61a lecture 29 - inst.eecs.berkeley.educs61a/fa11/61a...61a lecture 29 monday, november 7 monday,...

61A Lecture 29

Monday, November 7

Monday, November 7, 2011

Homework: Huffman Encoding Trees

2



Efficient encoding of strings as ones and zeros (bits).

2




2

A 0 C 1010 E 1100 G 1110

B 100 D 1011 F 1101 H 1111




2

A 0 C 1010 E 1100 G 1110

B 100 D 1011 F 1101 H 1111

A

B

C D

E F G H

0 1

0 1

0 1

0 1

0 1

0 1 0 1


Decoding a sequence of bits:



2

A 0 C 1010 E 1100 G 1110

B 100 D 1011 F 1101 H 1111

A

B

C D

E F G H

0 1

0 1

0 1

0 1

0 1

0 1 0 1





2

A 0 C 1010 E 1100 G 1110

B 100 D 1011 F 1101 H 1111

A

B

C D

E F G H

0 1

0 1

0 1

0 1

0 1

0 1 0 1

1 0 0 0 1 0 1 0





2

A 0 C 1010 E 1100 G 1110

B 100 D 1011 F 1101 H 1111

A

B

C D

E F G H

0 1

0 1

0 1

0 1

0 1

0 1 0 1

1 0 0 0 1 0 1 0

B





2

A 0 C 1010 E 1100 G 1110

B 100 D 1011 F 1101 H 1111

A

B

C D

E F G H

0 1

0 1

0 1

0 1

0 1

0 1 0 1

1 0 0 0 1 0 1 0

B A





2

A 0 C 1010 E 1100 G 1110

B 100 D 1011 F 1101 H 1111

A

B

C D

E F G H

0 1

0 1

0 1

0 1

0 1

0 1 0 1

1 0 0 0 1 0 1 0

B A C


Logo Refresher

3


Logo Refresher

Data types: Words and sentences (immutable sequences)

3


Logo Refresher


Syntactic forms: Call expressions, literals, and to-statements

3


Logo Refresher



3

? print sum 10 difference 7 3

14


Logo Refresher



3


14

? run [print sum 1 2]

3


Logo Refresher



3


14

? to double :x

> output sum :x :x

> end


3


Logo Refresher



3


14

? to double :x

> output sum :x :x

> end

? print double 4

8


3


Logo Interpreter Architecture

4



4

parser



4

parser Evaluator



4

string parser Evaluator



4

string parser Evaluator

'run [print sum 1 2]'



4

string parser line Evaluator

'run [print sum 1 2]'



4


'run [print sum 1 2]' ['run', ['print', 'sum', '1', '2']]



4



Logo words are represented as Python strings



4




Logo sentences are represented as Python lists



4





The Parser creates nested sentences, but does not build full expression trees for nested call expressions



4






A line of Logo code



4






A Logo sentence

A line of Logo code



4






A Logo sentence

Another Logo sentence

A line of Logo code


Tracking Positions in Lines

5



A line is used up as it is evaluated

5




A Buffer instance tracks how much of a line has been used up.

5





5

>>> buf = Buffer(['show', '2'])





5


show 2





5


>>> buf.current

'show'

show 2





5


>>> buf.current

'show'

>>> print(buf)

[ >> show, 2 ] show 2





5


>>> buf.current

'show'

>>> print(buf)

[ >> show, 2 ]

>>> buf.pop()

'show'

show 2





5


>>> buf.current

'show'

>>> print(buf)

[ >> show, 2 ]

>>> buf.pop()

'show'

>>> print(buf)

[ show >> 2 ]

show 2





5


>>> buf.current

'show'

>>> print(buf)

[ >> show, 2 ]

>>> buf.pop()

'show'

>>> print(buf)

[ show >> 2 ]

>>> buf.pop()

'2'

show 2





5


>>> buf.current

'show'

>>> print(buf)

[ >> show, 2 ]

>>> buf.pop()

'show'

>>> print(buf)

[ show >> 2 ]

>>> buf.pop()

'2'

show 2

Demo


Evaluating Lines

6


Evaluating Lines

Evaluating a line of Logo involves evaluating each expression

6


Evaluating Lines


6

Evaluate a line eval_line


Evaluating Lines


6


Evaluate the next expression

logo_eval


Evaluating Lines


6



logo_eval

Calls repeatedly


Evaluating Lines


6

? print 1 print 2

1

2



logo_eval

Calls repeatedly


Evaluating Lines


6

? print 1 print 2

1

2



logo_eval

Calls repeatedly

first call

second call

Argumentlogo_eval Effect


Evaluating Lines


6

? print 1 print 2

1

2



logo_eval

[ >> print, 1, print, 2 ]

Calls repeatedly

first call

second call

Argumentlogo_eval Effect


Evaluating Lines


6

? print 1 print 2

1

2



logo_eval


Calls repeatedly

first call

second call

Argumentlogo_eval Effectprints 1, returns None


Evaluating Lines


6

? print 1 print 2

1

2



logo_eval


Calls repeatedly

[ print, 1 >> print, 2 ]

first call

second call



Evaluating Lines


6

? print 1 print 2

1

2



logo_eval


Calls repeatedly

[ print, 1 >> print, 2 ]

first call

second call


prints 2, returns None


Logo Evaluation

7


Logo Evaluation

The logo_eval function dispatches on expression form:

7


Logo Evaluation


• A primitive expression is a word that can be interpreted as a number, True, or False. Primitives are self evaluating.

7


Logo Evaluation



• A variable is looked up in the current environment.

7


Logo Evaluation



• A variable is looked up in the current environment.• A procedure definition creates a new user-defined procedure.

7


Logo Evaluation



• A variable is looked up in the current environment.• A procedure definition creates a new user-defined procedure.• A quoted expression evaluates to the text of the quotation, which is a string without the preceding quote. Sentences are quoted and evaluate to themselves.

7


Logo Evaluation




• A call expression is evaluated with apply_procedure.

7


Logo Evaluation





7

def logo_eval(line, env):


Logo Evaluation





7

def logo_eval(line, env): """Evaluate the first expression in a line."""


Logo Evaluation





7

def logo_eval(line, env): """Evaluate the first expression in a line.""" token = line.pop()


Logo Evaluation





7

def logo_eval(line, env): """Evaluate the first expression in a line.""" token = line.pop()The expression

form can be inferred from

the first token


Logo Evaluation





7

def logo_eval(line, env): """Evaluate the first expression in a line.""" token = line.pop() if isprimitive(token):

The expression form can be

inferred from the first token


Logo Evaluation





7

def logo_eval(line, env): """Evaluate the first expression in a line.""" token = line.pop() if isprimitive(token): return token




Logo Evaluation





7

def logo_eval(line, env): """Evaluate the first expression in a line.""" token = line.pop() if isprimitive(token): return token elif isvariable(token):




Logo Evaluation





7

def logo_eval(line, env): """Evaluate the first expression in a line.""" token = line.pop() if isprimitive(token): return token elif isvariable(token): ...




Evaluating Call Expressions

8



8

apply_procedureApply a named procedure



8


collect_argsEvaluate n operands



8


logo_applyApply a procedure toa sequence of arguments




8

apply_procedureApply a named procedure Return the output value





8


Return n arguments





8


Return n arguments

Return the output valuelogo_applyApply a procedure toa sequence of arguments




8


Return n arguments



[ print >> 2 ]



8


Return n arguments



[ print >> 2 ]

Popped by logo_eval



8


Return n arguments



[ print >> 2 ]

Popped by logo_eval

1. Collect 1 argument via logo_eval(collect_args)



8


Return n arguments



[ print >> 2 ]

Popped by logo_eval

[ print, 2 >> ]




8


Return n arguments



[ print >> 2 ]

Popped by logo_eval

[ print, 2 >> ]

Popped by logo_eval also

(recursive call)




8


Return n arguments



[ print >> 2 ]

Popped by logo_eval

[ print, 2 >> ]

Popped by logo_eval also

(recursive call)


2. Apply print procedure to the argument '2'(logo_apply)


Procedures

9


Procedures

9

class Procedure():


Procedures

9

class Procedure():

def __init__(self, name, arg_count, body, isprimitive=False,

needs_env=False, formal_params=None):


Procedures

9

class Procedure():



self.name = name

self.arg_count = arg_count

self.body = body

self.isprimitive = isprimitive

self.needs_env = needs_env

self.formal_params = formal_params


Procedures

9

class Procedure():



self.name = name


self.body = body




def logo_apply(proc, args):

"""Apply a Logo procedure to a list of arguments."""


Procedures

9

class Procedure():



self.name = name


self.body = body






if proc.isprimitive:

return proc.body(*args)


Procedures

9

class Procedure():



self.name = name


self.body = body






if proc.isprimitive:

return proc.body(*args)

else:

"""Apply a user-defined procedure"""


Logo Interpreter

10

Apply

Eval


Logo Interpreter

10

Apply

Evaleval_line

logo_eval


Logo Interpreter

10

Apply

Evaleval_line

logo_eval

apply_procedure

collect_args

logo_apply


Eval/Apply in Lisp 1.5

11


Eval/Apply in Logo

12

Apply

eval_line

apply_procedure

collect_args

logo_apply

Eval

logo_eval


Eval/Apply in Logo

12

Apply

eval_line

apply_procedure

collect_args

logo_apply

Eval

logo_eval

Call expressions


Eval/Apply in Logo

12

Apply

eval_line

apply_procedure

collect_args

logo_apply

Eval

logo_eval

Call expressions

Operand expressions


Eval/Apply in Logo

12

Apply

eval_line

apply_procedure

collect_args

logo_apply

Eval

logo_eval

Call expressions User-defined

procedures

Operand expressions


61a lecture 29 - inst.eecs.berkeley.educs61a/fa11/61a...61a lecture 29 monday, november 7 monday,...

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