DYNALLOY : AN EXTENSION OF ALLOY FOR WRITING AND ANALYZING - - PowerPoint PPT Presentation

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DYNALLOY : AN EXTENSION OF ALLOY FOR WRITING AND ANALYZING - - PowerPoint PPT Presentation

Aug 20, 2022 202 likes •453 views

DYNALLOY : AN EXTENSION OF ALLOY FOR WRITING AND ANALYZING BEHAVIOURAL MODELS Germn Regis | Csar Cornejo | Simn Gutirrez Brida | Mariano Politano | Fernando Raverta | Pablo Ponzio | Nazareno Aguirre | Juan Pablo Galeotti | Marcelo Frias

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SLIDE 1

DYNALLOY: AN EXTENSION OF ALLOY FOR WRITING AND ANALYZING BEHAVIOURAL MODELS

Germán Regis | César Cornejo | Simón Gutiérrez Brida | Mariano Politano | Fernando Raverta | Pablo Ponzio | Nazareno Aguirre | Juan Pablo Galeotti | Marcelo Frias

Workshop on the Future of Alloy

Universidad Nacional de Río Cuarto Universidad de Buenos Aires Instituto Tecnológico Buenos Aires

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SLIDE 2

EXAMPLE - RIVER CROSSING PUZZLE

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SLIDE 3

EXAMPLE - RIVER CROSSING PUZZLE

Fa Ch Fox Gr Fa Ch Fox Gr

near far near far

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SLIDE 4

RIVER CROSS - ALLOY SPECIFICATION

abstract sig Object { eats: set Object}

  • ne sig Farmer, Fox, Chicken, Grain extends Object { }

fact { eats = Fox->Chicken + Chicken->Grain }

Fa Ch Fox Gr

sig State { near, far: set Object }

Fa Ch Fox Gr

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SLIDE 5

RIVER CROSS - DYNAMIC BEHAVIOR

Fa Ch Fox Gr Fa Ch Fox Gr

State Change

Fa Ch Fox Gr Fa Ch Fox Gr

…

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SLIDE 6

RIVER CROSS - DYNAMIC BEHAVIOR

Fa Ch Fox Gr Fa Ch Fox Gr

State Change

Fa Ch Fox Gr Fa Ch Fox Gr

…

1 2 3 4 5 6 7 8

Ordering

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SLIDE 7

RIVER CROSS - ALLOY SPECIFICATION

Fa Ch Fox Gr

fact { first.near = Object && no first.far}

  • pen util/ordering[State]

sig State { near, far: set Object }

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SLIDE 8

RIVER CROSS - ALLOY SPECIFICATION

Fa Ch Fox Gr

fact { first.near = Object && no first.far}

  • pen util/ordering[State]

sig State { near, far: set Object } pred crossRiver[from, from', to, to': set Object] { one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } }

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SLIDE 9

RIVER CROSS - ALLOY SPECIFICATION

Fa Ch Fox Gr

fact { first.near = Object && no first.far}

  • pen util/ordering[State]

sig State { near, far: set Object }

… … …

fact { all s: State, s': s.next | { Farmer in s.near => crossRiver[s.near, s'.near, s.far, s'.far]
 else crossRiver[s.far, s'.far, s.near, s'.near] } } pred crossRiver[from, from', to, to': set Object] { one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } }

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SLIDE 10

RIVER CROSS - ALLOY SPECIFICATION

Fa Ch Fox Gr

fact { first.near = Object && no first.far}

  • pen util/ordering[State]

sig State { near, far: set Object }

… … …

fact { all s: State, s': s.next | { Farmer in s.near => crossRiver[s.near, s'.near, s.far, s'.far]
 else crossRiver[s.far, s'.far, s.near, s'.near] } } pred crossRiver[from, from', to, to': set Object] { one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } } run { last.far = Object } for 8 States

SATisfying valuations of the predicate are solutions to the puzzle

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SLIDE 11

RIVER CROSS - ALLOY SPECIFICATION

Fa Ch Fox Gr

fact { first.near = Object && no first.far}

  • pen util/ordering[State]

sig State { near, far: set Object }

… … …

fact { all s: State, s': s.next | { Farmer in s.near => crossRiver[s.near, s'.near, s.far, s'.far]
 else crossRiver[s.far, s'.far, s.near, s'.near] } } pred crossRiver[from, from', to, to': set Object] { one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } } run { last.far = Object } for 8 States

SATisfying valuations of the predicate are solutions to the puzzle

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SLIDE 12
  • Execution traces are indirectly defined through:
  • Atomic Actions (State Change)
  • Programs (imperative style & nondeterminism) 


Assumptions | Test ? | Choice + | 
 Sequential Composition ; | Iteration *

DYNALLOY

= ALLOY + DYNAMIC LOGIC

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SLIDE 13

{ one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } } fact { first.near = Object && no first.far}

RIVER CROSS - DYNALLOY SPECIFICATION

fact { all s: State, s': s.next | { Farmer in s.near => crossRiver[s.near, s'.near, s.far, s'.far]
 else crossRiver[s.far, s'.far, s.near, s'.near] } } crossRiver[from,

  • pen util/ordering[State]

run { last.far = Object } for 8 States sig State { near, far: set Object } pred from’, , to’ : set Object] to

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SLIDE 14

{ one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } } fact { first.near = Object && no first.far}

RIVER CROSS - DYNALLOY SPECIFICATION

fact { all s: State, s': s.next | { Farmer in s.near => crossRiver[s.near, s'.near, s.far, s'.far]
 else crossRiver[s.far, s'.far, s.near, s'.near] } } crossRiver[from, run { last.far = Object } for 8 States sig State { near, far: set Object } pred from’, , to’ : set Object] to

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SLIDE 15

{ one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } }

RIVER CROSS - DYNALLOY SPECIFICATION

fact { all s: State, s': s.next | { Farmer in s.near => crossRiver[s.near, s'.near, s.far, s'.far]
 else crossRiver[s.far, s'.far, s.near, s'.near] } } crossRiver[from, run { last.far = Object } for 8 States sig State { near, far: set Object } pred from’, , to’ : set Object] to

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SLIDE 16

{ one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } }

RIVER CROSS - DYNALLOY SPECIFICATION

fact { all s: State, s': s.next | { Farmer in s.near => crossRiver[s.near, s'.near, s.far, s'.far]
 else crossRiver[s.far, s'.far, s.near, s'.near] } } crossRiver[from, run { last.far = Object } for 8 States sig State { near, far: set Object } : set Object] to action pre { Farmer in from } post

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SLIDE 17

{ one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } }

RIVER CROSS - DYNALLOY SPECIFICATION

crossRiver[from, run { last.far = Object } for 8 States sig State { near, far: set Object } : set Object] to action pre { Farmer in from } post program solvePuzzle[near, far: set Object] { assume (Object in near && no far); (crossRiver[near, far] + crossRiver[far, near])*; [Object in far]? }

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SLIDE 18

{ one x: from | { from' = from - x - Farmer - from’.eats && to' = to + x + Farmer } }

RIVER CROSS - DYNALLOY SPECIFICATION

crossRiver[from, sig State { near, far: set Object } : set Object] to action pre { Farmer in from } post program solvePuzzle[near, far: set Object] { assume (Object in near && no far); (crossRiver[near, far] + crossRiver[far, near])*; [Object in far]? } run solvePuzzle for 4 lurs 8

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SLIDE 19

RIVER CROSS - DYNALLOY PARTIAL CORRECTNESS ASSERTIONS

{ precondition } PROGRAM { postcondition }

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SLIDE 20

RIVER CROSS - DYNALLOY PARTIAL CORRECTNESS ASSERTIONS

assert noResurrection[near, far: set Object, x: Object] { pre { no (near & far) } prog { (crossRiver[near, far] + crossRiver[far, near])*; [x !in (near+far)] ? ; (crossRiver[near, far] + crossRiver[far, near])*; } post { x !in (near’+far') } } check noResurrection for 4 lurs 8

… …

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SLIDE 21

DYNALLOY FEATURES

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SLIDE 22

DYNALLOY FEATURES

  • Completely integrated into Alloy Analyzer
  • Fully compatible with standard Alloy, produces detailed

compile-time error reports

  • Supports abstract syntax of programs, as well as

imperative programming constructs (assignment, while loops, subprogram calls, …)

  • Trace visualization (in the style of a program debugger)
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SLIDE 23

DYNALLOY FEATURES

  • Completely integrated into Alloy Analyzer
  • Fully compatible with standard Alloy, produces detailed

compile-time error reports

  • Supports abstract syntax of programs, as well as

imperative programming constructs (assignment, while loops, subprogram calls, …)

  • Trace visualization (in the style of a program debugger)
  • Next release:
  • Efficient characterization of traces using skolemization
  • Efficient real and integer arithmetical representation
  • Control flow graph visualization for analyzing execution

traces