[PPT] - Kernel Implementations III 8 February 2019 OSU CSE 1 Implementing PowerPoint Presentation

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Kernel Implementations III

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Implementing a Kernel Class

From the examples so far, you should see

there are two major questions to address:

– Q1: What data representation (a.k.a. data structure) should be used to represent a value of the new type being implemented? – Q2: What algorithms should be used to manipulate that data representation to implement the contracts of the kernel methods?

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How To Think About Q1

Two-level thinking: Restrict your attention

to exactly two adjacent levels in the tower

– One is the level for which you are implementing a new kernel class

See the kernel interface for the new type you are

creating

– The other is the level directly below the level for the new kernel class you are creating

See the interfaces for the types of the variables

you are using to represent a value of the new type

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Queue Queue3 implements QueueKernel extends QueueSecondary extends Object extends Standard extends Iterable extends

Example revisited: Queue represented using a Sequence.

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Queue Queue3 implements QueueKernel extends QueueSecondary extends Object extends Standard extends Iterable extends

The class Queue3 uses the interface Sequence.

Sequence uses

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Queue Queue3 implements QueueKernel extends QueueSecondary extends Object extends Standard extends Iterable extends Sequence uses

The two levels

f the tower of

abstractions for Queue3 are this level with Queue ...

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Queue Queue3 implements QueueKernel extends QueueSecondary extends Object extends Standard extends Iterable extends Sequence uses

... and this level with Sequence.

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Example: Queue3 on Sequence

public class Queue3<T> extends QueueSecondary<T> { private Sequence<T> entries; ... }

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public class Queue3<T> extends QueueSecondary<T> { private Sequence<T> entries; ... }

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There is one instance variable (a.k.a. data member) in this representation of a Queue: a Sequence called entries.

Example: Queue3 on Sequence

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Picture: Queue3 on Sequence

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< 4, 7, 3 > What the client sees: a Queue whose value is < 4, 7, 3 >.

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Picture: Queue3 on Sequence

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< 4, 7, 3 > < 4, 7, 3 > What the implementer can manipulate: a Sequence whose value is < 4, 7, 3 >.

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NaturalNumber NaturalNumber2 implements NaturalNumber- Kernel extends NaturalNumberSecondary extends Object extends Standard extends Comparable extends

Example revisited: NaturalNumber represented using a Stack.

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NaturalNumber NaturalNumber2 implements NaturalNumber- Kernel extends NaturalNumberSecondary extends Object extends Standard extends Comparable extends Stack uses

The class NaturalNumber2 uses the interface Stack.

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NaturalNumber NaturalNumber2 implements NaturalNumber- Kernel extends NaturalNumberSecondary extends Object extends Standard extends Comparable extends Stack uses

The two levels

f the tower of

abstractions for NN2 are this level with NN ...

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NaturalNumber NaturalNumber2 implements NaturalNumber- Kernel extends NaturalNumberSecondary extends Object extends Standard extends Comparable extends Stack uses

... and this level with Stack.

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Example: NaturalNumber2 on Stack

public class NaturalNumber2 extends NaturalNumberSecondary { private Stack<Integer> digits; ... }

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public class NaturalNumber2 extends NaturalNumberSecondary { private Stack<Integer> digits; ... }

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There is one instance variable (a.k.a. data member) in this representation of a NaturalNumber: a Stack<Integer> called digits.

Example: NaturalNumber2 on Stack

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Picture: NaturalNumber2 on Stack

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724 What the client sees: a NaturalNumber whose value is 724.

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724 < 4, 2, 7 > What the implementer can manipulate: a Stack whose value is < 4, 2, 7 >.

Picture: NaturalNumber2 on Stack

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Two-Level Thinking

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client view: mathematical model, method contracts implementer view: data representation, algorithms

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Two-Level Thinking

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client view: mathematical model, method contracts implementer view: data representation, algorithms See the kernel interface for a description of what the software behaves like, what the client sees.

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Two-Level Thinking

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client view: mathematical model, method contracts implementer view: data representation, algorithms See the kernel class for a description of how the software achieves its behavior.

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Two-Level Thinking

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client view: mathematical model, method contracts implementer view: data structure, algorithms The ovals denote sets

f mathematical

model values, this

ne for the client’s

view of the new type ...

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Two-Level Thinking

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client view: mathematical model, method contracts implementer view: data structure, algorithms ... and this one for the kernel-class implementer’s view of the chosen data representation.

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Two-Level Thinking

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This is the abstract state space: the set of all possible math model values as seen by a client.

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Two-Level Thinking

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This is the concrete state space: the set of all possible math model values of the data representation.

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Two-Level Thinking

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This is the interpretation of each concrete value (below) as an abstract value (above).

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Two-Level Thinking

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Example: For interface NaturalNumber this is the set of all integer values that are non- negative. 7 165 29

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Two-Level Thinking

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Example: For class NaturalNumber2 this is the set of all string of integer values that satisfy the properties we want in the data representation. 7 165 29 <> <7> <9,2> <5,6,1>

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Two-Level Thinking

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Example: For class NaturalNumber2 the interpretation maps a string of integer to the integer whose decimal digits are those in the string, in reverse order. 7 165 29 <> <7> <9,2> <5,6,1>

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Implementing a Kernel Class

Recall, there are two major questions to

address:

– Q1: What data representation (a.k.a. data structure) should be used to represent a value of the new type being implemented? – Q2: What algorithms should be used to manipulate that data representation to implement the contracts of the kernel methods?

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How To Think About Q2

One-step thinking: Restrict your attention

to the states just before and just after a method call

Combined with two-level thinking about

the data representation, this leads to a device called a commutative diagram

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Commutative Diagram

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7 165 29 <> <7> <9,2> <5,6,1> 7 165 29 <> <7> <9,2> <5,6,1> before the method call after the method call

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Commutative Diagram

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7 165 29 <> <7> <9,2> <5,6,1> 7 165 29 <> <7> <9,2> <5,6,1> This is the abstract transition: for each state before the call, where it might end up according to the method’s contract.

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Commutative Diagram

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7 165 29 <> <7> <9,2> <5,6,1> 7 165 29 <> <7> <9,2> <5,6,1> This is the concrete transition: for each state before the call, where it might end up according to the method’s body.

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7 165 29 <> <7> <9,2> <5,6,1> 7 165 29 <> <7> <9,2> <5,6,1> The contract says that, if n = 0, then the call n.multiplyBy10(7); will result in n = 7.

Example: n.multiplyBy10(7)

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Example: n.multiplyBy10(7)

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7 165 29 <> <7> <9,2> <5,6,1> 7 165 29 <> <7> <9,2> <5,6,1> So, given any data representation of n = 0, the method body must change it so that after the call it has some data representation of n = 7.

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Over-Up and Up-Over “Commute”

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7 165 29 <> <7> <9,2> <5,6,1> 7 165 29 <> <7> <9,2> <5,6,1>

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Over-Up and Up-Over “Commute”

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7 165 29 <> <7> <9,2> <5,6,1> 7 165 29 <> <7> <9,2> <5,6,1> Starting here, going over then up ...

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Over-Up and Up-Over “Commute”

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7 165 29 <> <7> <9,2> <5,6,1> 7 165 29 <> <7> <9,2> <5,6,1> ... is the same as going up then over.

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Correctness

The kernel class correctly implements

the kernel interface if and only if, for every method and for every legal input state for that method, the method body (over-then- up) always results in a state that satisfies the method contract (up-then-over)

The commutative diagram lets you think

clearly about how to make your code correct

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Some Questions To Think About

Given a kernel class, can there ever be

more than one data representation for a given abstract value? In other words, can there be more than one concrete value that can be interpreted as the same abstract value?

– If so, what would it look like in the diagram?

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Some Questions To Think About

Given a kernel interface, can there ever be

more than one possible correct (abstract) result of a call, according to a method’s contract?

– If so, what would it look like in the diagram?

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Some Questions To Think About

Given a kernel class, can there ever be

more than one possible correct (concrete) result of a call, according to a method’s body?

– If so, what would it look like in the diagram?

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