programming review

1
programming review
2
Data

• Everything in your computer is data
• Including programs
• Data is divided into objects
• Objects can be inside of other objects
• Boxes inside groups
• Colors inside bitmaps
• Objects have types
• Procedures
• Numbers (1, -3.5)
• Strings (this is a string, blue)
• Bitmaps
• Picture objects (lines, groups, boxes, etc.)

3
names
4
Names in Meta

• Denote specific objects
• Constants (numbers, text strings, )
• 1.5
• this is a text string
• -7
• Variables (words)
• point
• box
• ellipse
• translate
• rotate

5
Defining new names in Meta

• define name value
• Tells Meta that name now refers to value
• Name must be a single word
• But value can be an arbitrary expression
• Has to be executed to take effect
• If name already has been defined, redefines it to
  mean value
• Naming is the most basic abstraction mechanism

6
A box figure

• ? group box 400 400
• translate point 100 100
• box 70 70
• translate point 100 -100
• box 70 70
• translate point -100 -100
• box 70 70
• translate point -100 100
• box 70 70

7
Simplifying with names

• ? define frame box 400 400
• ? define little box 70 70
• ? group frame
• translate point 100 100
• little
• translate point 100 -100
• little
• translate point -100 -100
• little
• translate point -100 100
• little

8
Local names in Meta

• with name1 value1 name2 value2
  namen valuenexpression
• Sort of like pronouns in English
• Name objects, but only inside the expression that
  defines them

9
Simplifying with local names

• ? with frame box 400 400
• little box 70 70
• group frame
• translate point 100 100
• little
• translate point 100 -100
• little
• translate point -100 -100
• little
• translate point -100 100
• little

10
An intentionally confusing example

• 1 with
• 3 2
• The names , -, , /, etc. are pre-bound to
  procedures for addition, subtraction, etc.
• But you can always override those by redefineing
  them or by shadowing them with new, local names
• So the value of the expression above is 7
• I.e. 132, not 1(32)

11
What we want to be able to say

• ? define frame box 400 400
• ? group frame
• shifted 100 100
• shifted 100 -100
• shifted -100 -100
• shifted -100 100

12
compound procedures
13
Compound procedures

• arg1 arg2 argn ? exp
• Procedures are just another data object
• You can construct new procedures from old using
  the ? operator
• When called, the procedure
• Sets the local names arg1 arg2 argn to the
  arguments passed to the procedure
• Computes the value of exp using the values of the
  arguments
• Returns the value of exp
• Note you type the ? symbol
• by first typing and then gt

14
Defining shifted

• ? define shifted x y ? translate
  point x y
  little
• ? group frame
• shifted 100 100
• shifted 100 -100
• shifted -100 -100
• shifted -100 100

15
Procedures can be inputs to other procedures

• iterated-groupn ? line point n 20
  0 point
  n 20 30010

16
Using iterated-group

• iterated-groupn ? ink pen 'black n
  line point n 20
  0 point n
  20 30021

Makes a pointin a specified position
17
Using iterated-group

• iterated-groupn ? ink pen 'black n
  line point n 20
  0 point n
  20 30021

Makes a linein a specified position
18
Using iterated-group

• iterated-groupn ? ink pen 'black n
  line point n 20
  0 point n
  20 30021

Makes a black lineof a given width
19
Using iterated-group

• iterated-groupn ? ink pen 'black n
  line point n 20
  0 point n
  20 30021

Makes a procedurefor making lines.
20
Using iterated-group

• iterated-groupn ? ink pen 'black n
  line point n 20
  0 point n
  20 30021

Makes a bunch of lines.
21
Using iterated-group

• ? iterated-group n ?
  translate point n 20
  n 20
  box
  10 10
• 5
• ?

22
Using iterated-group

• ? iterated-group n ?
  translate point 0
  n 10
  box 10
  10
• 5
• ?

23
Using iterated-group

• ? iterated-group n ? translate point n
  10
  sin / n 2
  
  30
  box 10 10 20
• ?

24
What about this one?

• ? iterated-group m ? iterated-group
  n ? translate
  point m 10
  n
  10
  box 10 10
• 5
  5?
• ?

25
What about this one?

• ? iterated-group m ? iterated-group
  n ? translate
  point m 10
  n
  10
  box 10 10
• 5
  5
• ?

26
rules of execution
27
Review rules for execution

• Look at the expression
• If its a number or string
• Its its own value
• If its a name (i.e. a word)
• Look its value up in the dictionary
• (Check if its one of the special cases from the
  next slide)
• Otherwise its a procedure call
• proc-expression arg-expression1
  arg-expressionn
• Execute all the subexpressions(proc-expression
  and arg-expression1 through arg-expressionn )
• Run the value of, passing it the values of
  proc-expression , passing it the values of
  arg-expression1 through arg-expressionn as inputs
• Use its output as the value of the expression

These rules are worth memorizing
28
Special cases

• If it starts with define
• define name value-expression
• Run value-expression
• Assign its value to namein the dictionary
• If it starts with the words with or with
• with name1 value-expression1 namelast
  value-expressionlastresult-expression
• Run the value-expressions
• Assign their values to their respectivenames in
  the dictionary
• Run result-expression
• Set the dictionary back the way it was
• Return the value from result-expression

• If it has a ? inside it
• name1 namelast ? result-expression
• Make a procedure
• That names its inputsname1 namelast
• And returns the valueof result-expression(presum
  ably using those names)
• If it starts with if
• if test-expression result-expression
  alternative-expression
• Run test-expression
• If it returns true
• Run result-expression and return its value
• Otherwise,
• Run alternative-expression and return its value

29
What is the value of this expression?

• 2 2 3

30
What is the value of this expression?

• 2 2 3
• 7

31
What is the value of this expression?

• n ? n 1 3

32
What is the value of this expression?

• n ? n 1 3
• Find the values of the subexpressions
• n ? n 1 is a procdure
• 3 is the number 3

33
What is the value of this expression?

• n ? n 1 3
• Find the values of the subexpressions
• n ? n 1 is a procdure
• 3 is the number 3
• Okay, call the procedure with 3 as its argument
• Add n to the dictionary with the value 3
• Execute n 1
• Find the values of the subexpressions
• is a procedure
• n is 3
• 1 is 1
• Call the procedure with 3 and 1 as arguments
• Output is 4
• Output of procedure is 4
• Value of the overall expression is 4

34
What is the value of this expression?

• n ? n 1 3
• 4
• The rules are simple, but very subtle

35
writing procedures using abstraction
36
Drawing a line

• How do we make a 300 pixel vertical line?

37
Drawing a line

• How do we make a 300 pixel vertical line?
• line point 0 0 point 0 300

38
Drawing a line

• How do we make it two pixels wide?
• line point 0 0 point 0 300

39
Drawing a line

• How do we make it two pixels wide?
• ink pen black 2 line point 0 0
  point 0 300

40
Drawing a line

• How do we make it three pixels wide?
• ink pen black 2 line point 0 0
  point 0 300

41
Drawing a line

• How do we make it three pixels wide?
• ink pen black 3 line point 0 0
  point 0 300

42
Drawing a line

• How do we make a procedure that creates lines of
  specified widths?
• ink pen black 3 line point 0 0
  point 0 300

43
Drawing a line

• How do we make a procedure that creates lines of
  specified widths?
• n ? ink pen black n line point
  0 0 point 0 300

44
Drawing a line

• How do we make it shift the line right by n
  pixels?
• n ? ink pen black n line point
  0 0 point 0 300

45
Drawing a line

• How do we make it shift the line right by n
  pixels?
• n ? ink pen black n line point
  n 0 point n 300

46
Drawing a line

• How do we make it shift the line more?
• n ? ink pen black n line point
  n 0 point n 300

47
Drawing a line

• How do we make it shift the line more?
• n ? ink pen black n line point
  20 n 0
  point 20 n
  300

48
Theme and variation

• How do we get a whole series of lines of
  progressive widths?

49
Theme and variation

• iterated-groupn ? ink pen black n
  line point n 20
  0 point n
  20 30021

generates a single line
number of lines to make
calls the line generator repeatedly and collects
the results
50
Abstraction

• Adding variables to expressions make them less
  specific
• The expression line point n 0
  point n 300
• doesnt express any particular line
• It expresses something more like the abstract
  notion of vertical 300 pixel black lines
• Without specifying which vertical 300 pixel black
  line we mean

51
Programming through abstraction

• A good way to write simple procedures
• Think of what its output should look like in some
  specific case
• Write an expression for it
• Change part of it into a variable
• Wrap it with variable ?
• This technique is called abstracting the
  expression
• Or, if you want to intimidate your friends, you
  can call it?-abstraction

• line point 0 0 point 0 300
• line point n 0 point n 300
• n ? line point n 0 point n
  300

52
Programming through abstraction

• Alas, it usually isnt that simple
• You often have to do something to the input
  before its really in the form you want
• And often times you have to play with it a bit to
  make it work the way you really want

• line point 0 0 point 0 300
• line point n 0 point n 300
• n ? line point n 0 point n
  300
• n ? line point 20 n
  0 point 20 n
  300

53
Making a radial line pattern

• How do we make a pattern of lines radiating out
  from a central point?

54
Making a radial line pattern

• How do we makeone line?
• line point 0 0 point 0 300

55
Making a radial line pattern

• How do we makeone rotated line?
• rotate 30 line point 0 0
  point 0 300

56
Making a radial line pattern

• How do we makean arbitrary rotated line?
• rotate n line point 0 0
  point 0 300

57
Making a radial line pattern

• How do we makea procedure that makes arbitrary
  rotated lines?
• n ? rotate n line point 0 0
  point 0 300

58
Making a radial line pattern

• How do we makea lot of rotated lines?
• iterated-group n ? rotate n
  line point 0 0 point 0
  300 10

59
Fixing it up

• How do we makea full circle?
• iterated-group n ? rotate 36 n
  line point 0 0
  point 0 300 10

60
Example animation
61
imperative programming

• programming where you change objects and
  variables over time

62
Assignment statements

• The simplest change primitive is assignment (?)
• name ? new-value
• After execution, the variable name is changed to
  have the value new-value
• Variable must have already been created using
  define or with
• You type ? as lt -
• Why is this different from define?
• You use define to make new global variables
• You shouldnt use it inside of a procedure
• You use ? to change a variables value, be it a
  local or global variable, while the program is
  running
• Safe to use inside a procedure

63
Sequencing

• Changes are most useful when we can chain them
  together
• That means we need some way of specifying that
• We want to do several things in a row
• And we want them done in a specific order

64
Sequencing with procedures

• Procedures can specify a series of expressions to
  run
• args ? expression expression
• define name args expression
  expression
• The expressions are run in order, first to last
• The value of the last expression is returned as
  the value of the procedure
• The values of the other expressions are ignored
  (although the expressions are still executed)

65
Iteration (aka looping) so far

• So far, when weve wanted to do something
  repeatedly, weve
• Written the something as a procedure
• Call another procedure that iterates and passed
  our procedure to it as an argument
• So forms of iteration are represented by
  specialized procedures

• iterated-group n ? box n 2
  n 2 10
• filter beatles? list
• map album-title filter beatles? list
• fold list

66
Looping as a sequencing primitive

• Most imperative languages have special constructs
  for iteration
• The most basic is the while loop
• Like an if that keeps running

• while test expressions
• Means
• Run test
• If its true, run expressions
• And run test again, etc,
• Keep going until test is false

67
macros and syntactic sugar

• saving you typing

68
Sussman-form definitions

• You spend a lot of time typing things like
  define square n ? n n
• Theres an alternate form of define we sometimes
  use define square n n n
• Notice this is
• More compact
• Has fewer brackets to screw up
• Makes it easier to see what a call to the
  procedure would look like
• This is sometimes called signature define or
  Sussman-form, after its inventor, Gerry Sussman

69
Syntactic sugar

• Meta handles Sussman definitions by rewriting
  them into the long form and then running them
  normally
• So Sussman form doesnt actually let you do
  anything you couldnt do before
• It just lets you express it more easily
• Convenience features like this that just give you
  a better syntax for something you could have done
  anyway are called syntactic sugar.

70
When and unless

• You also spend a lot of time saying
• if test begin stuff to do
• Or worse
• if not test begin stuff
• Meta provides sugar for these common idioms too
• Again, they just get rewritten into an if

• when test stuff to do
• Runs stuff to do if test is true
• Otherwise does nothing
• unless test stuff to do
• Same, but runs it when test is false

71
Cond

• You also spend a lot of time typing
• if test1 result1 if test2
  result2 if test3 result3
  etc
• Cond is an abbreviation for nested ifs
• It also is an abbreviation for a begin in an if,
  like when and unless

• cond test1 expressions
  test2 expressions .
  else expressions
• Runs each test, in order, until it finds one
  thats true
• Then runs the corresponding expressions
• If no tests are true, runs the expressions from
  the else clause

72
One last trick with define

• Suppose you define a procedure define
  iterated-group proc count apply group
  up-to count proc
• Suppose you write this and give it to a beginning
  programming student who accidentally calls it
  with the arguments backwards
• iterated-group 10 n ?
  box n n
• Then they get an error saying that the type of
  one of the arguments to up-to is wrong
• And they say to you whats up-to? I never
  called up-to!

73
Specifying argument types (new)

• You can specify the types of arguments to
  procedures in the definition
• define iterated-group Procedure proc
  Number count apply group
  up-to count proc
• Now the procedure will automatically signal an
  error itself whenever its called with the wrong
  arguments
• This is a good habit to get into because it helps
  track down errors

74
Looking inside data objects
Ellipse Width 15 Height 10

• Data objects are like forms
• They have fields (aka members)
• Filled in by values
• The fields
• Have names (Width, Height)
• The fields are filled in by other data objects
• The objects type (Box, Color) determines what
  fields it has

Box Width 10 Height 10
Number Value 10
Procedure Name iterated-group Arguments proc
count Body apply group
up-to count proc
Color R 240 G 220 B 0
75
Member notation
Ellipse Width 15 Height 10

• You can ask for a field of a data object using
  the . notation object.memberName
• myColor.R
• pixel myBitmap 0 0.R
• iterated-group.Name
• iterated-group.Arguments
• mybox.Width
• Note to simplify the presentation, Ive lied
  here about what the actual fields of boxes,
  procedures, etc. are.
• You can find out what fields are really in an
  object using the inspector.

Box Width 10 Height 10
Number Value 10
Procedure Name iterated-group Arguments proc
count Body apply group
up-to count proc
Color R 240 G 220 B 0
76
Member procedures (aka methods)

• Some of an objects members are procedures
• They act like theyre stored inside the object
• You call them by saying object.name args
• They are usually called methods
• N.B. method is also used to refer to a
  slightly different kind of procedure well talk
  about in the next unit
• Examples
• x.ToStringReturns a string that represents x
• g.DrawLine startx starty endx endyDraws a line
  in a window given its

77
Creating new data objects

• new type arguments
• Creates a new object of the specified type
• The arguments depend on the type
• For windows forms classes, they generally dont
  take any arguments
• Great, but how do we get at the data in the
  object?

• ? define my-form new Form

78
The make command

• The make command Is like new, but it lets you
  specify values for the objects fields
• Creates the object using new
• Set any optional fields fields you specify
• Colons need to be included at the ends of the
  field names (without a space)

• make Type args field value
• Runs new Type args
• Then sets each field of the new object to its
  corresponding value

79
Types and subtypes
Object

• Types often have subtypes
• Integers are a subtype of numbers
• Boxes are a subtype of Pictures
• All types are subtypes of the magic type Object
• Subtyping means objects can have many types
• All Integers are also Numbers
• All Boxes are also Pictures
• And all objects are Objects

List
Number
Array
Integer
Float
Picture
Box
Line
Group
80
Example 1The Windows Forms class hierarchy
Control

• User-interface components (windows, buttons,
  etc.) are all objects
• Individual windows are Form objects
• Individual elements of windows are objects of
  type Button, TextBox, Label, etc.
• Form, Button, etc. are all subtypes of the type
  Control
• Controls can have other Controls inside of them
• Which is how buttons can be inside forms
• All these classes are in the System.Windows.Forms
  namespace

Form
TextBox
Button
TrackBar
Label
PictureBox
Greatly simplified version of the winforms class
hierarchy
81
Fields of the Control class

• These can be used to change the appearance of any
  control
• There are many more, but these should be enough
  for you for now.

• BackColor, ForeColor
• Background/foreground color for the control
• Font
• Font that text appears in (see the slide at the
  end for how to specify a font)
• Text
• Text that appears in the control (if any)
• Height, Width
• The size of the control
• Location
• The X,Y coordinate of the top-left corner (as a
  point)
• Left, Top
• The individual X- and Y- coordinates of the
  control within its window

82
The Form class

• A form is a window that can hold controls
• Its also a special kind of control, so you can
  set things like its Width, Height, BackColor, etc.

• using System.Windows.Forms
• Tells system to use classes in the Windows Forms
  namespace
• new Form
• Makes a form
• form.Controls.Add control
• Adds a control to a form
• Application.Run form
• Displays form and lets the user work with it
  until they close it.
• form.Show
• Used to show a new form after Application.Run has
  already been invoked

83
The TrackBar control

• make TrackBar Minimum number
  Maximum number ValueChanged
  handler-procedure
• Makes a slider control
• Other useful fields (plus Controls fields)
• Value
• The current numeric value the user has chosen
• TickFrequency
• How often to draw tick marks
• Orientation
• Whether it should be a horizontal or vertical
  control.Set it to either Orientation.Horizontal
  or Orientation.Vertical

84
Event handling

• You tell the system what to do when the use
  changes the position of the TrackBar by giving it
  a procedure to run
• This is called an event handler or callback
• Whenever the user moves the TrackBar, the system
  calls the procedure for you
• And passes it two inputs that we wont talk about
  here because they arent useful to us

85
Making a color picker

• with f new Form r make TrackBar Top
  10 g make TrackBar Top 60 b make
  TrackBar Top 110
• f.BackColor ? color 0 0 0
• for-each slider ?
• f.Controls.Add slider
• slider.Width ? 255
• slider.Minimum ? 0
• slider.Maximum ? 255
• slider.ValueChanged ?
  ignore ignore ?
  f.BackColor ? color r.Value
  g.Value b.Value
• list r g b
• Application.Run f

86
Defining new data types

• class name required-fields
  parent-type optional-fields
• The parent-type field specifies what the new type
  is a subtype of
• In the past, weve just make this be type Object,
  which is the most generic type
• But you can use any of the types you define

• define Thing class Thing name
  location Object
• define Player class Player name
  location Thing
• define Place class Place name
  Thing contents

87
Class hierarchy (partial)
Object No fields
Thing name, location
Place name, location, contents
Player name, location
88
Making a simulation program (e.g. a game)

• Model the world as a set of data object
• One data object for each object in the world
• Make whatever classes you need to represent the
  different kinds of object
• E.g. Places, Doors, Things, Monsters, etc.
• Group classes into subclasses when reasonable
• Place fields in the classes to hold whatever data
  you need to remember
• E.g. name, position, etc.
• Implement procedures to mimic the kinds of
  actions that happen in the world
• E.g. move, describe, attack, etc.

89
Making the procedure to behave differently for
different types of inputs

• define describe objectif is? object
  Person concat A person named
  object.name if is? object Place
  object.name if is? object Door
  concat A door to
  object.name etc

90
This is pretty uglyCan we make it easier to read?

• define describe objectif is? object
  Person concat A person named
  object.name if is? object Place
  object.name if is? object Door
  concat A door to
  object.name etc

91
This is pretty uglyCan we make it easier to read?

• This is a little less odious
• At least all the types line up so you can search
  through it easier
• But it still means that every time you add a new
  type you need to edit this one procedure
• Makes the procedure really big
• Makes it hard for two people to work on the
  program at once
• Also means you have to organize the code by
  procedure, rather than by data type
• Often less natural

• define describe objectcond is? object
  Person concat A person named
  object.name is?
  object Place object.name
  is? object Door concat A door to
  object.name
  etc

92
This is pretty uglyCan we make it easier to read?

• Well you can specify the type of an argument in a
  define

• define describe Person objectconcat A
  person named object.name

93
This is pretty uglyCan we make it easier to read?

• Well you can specify the type of an argument in a
  define
• Wouldnt it be nice if you could just
• Give different defines
• For the different types?

• define describe Person objectconcat A
  person named object.name
• define describe Place objectobject.name
• define describe Door object concat A door
  to object.name
• etc

94
This is pretty uglyCan we make it easier to read?

• Well you can specify the type of an argument in a
  define
• Wouldnt it be nice if you could just
• Give different defines
• For the different types?
• Actually, you can

• define describe generic-procedure
• define-method describe Person objectconcat
  A person named object.name
• define-method describe Place
  objectobject.name
• define-method describe Door object concat
  A door to object.name
• etc

95
Generic procedures

• define name generic-procedure
• define-method name type arg body
• A generic procedure is a procedure that bases its
  behavior on the type(s) of its argument(s)
• You can then use define-method to specify code to
  run when the procedure is called with specific
  types of arguments
• These are related to the methods that you get at
  by saying object.method args
• For a bunch of technical reasons, Meta can only
  make classes that contain fields, not events or
  the object.method kind of methods
• But generic procedures are a more versatile way
  of programming anyway

96
The initialize procedure

• Initialize is a built-in generic procedure
• Its always called by new and make when they
  create an object
• Used to specify code to run when an object is
  created
• You dont need to specify methods for it
• But you can if you want to
• Incidentally, this is a case where you almost
  always want to use call-next-method

• define-method initialize Type
  namecall-next-method code to initialize
  your object

97
Generic procedures vs. member procedures

• You may have noticed weve called two different
  things methods
• Things you add to generic procedures using
  define-method
• Things you call by saying x.y bla bla bla
• Why are we using both?
• In systems like Java and .NET (on which Meta is
  built)
• You have to specify all the x.y methods when you
  make the class
• So the code has to be inside of class-type
• Which makes it big and hard to read
• And to change something, you have to completely
  redo the class
• So this quarter, were making life simpler (in
  some ways) by using generic procedures
• Next quarter, well focus on the Java/C style
  methods

98
lists
99
The list

• Lists are sequences of data objects
• Any length
• Any type of data object
• Different types of data can appear in the same
  list
• Example a CD database
• A list of data objects representing CDs
• Each CD could, in fact be represented as its own
  list
• But well represent them as Album objects

100
Okay, what can we do with lists?

• list item1 item2 itemn
• Creates a list containing the specified items, in
  order
• item list index
• Extracts the item from list at position index (a
  number)
• Index counts from zero
• So for an 5-element list, the elements are
  numbered 0, 1, 2, 3, 4
• first list, second list, , tenth list
• Extracts the specified element of list.
• length list
• Returns the number of items in list
• append list1 list2 listn
• Creates a new list with all the items in the
  input lists, in order

101
Mapping and folding

• fold p listor fold p start-value list
• Joins all the values of list together using
  procedure p
• Mostly useful for summing, multiplying, or
  otherwise mushing together the elements of a list
• fold list 1 2 3 returns 3 2 1
• fold 0 list 1 2 3 returns 3 2
  1 0
• map procedure list
• Runs procedure on every element of list and
  returns their return values as a new list
• map list 1 2 3 4 returns -1 -2 -3 -4

102
Averaging
? define sum list ? fold
list ltProcedure sumgt ? define mean list ?
/ sum list length list ltProcedure
meangt ? define rms list ? sqrt mean
map square list ltProcedure rmsgt ? define
square number ? number number ltProcedure
squaregt ? rms list 1 2 3 4 5
6 3.8944405226628

• Sum of a list
• fold over all elements
• Mean (average) of list
• Divide by the length (number of elements)
• RMS (root-mean-square)
• A.k.a. standard deviation
• Easy
• Take the root of the mean of the squares of all
  elements
• Get the squares by mapping square over all the
  elements

103
Searching and filtering

• list-index predicate list
• Returns the position within list of the first
  item that satisfies predicate
• find predicate list
• Same, but returns the item itself
• filter predicate list
• Same, but returns all the items (as a list)
  satisfying predicate

104
Example a CD database

• ? define Album Class Album title
  artist Object
  print-fields title
• ltType Albumgt
• ? define cd-database
• list new Album The
  white album The Beatles
• new Album Sgt.
  Pepper's Lonely Hearts Club
  Band The Beatles
• new Album Pod
  The Breeders
• new Album
  Dummy
  Portishead

• ? define Beatles?
• album ? album.artist
• The
  Beatles
• ? filter Beatles? cd-database
• ltAlbum The white albumgt
• ltAlbum Sgt. Peppers Lonely Hearts Club Bandgt
• ? map cd ? cd.title cd-database
• The white album Sgt.Peppers Lonely Hearts
  Club Band Pod Dummy
• ?delete-duplicates map cd ? cd.artist
  cd-database
• The Beatles The Breeders Portishead

105
Any and every item in a list
? define Album Class Album title artist
Object
print-fields
title ? define cd-database list
new Album The white
album The Beatles new Album
Sgt. Pepper's Lonely
Hearts Club Band The
Beatles new Album
Pod The Breeders
new Album Dummy Portishead ? define
Beatles? album ?
album.artist
The Beatles ? any Beatles?
cd-database True ? every Beatles?
cd-database False

• any predicate list
• True when any item in list satisfies predicate
• every predicate list
• True when every item in list satisfies predicate

106
Last, but not least, the apply procedure
? apply list 1 2 3 4 5 15 ? apply max
list 1 2 3 4 5 1 5 ? apply get
list list 1 2 3 4 5
2 3 ? apply append list list
1 2 list 3 4
list 5 6 1 2 3 4 5 6

• apply procedure list
• Calls procedure and passes it the elements of
  list as arguments
• Really, really useful

107
The mystery revealed

• define iterated-group proc count ?
  apply group
  up-to count proc
• First, up-to calls proc with inputs from 0 to
  count
• And returns their results as a single list
• Then, apply calls group with the elements of that
  list as arguments
• Finally, group makes them into a single picture

108
Namespaces

• All global variables are stored in namespaces
• The proper name for a variable is
  namespace.name where
• Name is the name of the variable
• Namespace is the name of the namespace
• The system keeps track of your current
  namespace
• If the variable youre using is in the current
  namespace, you can just type its name
• Thats why you havent had to type namespace.name
  much before
• The system also keeps track of a set of namespace
  that youre using
• You also dont have to the the namespace prefix
  if the variable is in one of the namespaces
  youre using.
• To use a namespace, type using namespace