The Sequence Abstraction
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There isn't just one sequence type (in Python or in general)
CS 61A Lecture 9
This abstraction is a collection of behaviors:
Length. A sequence has a finite length.
Friday, September 16
Element selection. A sequence has an element
corresponding to any non-negative integer index less
than its length, starting at 0 for the first element.
The sequence abstraction is shared among several types.
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Tuples are Sequences
Box-and-Pointer Notation for Nested Pairs
(1, 2)
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Every object is
an arrow pointing
to a box
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The number 2
Boxes for tuples have
multiple parts
((1, 2), (3, 4))
(Demo)
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(1, 2) tuple
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Alternative Nested Structures
The Closure Property of Data Types
(1, (2, (3, 4)))
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(1, 2, 3, 4)
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((1, 2), (3, 4))
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2
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2
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A method for combining data values satisfies the closure
property if:
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The result of combination can itself be combined using the
same method.
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Closure is the key to power in any means of combination
because it permits us to create hierarchical structures.
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Hierarchical structures are made up of parts, which
themselves are made up of parts, and so on.
Tuples can contain tuples as elements
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Recursive Lists
Implementing Recursive Lists with Pairs
Constructor:
A recursive list
is a pair
def make_rlist(first, rest):
"""Make a recursive list from its first element and the rest."""
None represents
the empty list
Selectors:
None
def first(s):
"""Return the first element of a recursive list s."""
def rest(s):
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"""Return the rest of the elements of a recursive list s."""
9_rlist.py
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9_rlist.py
Page 1
Behavior condition(s):
# Recursive list abstract data type
The first element of
the pair is the first
If a recursive
s wasdata
constructed
from first element f
# Recursive
list list
abstract
type
empty_rlist
= None
element of the list
and recursive
list r, then
empty_rlist = None
def make_rlist(first, rest):
f, and
• first(s) areturns
recursive
list from its first element and the rest."""
def """Make
make_rlist(first,
rest):
return
rest)list from its first element and the rest."""
"""Make(first,
a recursive
rest(s) (first,
returns rest)
r, which is a recursive list.
• return
def first(s):
def """Return
first(s): the first element of a recursive list s."""
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return
s[0]
"""Return
the first element of a recursive list s."""
return s[0]
def rest(s):
def """Return
rest(s): the rest of the elements of a recursive list s."""
return
s[1]
"""Return
the rest of the elements of a recursive list s."""
return s[1]
# Manipulating recursive lists
# Manipulating recursive lists
counts = make_rlist(1, make_rlist(2, make_rlist(3, make_rlist(4, empty_rlist))))
first(counts)
counts
= make_rlist(1, make_rlist(2, make_rlist(3, make_rlist(4, empty_rlist))))
rest(counts)
first(counts)
Implementing
Environment Diagram for
rest(counts) the Sequence Abstraction
# Implementing the sequence abstraction
#
Implementing
the
sequence
abstraction
def len_rlist(s):
first:
"""Return the length of recursive list s."""
def length
len_rlist(s):
first
= 0
rest:
"""Return
the
length
of
recursive
list
s."""
while s != empty_rlist:
rest
length
=
0
...
s, length = rest(s), length + 1
(Demo)
while slength
!= empty_rlist:
counts:
return
s, length = rest(s), length + 1
return length
def getitem_rlist(s,
i):
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"""Return the element at index i of recursive list s."""
def while
getitem_rlist(s,
i):
i > 0:
s:
"""Return
the
element
at
index
i
of
recursive
list
s."""
s, i = rest(s), i é 1
i: 1
while ifirst(s)
> 0:
return
s, i = rest(s), i é 1
getitem_rlist
return first(s)
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The second element of
the pair is the rest
of the list
(Demo)
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getitem_rlist
None
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getitem_rlist(counts, 1)
while i > 0:
s, i = rest(s), i - 1
return first(i)
Length. A sequence has a finite length.
Element selection. A sequence has an element
corresponding to any non-negative integer index less
than its length, starting at 0 for the first element.
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Environment Diagram for getitem_rlist
Environment Diagram for getitem_rlist
first:
first:
first
rest:
...
counts:
None
1
2
3
first
rest:
...
counts:
rest
4
rest
None
1
s:
i: 1 0
getitem_rlist
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2
s:
i: 1 0
while i > 0:
s, i = rest(s), i - 1
return first(i)
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getitem_rlist(counts, 1)
getitem_rlist
getitem_rlist(counts, 1)
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while i > 0:
s, i = rest(s), i - 1
return first(s)
s:
first
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first(s)
return s[0]
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Sequence Iteration
For Statement Execution Procedure
(Demo)
for <name> in <expression>:
<suite>
1. Evaluate the header <expression>, which must yield an
iterable value.
def count(s, value):
total = 0
for elem in s:
2. For each element value in that sequence, in order:
Name bound in the first frame
of the current environment
A. Bind <name> to that value in the local environment.
if elem == value:
total = total + 1
return total
B. Execute the <suite>.
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