Lecture 5

Question 1

What is an abstract machine (or VM)?

Answer 1

A model of computation, explaining the execution of programs.

Abstracts away the physical machine details for the programmer.

Question 2

What are the components of an Abstract machine?

Answer 2

Single assignment store
Semantic stack

M = (S, o)
M: Machine
S: Semantic stack
o: Single assignment store

Question 3

What does the semantic stack contain?

Answer 3

Semantic statements (pair composed of a statement and an environment)

(<s1>, E_1)</s1>

Statement: Program to be evaluated
Environment: Mappings from identifiers in code to variables in store

Question 4

What is the notation of environments?

Answer 4

E = {<id1> -> x1, <id2> -> x2, ..., <id_n> -> x_n}</id_n></id2></id1>

Question 5

What does the single assignment store contain?

Answer 5

Dataflow variables

Question 6

What operations are allowed on variables in the store?

Answer 6

Creation of unbound variable

Binding to another unbound

Binding to another bound

Unification of two bound variables

Testing if variable is bound

Retrieving a variable value

Testing equivalence between two variables

Question 7

How to variables bound to other variables behave?

Answer 7

Variables bound to another variable will always have the same value as that variable.

Question 8

When does unification succeed?

Answer 8

When two complete values are of the same type and have the same structure and content.
Then no additional binding is performed.

When two partial values contain content that can be unified, unification succeeds. Additional binding is however performed.

Question 9

When does evaluation of equality return true?

Answer 9

When it can be established that two variables will always have the same value.

If the two variables are bound, and have unifiable complete values (type and content).

When two variables are equivalent (bound together in store, X= Y)

Question 10

When can equality not be established?

Answer 10

When one variable is bound to a partial value, and we are comparing a complete variable. In this case we do not know what the content of the first is.

Question 11

What is adjunction?

Answer 11

Adding a mapping to an Environment, extending this environment.

If the <id> of an additional mapping already exist in the environment, this will be overwritten.</id>

Environments are immutable, does not change, new environment is created.

Question 12

What is restriction?

Answer 12

Removing a mapping from an Environment.

E’ = E | {<id1>, ..., <id_n>}</id_n></id1>

E’ contain only mapping specified

Question 13

What is lookup?

Answer 13

Retrieving variable from an environment by its ID.

E(<id1>) = x1</id1>

Question 14

What components does Execute use?

Answer 14

Statements from stack

Mappings from the enclosed environment

Bindings from single assignment store

Question 15

What is the execution rule of the skip statement?

Answer 15

Pop statement from stack

Leave the rest of the stack and store unchanged

Question 16

What is the execution rule for:

(<statement1> <statement2>, E)</statement2></statement1>

Answer 16

Push (<statement1>, E) to stack
Push (<statement2>, E) to stack</statement2></statement1>

Store is unchanged

Question 17

What is the execution rule for:

(local <id> in <statement> end, E)</statement></id>

Answer 17

Update store with new unbound variable v

Update environment with mapping <id> -> v, E'</id>

push (<statement>, E') to stack</statement>

Question 18

What is the execution rule of:

(<id1> = <id2>, E)</id2></id1>

Answer 18

Bind E(<id1>) and E(<id2>) in store</id2></id1>

Leave rest of stack unchanged

Question 19

What is the execution rules of:

(<id> = <value>, E)</value></id>

Answer 19

Compute value of <value> (= c)</value>

Bind E(<id>) to value c</id>

Store O: O U {E(<id>) = c}</id>

Question 20

What is the execution rules of:

if <id> then <statement1> else <statement2> end</statement2></statement1></id>

Answer 20

Check E(<id>)
If true, push <statement1>
If false, push <statement2>
otherwise raise error</statement2></statement1></id>

Question 21

What is the execution rules of procedures?

Answer 21

({<id>0 <id>1 ... <id>n}, E)</id></id></id>

Check E(<id>0)
If bound to a procedure (p_c, E_c) where p_c has form</id>

proc {$ <id1> ... <id_n>} <statement>end</statement></id_n></id1>

Push (<statement>, Ep U E) to stack</statement>

E’ adds mapping <id_n> -> E(<id>n)</id></id_n>

Question 22

What are formal parameters?

Answer 22

Identifiers in a procedure definition

proc {$ A B}

A and B are formal

Question 23

What are actual parameters?

Answer 23

Identifier in an application

P = proc {$ A B}
{P X Y}

X and Y are actual