (where j is an icon not on d) Let d = the second Desktop and i = an icon on the second Desktop. The third Desktop = d - i, or The third Desktop = d + j (where j is an icon not on d) And so forth.

Here is one of the instances that Alloy generated: Desktop0 Desktop1 Desktop2 cut paste icon1 icon3 icon2 icon3 icon3 paste Desktop4 Desktop3 cut icon1 icon0 icon1 icon3 icon3

Desktop signature is same as before open util/ordering[Desktop] sig Desktop { icons: set Icon }

Instead of enumerating the icons, have a set of icons: sig Icon {}

The first Desktop contains a set of icons: fact init { some i: set Icon | first.icons = i }

A Desktop cannot hold just any set of icons, a Desktop is derived from its previous Desktop: it has the icons on the previous Desktop, plus or minus one icon fact Desktops_through_cut_and_paste { all d: Desktop - first | (some i: d.prev.icons | d.icons = d.prev.icons - i) or (some i: Icon - d.prev.icons | d.icons = d.prev.icons + i) }

open util/ordering[Desktop] sig Desktop { icons: set Icon } sig Icon {} fact init { some i: set Icon | first.icons = i } fact Desktops_through_cut_and_paste { all d: Desktop - first | (some i: d.prev.icons | d.icons = d.prev.icons - i) or (some i: Icon - d.prev.icons | d.icons = d.prev.icons + i) } run {} for 5 Do Lab3