Question

道路急转弯。

速度限制是40。

宝马可以轻松转弯。卡车可以转弯，还是会离开公路？

使用Alloy创建模型。

断言：所有车辆都可以转弯。

邀请合金分析仪查看该断言是否存在反例。

...

这是合金能做的吗？

如果是，请提供有关如何创建模型的提示，

Answer 1

所有内容都可以在Alloy中建模，问题在于您是否正在尝试解决问题的正确抽象级别。

以下是一个示例，您可以如何抽象地模拟汽车制造急转弯并检查有关模型的各种断言：

enum Angle { a45, a90, a135 }

sig Turn {
  angle: one Angle
}

sig Speed in Int {}

abstract sig Car {
  canMake: Turn -> Speed
}
sig SportsCar extends Car {}
sig Truck extends Car {}

pred isSharpTurn[t: Turn] {
  t.angle = a45
}

fun speedsUnder[limit: Int]: set Speed {
  {s: Speed | s <= limit}
}  

fact {
  // speeds must be non-negative
  Speed in {i: Int | i >= 0}

  // sports cars can make any turn if going below 40
  SportsCar -> Turn -> speedsUnder[40] in canMake

  // any car can make any non-sharp turn if going below 40
  Car -> {t: Turn | !isSharpTurn[t]} -> speedsUnder[40] in canMake

  // any car can make any turn if going below 20
  Car -> Turn -> speedsUnder[20] in canMake
}

pred allCarsCanMakeAllTurnsAtAllSpeeds {
  all c: Car, t: Turn, s: Speed | c -> t -> s in canMake
} 

// counterexample: car = Truck1, turn.angle = 45, speed = 127
check AllCarsCanMakeAllTurnsAtAllSpeeds {
  allCarsCanMakeAllTurnsAtAllSpeeds  
} for 3 but 8 Int

// counterexample: car = SportsCar1, turn.angle = 45, speed = 127
check GivenNoTrucks_AllCarsCanMakeAllTurnsAtAllSpeeds {
  no Truck 
    implies allCarsCanMakeAllTurnsAtAllSpeeds
} for 3 but 8 Int

// counterexample: car = Truck1, turn.angle = 45, speed = 32
check GivenSpeedLimit40_AllCarsCanMakeAllTurnsAtAllSpeeds {
  (all s: Speed | s <= 40) 
    implies allCarsCanMakeAllTurnsAtAllSpeeds
} for 3 but 8 Int

// no counterexample found
check GivenNoTrucksAndSpeedLimit40_AllCarsCanMakeAllTurnsAtAllSpeeds {
  (no Truck and (all s: Speed | s <= 40)) 
    implies allCarsCanMakeAllTurnsAtAllSpeeds
} for 3 but 8 Int

// no counterexample found
check GivenNoSharpTurnsAndSpeedLimit40_AllCarsCanMakeAllTurnsAtAllSpeeds {
  ((no t: Turn | isSharpTurn[t]) and (all s: Speed | s <= 40)) 
    implies allCarsCanMakeAllTurnsAtAllSpeeds
} for 3 but 8 Int

合金模型是否所有汽车都可以在道路上急转弯？

1 个答案: