Alloy Analyzer のこと

Alloy Analyzer2011 9 23

• (id:mr_konn / @mr_konn) • • • Haskell Lover • 2010 Summer Intern PFI2011 9 23

• Alloy • • Alloy Analyzer http://alloy.mit.edu/alloy4/2011 9 23

Alloy Analyzer • • → / • •“ ”2011 9 23

• …… • • •2011 9 23

“ ” • Alloy SAT • • (10 ) • • •2011 9 23

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• • , •2011 9 23

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Alloy enum { , } enum { , } abstract sig { : one } abstract sig { : lone , : } { some => ( = <=> . = ) } • •2011 9 23

Alloy (2) one sig extends {} { in } one sig extends {} { no } one sig extends {} { = <=> ( . = => . = ) } pred show {} run show • • run : pred2011 9 23

• •2011 9 23

• • • Yes/No2011 9 23

Alloy (1) module marsandvenus abstract sig { : , enum { , } : , enum { , } : -> one enum { , } } { all q : | sig { (( = and = ) ! : -> one or ( = and = )) } <=> [q] = q. [this] } • • /2011 9 23

Alloy (2) • …… one sig extends {} { in and in } • • ……2011 9 23

pred ( : ) { all : | . in <=> ( . [ ] = ) } fact { one } run • Yes • run2011 9 23

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○ No ○ Yes × No × Yes • YES2011 9 23

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• • …… • • • or2011 9 23

module tour/filesystem abstract sig Object {} sig Directory extends Object { contents: set Object } one sig Root extends Directory {} sig File extends Object {} sig Alias extends File {to: Object} pred show {} run show2011 9 23

…… • 1. (File) 2. 3.2011 9 23

fact FileBelongsSomewhere { all f : File | one d : Directory | f in d.contents } fact NoRecursiveDirs { ! no d : Directory | d in d.contents } fact RootHasNoSuperDir { no d: Directory | Root in d.contents } • fact : • • ( )2011 9 23

• Directory • FileBelongsSomewhere fact ObjBelongsSomewhere { all o : Object | one d : Directory | o in d.contents }2011 9 23

…… • • RootHasNoSuperDir ObjBelongsSomewhere • all o : Object all o : Object - Root2011 9 23

• • • ……2011 9 23

Alloy • Alloy • Object = Directory ⊔ File, Alias ⊆ File • • ( ) • Root one • contents : Directory Object • n n • 12011 9 23

• A+B:A B • A&B:A B • A-B:A B • A in B : A B (A ⊆ B) • (A∈B) • A = B :A B2011 9 23

• P→Q: P, Q • A.B : • A B • {(1)} . {1→A, 1→B, 3→B} = {(A), (B)} {1→A, 1→B, 3→B} . {(B)} = {(1), (3)} •2011 9 23

• A[B] : B. A • a.b [c] = c.(a.b) • • ~a : a • ^a, *a : • ^{1→2, 2→3} = {1→2, 2→3, 1→3} • *{1→2, 2→3} = {1→2, 2→3, 1→3, 1→1, 2→2, 3→3}2011 9 23

• none : • • univ : • • iden : • a.iden = a , iden.a = a (forall a)2011 9 23

… • / •2011 9 23

fact NoRecursiveDirs { ! no d : Directory | d in d.^contents } fact NoRecursiveAliases { ! no a : Alias | a in a.^to } • •2011 9 23

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run pred show {} run show • run hoge : hoge • show • ( )2011 9 23

pred show {} for 4 run show • for n n • n=3 • • for 4 but 2 Alias, exactly 1 Directory • 4 2 Alias, 1 Dir •2011 9 23

• Object Root • … •2011 9 23

assert assert TrackableFromRoot { all o : Object | o in Root.^contents } check TrackableFromRoot • ( ) • check hoge hoge • run (default: 3)2011 9 23

• …… • Root Root • Object - Root Root.*contents2011 9 23

assert TrackableFromRoot { all o : Object | o in Root.*contents } check TrackableFromRoot • •2011 9 23

Alloy • fact NoRecursiveDirsOrAlias { ! no iden & (^contents + ^to) } fact RootHasNoSuperDir {no contents.Root} fact AllObjBelongSomewhere { all o : Object - Root | some contents.o } assert TrackableFromRoot { Object in Root.*contents }2011 9 23

• Alloy • • • Alloy •2011 9 23

Any Questions?2011 9 23

2011 9 23

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Alloy Analyzer のこと

by Hiromi Ishii on Sep 22, 2011

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