pictures, a case study(4)

7/31/2019 Pictures, A Case Study(4)

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Pictures: A Case Study

Lecture 4,

Programmeringsteknik del A.


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Purpose

We will go through a larger example of designing a part of a

program: a library of functions for manipulating pictures.

Why?

See examples of programming with lists; practice what we

have learned.

Introduce the type Char of characters.

Discuss the design of larger parts of programs than individual

functions.


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Top-Down Design

Original

problemBreak into

subproblems.

Problems

simple

enough to

solve with

one function.


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Top-Down Design

What functions might help me solve this problem?

Break down a difficult problem into manageable pieces -- an

effective problem solving strategy.

Work is directed towards solving the problem in hand -- nounnecessary programming.

May not result in many generally useful functions as a by-

product.


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Bottom-Up Design

Interesting

functions.

Interesting

combinations.

Desired

program.


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Bottom-Up Design

What can I do with the functions available to me?

An effective way to build up powerful program components.

Work is directed towards producing generally useful

functions, which can then be reused in many applications.

A solution looking for a problem!


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Interfaces

What can the user

assume?

What must the

implementor provide?

An interface defines the `contract

between two program components.

The implementation can be replaced by

any other that respects the interface.

Cf. Renting a

car.


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Example: Pictures

Top-down: We have discovered a need to manipulate

rectangular pictures.

Bottom-up: What interesting functions can we provide?

Interface: What should the `contract between pictureusers and the picture implementor specify?


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The Type of Pictures

Pictures are a kind of data; we will need a type for them.

type Picture = ...

Not known yet.

Part of the

interface.

Private to the

implementation.

A type whose name is public, but whose representation is

private, is called an abstract data type.


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Functions on Pictures

flipH

flipV

flipH, flipV :: Picture -> Picture


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Properties of Flipping

What properties should flipH, flipV satisfy?

flipH (flipH pic) == pic

flipV (flipV pic) == pic

flipH (flipV pic) == flipV (flipH pic)

Properties which

the user can assume.

Properties which the

implementor should guarantee.


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Combining Pictures

sideBySide

above

above, sideBySide ::

Picture -> Picture -> Picture


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Properties of Combinations

a àbove` (b àbove` c) == (a àbove` b) àbove` c


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flipH (a `above` b) == flipH a `above` flipH b


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flipV (a `above` b) == flipV b `above` flipV b


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Quiz: Using Pictures

white

black

check


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Quiz: Using Pictures

white

black

check

wb = white `sideBySide` black

check = wb `above` flipH wb


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Local Definitions

Wb is used only to define check. But when we read the

program, we cant tell.

check = wb `above` flipH wb

where wb = white `sideBySide` black

Only defined within

check.


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Quiz: Make a Chess Board


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Quiz: Make a Chess Board

quartet check

quartet (quartet check)


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Defining Quartet

quartet :: Picture -> Picture

quartet pic = two `above` two

where two = pic `sideBySide` pic

A local definition can

use the function arguments.


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Flipping Vertically

[ ## ,

# # ,

# # ,

########,

## ]

flipV

[ ## ,

########,

# # ,

# # ,

## ]

flipV :: Picture -> Picture

flipV pic = reverse pic


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Quiz: Flipping Horizontally

flipH

[ # ,

# ,

######, # ,

# ]

[ # ,

# ,

######, # ,

# ]

Recall: Picture = [[Char]]


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Quiz: Flipping Horizontally

flipH

[ # ,

# ,

######, # ,

# ]

[ # ,

# ,

######, # ,

# ]

flipH :: Picture -> Picture

flipH pic = [reverse line | line


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Combining Pictures Vertically

[ # ,

# ,

######,

# ,

# ]

[ # ,

# ,

######, # ,

# ]

[ # ,

# ,

######,

# ,

# ,

# ,

# ,

######,

# , # ]

above

above p q = p ++ q


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Combining Pictures Horizontally

[ # ,

# ,

######,

# ,

# ]

[ # ,

# ,

######,

# ,

# ]

`sideBySide`

[ # # ,

# # ,############,

# # ,

# # ]


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Combining Pictures Horizontally

[ # ,

# ,

######,

# ,

# ]

[ # ,

# ,

######,

# ,

# ]

`sideBySide`

sideBySide :: Picture -> Picture -> Picture

p `sideBySide` q = [pline ++ qline | (pline,qline)


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Extension: Superimposing

Pictures

superimpose

[ # ,

# ,

######,

# ,

# ]

[ # ,

# ,

######,

# ,

# ]

[ ## ,

# # ,

######,

# # ,

## ]


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Can We Solve a Simpler

Problem?We can superimpose two lines:

superimposeLine :: String -> String -> String

superimposeLine s s =

[superimposeChar c c | (c,c)


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Superimposing Pictures

superimpose :: Picture -> Picture -> Picture

superimpose p q =

[superimposeLine pline qline | (pline, qline)


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Lessons

Two problem solving strategies:

Top-down: break a problem into smaller subproblems.

Bottom-up: combine solutions into bigger solutions.

Collect useful related functions (often based around a common

type) into libraries for future use.


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pictures, a case study(4)

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