Data Abstraction

1
Data Abstraction

• CMSC 1150
• Introduction to Computer Programming
• October 2, 2002

2
Roadmap

• Recap
• Compound expressions Procedural Abstraction
• Data Abstraction
• Motivation Compound Data
• Abstract Interface Constructors and Selectors
• Concrete Implementation with define-struct
• Abstraction Barriers
• Good Design Data definitions and contracts
• Summary

3
Administrivia

• Add yourself to the course mailing list
• http//mailman.cs.uchicago.edu 11500-1
• TA office hours
• Leandro Cortes Thurs 2-4, Ry178
• Yu Tony Hu Fri 2-4, Ry 178
• Dinoj Surendran Wed 3-4, Fri 10-11am, Eckhart
  006
• First homework Due Monday
• Dr Scheme note Language set to R5RS

4
Recap Expressions and Procedures

• Primitives E.g. integers
• Primitive operators ,-,,..
• Primitive expressions ( 1 2), ( 3 4)
• Compound expressions
• ( ( 1 2) (5 6))
• Procedural abstraction (define (square x) ( x
  x))
• Conditionals if, cond
• Issues Substitution model, Evaluation order

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Compounding Abstraction

• Procedures and Expressions
• Combine primitives
• Create more complex, powerful expressions
• Abstractions
• Procedures as black boxes, apply to different
  input
• E.g. square procedure
• (define (area r) ( pi (square r)))
• Doesnt matter how implement square as long as it
  returns the square of the input.

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Compound Data Abstraction

• Similar issues arise for data
• Represent things more complex than integers
• Similar to building more complex functions
• Objects have many facets
• Abstract away from implementation
• Any structure that behaves correctly

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Compound Data Motivation

• Real world objects often have many facets
• Example Specifying a point in a plane
• (x,y) coordinate pair
• Create one data structure that holds BOTH
• In use, often want x- or y- coordinate
• E.g. to compute distance from origin, slope of
  line defined by two points, etc
• Need accessors for each facet

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Compound Data Structures

• Example (x,y) coordinates
• (make-posn x y)
• Takes two numbers
• Combines into a posn structure
• posn can be input or output of procedure
• E.g. (distance-to-0 (make-posn 5 0)) gt 5
• (distance-to-0 (make-posn 3 4)) gt 5

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Accessing Components

• To compute distance-to-0
• Need x and y coordinate values
• Two procedures posn-x, posn-y
• (posn-x (make-posn 1 3)) gt 1
• (posn-y (make-posn 1 3)) gt 3
• (define (distance-to-0 a-posn)
• (sqrt ( (square (posn-x a-posn))
• ( (square (posn-y a-posn))))

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Abstraction

• How do make-posn, posn-x, and posn-y work?
• As users, we dont need to know
• Key make-posn combines x and y
• posn-x, posn-y return coordinates
• Any implementation with this behavior is fine

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Interface

• Define an interface between abstract use and
  concrete implementation of structure
• Two types of procedures
• Constructors e.g. make-posn
• Selectors e.g. posn-x, posn-y
• Implement abstract data via concrete
  representation

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A Concrete Implementation

• (define-struct posn (x y))
• Structure definition creates 3 procedures
• Constructor make-posn
• Selector posn-x
• Selector posn-y
• Discussion Other structures

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Example Operations on Points

• (distance-to-0 a-posn)
• (line-length a-posn1 a-posn2)
• (line-slope a-posn1 a-posn2)
• etc.

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Abstraction Barriers

• Separate programs that use abstraction from those
  that implement abstraction

Points in problem domain
Distance-to-0 line-length line-slope
Points as x,y coordinates
make-posn posn-x posn-y
Points as structures
define-struct
However structures are implemented
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Why Abstraction?

• Can make programs much easier to maintain and
  modify
• Consider alternate implementations
• Limit changes to small of interface procedures
• But only successful if maintain abstraction

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Good Design Data Definition

• Problem (make-posn dog cat)
• Clearly wrong
• Would blow up in distance-to-0, line-length, etc
• Issue Guarantee that given correct types of
  input to constructor, processing output of
  selectors should yield intended result
• Solution Data Definition
• Establish agreement between programmers and users

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Data Definition

• What is it?
• Combination of Scheme and English specifying
• How to use a class of structures
• How to construct elements of this class
• Example posn
• A posn is a structure (make-posn x y)
• where x and y are numbers
• Discussion Other definitions

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Summary

• Compound data abstraction
• Parallel to use of compound expresssions
• Capture multiple facets of objects
• Interface Constructors and Selectors
• Abstraction Allow users of data to ignore
  implementation
• Abstraction barriers
• Concrete Implementation with define-struct
• Data definitions Establish covenant between
  users and programmers of data for behavior and
  input

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Next Time

• Today Finite compound data
• Friday Infinite compound data
• Lists constructors and selectors
• Recursion