Ne prennez pas la modèlisation à la légère

Par Thomas Bracher

Comment font ils pour avoir un modèle qui marche ?

L'ambiguïté dans le modèle

EmailChoosen

EmailConfirmed

UserValidated

Modèle = Abstraction

Exemple de modèle

  • Modèle mental
  • Diagrammes
  • Spécifications
  • Le code

Comment valider leur cohérence ?

Comment valider leur cohérence ?

LES MÉTHODES FORMELLES

Pourquoi utiliser des outils ?

Process 1

db.modify(x -> x + 1)

Process 2

db.modify(x -> x * 2)

x = 1

Process 1

tmp = db.get(x)
db.set(x, tmp + 1)

Process 2

tmp = db.get(x)
db.set(x, tmp * 2)

x = 1

State explosion problem

Vérifier la pensée magique

  • les user story
  • les tests unitaires
  • le langage naturel

Les familles de méthodes formelles

Coq

Require Import Arith.
Require Import List.
Require Import Omega.

(* Require Import listkit. *)

(** [cutn] breaks a list into prefix, suffix at [n]. *)
Definition cutn A n (xs : list A) := (firstn n xs, skipn n xs).

(** [cutn n] is inverse of [(++)] when [n] equals the length of the first arg to [(++)]. *)
Lemma cutn_app:
  forall A n (xs ys : list A),
    n = length xs -> cutn A n (xs ++ ys) = (xs, ys).
Proof.
 induction n; destruct xs; simpl; easy||auto.
 intros.
 unfold cutn in *.
 simpl.
 lapply (IHn xs ys).
 - congruence.
 - omega.
Qed.

Tables de vérité

has_id is_green healthy ok ?
T F F F
T F T T
T T F F
T T T T
F T F F
F T T T
F F T F
F F F F

DRAKON

XP : System metaphor

  • Design itératif
  • Ubiquitous language ?
  • Partage du modèle mental

Alloy Analyzer :

lightweight formal verification

Des concepts familiers

  • Proche de l'orienté objet
  • Théorie des sets
  • Algèbre relationnel

Les sets, tuples et atomes

Book = {(B0)}
Name = {(N0), (N1), (N2)}
names = {(B0, N0), (B0, N2)}
name1 = {(N1)}

-- Opération de lien (->)
{(B0)} -> {(N1), (N2)} = {(B0, N1), (B0, N2)}

ajouter et jointurer

Book = {(B0)}
Name = {(N0), (N1), (N2)}
names = {(B0, N0), (B0, N2)}
name1 = {(N1)}

-- Addition (+)
names + Book -> name1 = {(B0, N0), (B0, N1), (B0, N2)}
Book + Name = {(B0), (N0), (N1), (N2)}

-- Jointure (.)
Book.names = {(B0)} . {(B0, N0), (B0, N2)}
Book.names = {(N0), (N2)}
names.Name = {(B0, N0), (B0, N2)} . {(B0, N0), (B0, N2)}
names.Name = {(B0)}

Le carnet d'adresses

Découverte de la syntaxe

sig Name, Addr {}
sig Book {
  // addresses = {(B0, N0, A0), (B0, N1, A2), (B1, N2, A0)}
  addresses: Name -> lone Addr
}

run {} for 3
sig Name, Addr {}
sig Book {
  addresses: Name -> lone Addr
}

pred show (b: Book) {
  // {(B0)} . {(B0, N0, A0), (B0, N1, A2), (B1, N2, A0)}
  // {(N0, A0), (N1, A2)}
  #b.addresses > 1
}

run show for 3 but 1 Book
sig Name, Addr {}
sig Book {
  addresses: Name -> lone Addr
}

pred add (b, b': Book, n: Name, a: Addr) {
  b'.addresses = b.addresses + n -> a
}

pred showAdd (b, b': Book, n: Name, a: Addr) {
  add [b, b', n, a]
  #Name.(b'.addresses) > 1
}

run showAdd for 3 but 2 Book
sig Name, Addr {}
sig Book {
  addresses: Name -> lone Addr
}

pred add (b, b': Book, n: Name, a: Addr) {
  b'.addresses = b.addresses + n -> a
}

pred del (b, b': Book, n: Name) {
  b'.addresses = b.addresses - n -> Addr
}

fun lookup (b: Book, n: Name): set Addr {
  n.(b.addresses)
}

pred showAdd (b, b': Book, n: Name, a: Addr) {
  add [b, b', n, a]
  #Name.(b'.addresses) > 1
}

run showAdd for 3 but 2 Book
assert delUndoesAdd {
  all b, b', b'': Book , n: Name, a: Addr |
    add[b, b', n, a] and del[b', b'', n] implies b.addresses = b''.addresses
}

check delUndoesAdd for 3
assert delUndoesAdd {
  all b, b', b'': Book , n: Name, a: Addr |
    no n.(b.addresses) and add[b, b', n, a] and del[b', b'', n]
      implies b.addresses = b''.addresses
}

Jusqu'ici, on a :

  • Posé les bases de notre modèle
  • Généré des exemples avec facilité
  • Mis à l'epreuve notre modèle mental

2ème itération

Introduction des alias et des groupes

abstract sig Target {}
sig Addr extends Target {}
abstract sig Name extends Target {}
sig Alias, Group extends Name {}
sig Book { addresses: Name -> Target }

pred show (b: Book) { some b.addresses }
run show for 3 but 1 Book
abstract sig Target {}
sig Addr extends Target {}
abstract sig Name extends Target {}
sig Alias, Group extends Name {}
sig Book { addresses: Name -> Target } {
  no n: Name | n in n.^addresses
}

fact { all b: Book | no n: Name | n in n.^(b.addresses) }

pred show (b: Book) { some b.addresses }
run show for 3 but 1 Book
abstract sig Target {}
sig Addr extends Target {}
abstract sig Name extends Target {}
sig Alias, Group extends Name {}
sig Book { addresses: Name -> Target } {
  no n: Name | n in n.^addresses
  all a: Alias | lone a.addresses
}

pred show (b: Book) { some Alias.(b.addresses) }
run show for 3 but 1 Book
abstract sig Target {}
sig Addr extends Target {}
abstract sig Name extends Target {}
sig Alias, Group extends Name {}
sig Book {
  names: set Name,
  addresses: names -> some Target
} {
  no n: Name | n in n.^addresses
  all a: Alias | lone a.addresses
}

pred show (b: Book) { some Alias.(b.addresses) }
run show for 3 but 1 Book
pred add (b, b': Book, n: Name, t: Target) { b'.addresses = b.addresses + n -> t }
pred del (b, b': Book, n: Name, t: Target) { b'.addresses = b.addresses - n -> t }
fun lookup (b: Book, n: Name): set Addr { n.^(b.addresses) & Addr }
abstract sig Target { }
sig Addr extends Target { }
abstract sig Name extends Target { }
sig Alias, Group extends Name { }
sig Book {
	names: set Name,
	addresses: names->some Target
} {
	no n: Name | n in n.^addresses
	all a: Alias | lone a.addresses
}

pred add [b, b': Book, n: Name, t: Target] { b'.addresses = b.addresses + n->t }
pred del [b, b': Book, n: Name, t: Target] { b'.addresses = b.addresses - n->t }
fun lookup [b: Book, n: Name] : set Addr { n.^(b.addresses) & Addr }

assert delUndoesAdd {
	all b, b', b'': Book, n: Name, t: Target |
		no n.(b.addresses) and add [b, b', n, t] and del [b', b'', n, t]
		implies b.addresses = b''.addresses
}
check delUndoesAdd for 3

assert addIdempotent {
	all b, b', b'': Book, n: Name, t: Target |
		add [b, b', n, t] and add [b', b'', n, t]
		implies b'.addresses = b''.addresses
}
check addIdempotent for 3

assert addLocal {
	all b, b': Book, n, n': Name, t: Target |
		add [b, b', n, t] and n != n'
		implies lookup [b, n'] = lookup [b', n']
}
check addLocal for 3 but 2 Book

assert lookupYields {
	all b: Book, n: b.names | some lookup [b,n]
}
check lookupYields for 4 but 1 Book

Tracer la cynématique du modèle

module tour/addressBook

open util/ordering [Book] as BookOrder

abstract sig Target { }
sig Addr extends Target { }
abstract sig Name extends Target { }

sig Alias, Group extends Name { }

sig Book {
	names: set Name,
	addresses: names->some Target
} {
	no n: Name | n in n.^addresses
	all a: Alias | lone a.addresses
}

pred add [b, b': Book, n: Name, t: Target] { b'.addresses = b.addresses + n->t }
pred del [b, b': Book, n: Name, t: Target] { b'.addresses = b.addresses - n->t }
fun lookup [b: Book, n: Name] : set Addr { n.^(b.addresses) & Addr }

pred init [b: Book]  { no b.addresses }

fact traces {
	init [first]
	all b: Book-last | let b' = b.next | some n: Name, t: Target |
	      add [b, b', n, t] or del [b, b', n, t]
}

pred show { }

run show for 4
assert lookupYields { all b: Book, n: b.names | some lookup [b, n] }
check lookupYields for 3 but 4 Book

t in Addr or some lookup [b, t]

no b.addresses.n or some n.(b.addresses) - t

Était-ce bien utile ?

  • Les bugs sont "triviaux"
  • Les tests unitaires suffisent
  • Beaucoup de code pour rien

Hmm, pas exactement

  • Apple Mail a ce bug
  • Les bugs sont toujours triviaux
  • Alloy s'apprend

Les forces d'Alloy

  • Incrémental
  • Pas dépendant du runtime
  • Peu de maths
  • Pas de fausse alarme
  • Les graphiques générés

Minute honnêteté

Ça n'est pas mon usage d'Alloy

Pas de miracle

  • Formuler des spécifications cohérentes
  • Communiquer les besoins
  • Comprendre les contraintes du système

Les alternatives

  • Les systèmes de type fort
  • La programmation par contrat
  • Property-based testing

MÉTHODES FORMELLES

pensez-y quand même

Bibliographie

Merci pour votre attention

modelling

By Thomas Bracher

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