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PROFESSOR: All right, well,
we've seen how the query

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language works.

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Now, let's talk about how
it's implemented.

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You already pretty much can
guess what's going on there.

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At the bottom of it, there's
a pattern matcher.

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And we looked at a pattern
matcher when we did the

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rule-based control language.

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Just to remind you, here are
some sample patterns.

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This is a pattern that will
match any list of three things

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of which the first is a and the
second is c and the middle

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one can be anything.

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So in this little
pattern-matching syntax,

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there's only one distinction
you make.

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There's either literal things
or variables, and variables

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begin with question mark.

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So this matches any list of
three things of which the

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first is a and the
second is c.

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This one matches any list of
three things of which the

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first is the symbol job.

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The second can be anything.

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And the third is a list of two
things of which the first is

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the symbol computer and the
second can be anything.

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And this one, this next one
matches any list of three

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things, and the only difference
is, here, the third

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list, the first is the symbol
computer, and then there's

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some rest of the list. So this
means two elements and this

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means arbitrary number.

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And our language implementation
isn't even

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going to have to worry about
implementing this dot because

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that's automatically done
by Lisp's reader.

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Remember matchers also have
some consistency in them.

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This match is a list of
three things of which

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the first is a.

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And the second and third can be
anything, but they have to

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be the same thing.

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They're both called x.

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And this matches a list of four
things of which the first

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is the fourth and the second
is the same as the third.

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And this last one matches any
list that begins with a.

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The first thing is a, and the
rest can be anything.

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So that's just a review of
pattern matcher syntax that

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you've already seen.

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And remember, that's implemented
by some procedure

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called match.

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And match takes a pattern and
some data and a dictionary.

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And match asks the question is
there any way to match this

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pattern against this data object
subject to the bindings

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that are already in
this dictionary?

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So, for instance, if we're going
to match the pattern x,

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y, y, x against the data a, b,
b, a subject to a dictionary,

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that says x equals a.

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Then the matcher would say,
yes, that's consistent.

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These match, and it's consistent
with what's in the

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dictionary to say
that x equals a.

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And the result of the match is
the extended dictionary that

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says x equals a and
y equals b.

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So a matcher takes in pattern
data dictionary, puts out an

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extended dictionary if it
matches, or if it doesn't

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match, says that it fails.

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So, for example, if I use the
same pattern here, if I say

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this x, y, y, x match a, b, b, a
with the dictionary y equals

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a, then the matcher would
put out fail.

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Well, you've already seen the
code for a pattern matcher so

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I'm not going to go over it, but
it's the same thing we've

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been doing before.

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You saw that in the system
on rule-based control.

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It's essentially the
same matcher.

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In fact, I think the syntax is
a little bit simpler because

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we're not worrying about
arbitrary constants and

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expressions and things.

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There's just variables
and constants.

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OK, well, given that, what's
a primitive query?

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Primitive query is going to be
a rather complicated thing.

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It's going to be--

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let's think about the query
job of x is d dot y.

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That's a query we
might type in.

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That's going to be implemented
in the system.

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We'll think of it as
this little box.

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Here's the primitive query.

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What this little box is going
to do is take in two streams

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and put out a stream.

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So the shape of a primitive
query is that it's a thing

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where two streams come in
and one stream goes out.

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What these streams are
going to be is

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down here is the database.

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So we imagine all the things
in the database sort of

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sitting there in a stream and
this thing sucks on them.

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So what are some things that
might be in the database?

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Oh, job of Alyssa is
something and some

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other job is something.

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So imagine all of the facts in
the database sitting there in

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the stream.

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That's what comes in here.

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What comes in here is a stream
of dictionaries.

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So one particular dictionary
might say y equals programmer.

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Now, what the query does when
it gets in a dictionary from

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this stream, it finds all
possible ways of matching the

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query against whatever is coming
in from the database.

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It looks at the query as a
pattern, matches it against

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any fact from the database or
all possible ways of finding

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and matching the database with
respect to this dictionary

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that's coming in.

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So for each fact in the
database, it calls the matcher

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using the pattern, fact,
and dictionary.

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And every time it gets a good
match, it puts out the

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extended dictionary.

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So, for example, if this one
comes in and it finds a match,

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out will come a dictionary that
in this case will have y

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equals programmer and
x equals something.

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y is programmer, x is
something, and d

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is whatever it found.

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And that's all.

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And, of course, it's going to
try this for every fact in the

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dictionary.

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So it might find lots of them.

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It might find another one that
says y equals programmer and x

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equals, and d equals.

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So for one frame coming
in, it might put out--

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for one dictionary coming in,
it might put out a lot of

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dictionaries, or it might
put out none.

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It might have something
that wouldn't match

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like x equals FOO.

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This one might not match
anything in which case nothing

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will go into this stream
corresponding to this frame.

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Or what you might do is put in
an empty frame, and an empty

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frame says try matching
all ways--

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find all possible ways of
matching the query against

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something in the database
subject to no previous

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restrictions.

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And if you think about what that
means, that's just the

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computation that's done when you
type in a query right off.

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It tries to find all matches.

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So a primitive query sets
up this mechanism.

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And what the language does, when
you type in the query at

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the top level, it takes this
mechanism, feeds in one single

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empty dictionary, and then for
each thing that comes out

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takes the original query and
instantiates the result with

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all the different dictionaries,
producing a new

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stream of instantiated
patterns here.

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And that's what gets printed
on the terminal.

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That's the basic mechanism
going on there.

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Well, why is that
so complicated?

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You probably can think of a lot
simpler ways to arrange

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this match for a primitive query
rather than having all

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of these streams floating
around.

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And the answer is--

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you probably guess already.

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The answer is this thing extends
elegantly to implement

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the means of combination.

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So, for instance, suppose I
don't only want to do this.

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I don't want to say who to be
everybody's job description.

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Suppose I want to say AND the
job of x is d dot y and the

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supervisor of x is z.

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Now, supervisor of x is z is
going to be another primitive

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query that has the same shape
to take in a stream of data

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objects, a stream of initial
dictionaries, which are the

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restrictions to try and use when
you match, and it's going

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to put out a stream
of dictionaries.

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So that's what this primitive
query looks like.

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And how do I implement
the AND?

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Well, it's simple.

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I just hook them together.

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I take the output of this one,
and I put that to the

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input of that one.

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And I take the dictionary
here and I fan it out.

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And then you see how that's
going to work, because what's

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going to happen is a frame will
now come in here, which

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has a binding for x, y, and d.

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And then when this one gets
it, it'll say, oh, gee,

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subject to these restrictions,
which now already have values

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in the dictionary for y and
x and d, it looks in the

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database and says, gee, can I
find any supervisor facts?

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And if it finds any, out will
come dictionaries which have

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bindings for y and x
and d and z now.

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And then notice that because the
frames coming in here have

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these restrictions, that's the
thing that assures that when

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you do the AND, this x will mean
the same thing as that x.

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Because by the time something
comes floating in here, x has

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a value that you have to match
against consistently.

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And then you remember from the
code from the matcher, there

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was something in the way the
matcher did dictionaries that

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arrange consistent matches.

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So there's AND.

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The important point to notice
is the general shape.

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Look at what happened: the AND
of two queries, say, P and Q.

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Here's P and Q. The AND
of two queries, well,

203
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it looks like this.

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Each query takes in a stream
from the database, a stream of

205
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inputs, and puts out a
stream of outputs.

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And the important point to
notice is that if I draw a box

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around this thing and say this
is AND of P and Q, then that

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box has exactly the same
overall shape.

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It's something that takes in
a stream from the database.

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00:13:34,200 --> 00:13:37,020
Here it's going to get fanned
out inside, but from the

211
00:13:37,020 --> 00:13:38,160
outside you don't see that.

212
00:13:38,160 --> 00:13:42,230
It takes an input stream and
puts out an output stream.

213
00:13:42,230 --> 00:13:43,570
So this is AND.

214
00:13:43,570 --> 00:13:46,020
And then similarly, OR
would look like this.

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00:13:46,020 --> 00:13:48,030
OR would--

216
00:13:48,030 --> 00:13:49,840
although I didn't show
you examples of OR.

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00:13:49,840 --> 00:13:55,970
OR would say can I find all ways
of matching P or Q. So I

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00:13:55,970 --> 00:13:58,070
have P and Q. Each will
have their shape.

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00:13:58,070 --> 00:14:04,460


220
00:14:04,460 --> 00:14:08,720
And the way OR is implemented
is I'll

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00:14:08,720 --> 00:14:12,500
take my database stream.

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00:14:12,500 --> 00:14:13,490
I'll fan it out.

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00:14:13,490 --> 00:14:19,870
I'll put one into P and one into
Q. I'll take my initial

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00:14:19,870 --> 00:14:21,980
query stream coming
in and fan it out.

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00:14:21,980 --> 00:14:26,750


226
00:14:26,750 --> 00:14:29,460
So I'll look at all the answers
I might get from P and

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00:14:29,460 --> 00:14:32,950
all the answers I might get
from Q, and I'll put them

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00:14:32,950 --> 00:14:35,280
through some sort of thing that
appends them or merges

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00:14:35,280 --> 00:14:41,080
the result into one stream, and
that's what will come out.

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00:14:41,080 --> 00:14:48,240
And this whole thing from
the outside is OR.

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00:14:48,240 --> 00:14:52,350


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00:14:52,350 --> 00:14:55,540
And again, you see it has the
same overall shape when looked

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00:14:55,540 --> 00:14:56,790
at from the outside.

234
00:14:56,790 --> 00:15:01,000


235
00:15:01,000 --> 00:15:02,020
What's NOT?

236
00:15:02,020 --> 00:15:04,310
NOT works kind of
the same way.

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00:15:04,310 --> 00:15:14,690
If I have some query P, I take
the primitive query for P.

238
00:15:14,690 --> 00:15:19,600
Here, I'm going to implement NOT
P. And NOT's just going to

239
00:15:19,600 --> 00:15:20,720
act as a filter.

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00:15:20,720 --> 00:15:27,050
I'll take in the database and
my original stream of

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00:15:27,050 --> 00:15:32,210
dictionaries coming in, and what
NOT P will do is it will

242
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filter these guys.

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00:15:39,020 --> 00:15:41,850
And the way it will filter it,
it will say when I get in a

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00:15:41,850 --> 00:15:45,540
dictionary here, I'll find all
the matches, and if I find

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00:15:45,540 --> 00:15:47,460
any, I'll throw it away.

246
00:15:47,460 --> 00:15:49,670
And if I don't find any matches
to something coming in

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00:15:49,670 --> 00:15:52,500
here, I'll just pass
that through, so

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00:15:52,500 --> 00:15:55,560
NOT is a pure filter.

249
00:15:55,560 --> 00:15:56,890
So AND is--

250
00:15:56,890 --> 00:15:59,090
think of these sort
of electoral

251
00:15:59,090 --> 00:15:59,980
resistors or something.

252
00:15:59,980 --> 00:16:04,960
AND is series combination and
OR is parallel combination.

253
00:16:04,960 --> 00:16:06,780
And then NOT is not going
to extend any

254
00:16:06,780 --> 00:16:07,460
dictionaries at all.

255
00:16:07,460 --> 00:16:08,750
It's just going to filter it.

256
00:16:08,750 --> 00:16:10,220
It's going to throw away
the ones for which it

257
00:16:10,220 --> 00:16:12,640
finds a way to match.

258
00:16:12,640 --> 00:16:14,540
And list value is sort
of the same way.

259
00:16:14,540 --> 00:16:16,600
The filter's a little
more complicated.

260
00:16:16,600 --> 00:16:19,640
It applies to predicate.

261
00:16:19,640 --> 00:16:22,610
The major point to notice here,
and it's a major point

262
00:16:22,610 --> 00:16:24,980
we've looked at before, is
this idea of closure.

263
00:16:24,980 --> 00:16:28,490


264
00:16:28,490 --> 00:16:32,280
The things that we build as a
means of combination have the

265
00:16:32,280 --> 00:16:36,470
same overall structure
as the primitive

266
00:16:36,470 --> 00:16:39,750
things that we're combining.

267
00:16:39,750 --> 00:16:42,950
So the AND of two things when
looked at from the outside has

268
00:16:42,950 --> 00:16:44,630
the same shape.

269
00:16:44,630 --> 00:16:48,790
And what that means is that this
box here could be an AND

270
00:16:48,790 --> 00:16:51,560
or an OR or a NOT or something
because it has the same shape

271
00:16:51,560 --> 00:16:54,950
to interface to the
larger things.

272
00:16:54,950 --> 00:16:57,370
It's the same thing that allowed
us to get complexity

273
00:16:57,370 --> 00:17:00,980
in the Escher picture language
or allows you to immediately

274
00:17:00,980 --> 00:17:04,170
build up these complicated
structures just out of pairs.

275
00:17:04,170 --> 00:17:06,280
It's closure.

276
00:17:06,280 --> 00:17:10,920
And that's the thing that
allowed me to do what by now

277
00:17:10,920 --> 00:17:12,829
you took for granted when I
said, gee, there's a query

278
00:17:12,829 --> 00:17:15,369
which is AND of job and salary,
and I said, oh,

279
00:17:15,369 --> 00:17:17,190
there's another one,
which is AND of

280
00:17:17,190 --> 00:17:19,260
job, a NOT of something.

281
00:17:19,260 --> 00:17:22,185
The fact that I can do that is
a direct consequence of this

282
00:17:22,185 --> 00:17:25,230
closure principle.

283
00:17:25,230 --> 00:17:29,520
OK, let's break and
then we'll go on.

284
00:17:29,520 --> 00:17:30,710
AUDIENCE: Where does the
dictionary come from?

285
00:17:30,710 --> 00:17:35,140
PROFESSOR: The dictionary
comes initially from

286
00:17:35,140 --> 00:17:36,030
what you type in.

287
00:17:36,030 --> 00:17:40,390
So when you start this up, the
first thing it does is set up

288
00:17:40,390 --> 00:17:41,090
this whole structure.

289
00:17:41,090 --> 00:17:45,000
It puts in one empty
dictionary.

290
00:17:45,000 --> 00:17:48,560
And if all you have is one
primitive query, then what

291
00:17:48,560 --> 00:17:50,330
will come out is a bunch
of dictionaries with

292
00:17:50,330 --> 00:17:52,310
things filled in.

293
00:17:52,310 --> 00:17:55,330
The general situation that I
have here is when this is in

294
00:17:55,330 --> 00:17:59,710
the middle of some nest
of combined things.

295
00:17:59,710 --> 00:18:02,380


296
00:18:02,380 --> 00:18:03,790
Let's look at the picture
over here.

297
00:18:03,790 --> 00:18:06,730
This supervisor query gets
in some dictionary.

298
00:18:06,730 --> 00:18:08,730
Where did this one come from?

299
00:18:08,730 --> 00:18:13,480
This dictionary came from the
fact that I'm looking at the

300
00:18:13,480 --> 00:18:16,260
output of this primitive
query.

301
00:18:16,260 --> 00:18:20,370
So maybe to be very specific,
if I literally typed in just

302
00:18:20,370 --> 00:18:23,820
this query at the top level,
this AND, what would actually

303
00:18:23,820 --> 00:18:26,400
happen is it would build this
structure and start up this

304
00:18:26,400 --> 00:18:31,770
whole thing with one
empty dictionary.

305
00:18:31,770 --> 00:18:33,850
And now this one would process,
and a whole bunch of

306
00:18:33,850 --> 00:18:38,640
dictionaries would come out with
x, y's and d's in them.

307
00:18:38,640 --> 00:18:40,190
Run it through this one.

308
00:18:40,190 --> 00:18:42,160
So now that's the input
to this one.

309
00:18:42,160 --> 00:18:45,040
This one would now put
out some other stuff.

310
00:18:45,040 --> 00:18:50,110
And if this itself were buried
in some larger thing, like an

311
00:18:50,110 --> 00:18:54,860
OR of something, then
that would go feed

312
00:18:54,860 --> 00:18:56,110
into the next one.

313
00:18:56,110 --> 00:18:58,560


314
00:18:58,560 --> 00:19:00,780
So you initially get only one
empty dictionary when you

315
00:19:00,780 --> 00:19:03,380
start it, but as you're in the
middle of processing these

316
00:19:03,380 --> 00:19:05,640
compounds things, that's where
these cascades of dictionaries

317
00:19:05,640 --> 00:19:07,660
start getting generated.

318
00:19:07,660 --> 00:19:11,030
AUDIENCE: Dictionaries only
come about as a result of

319
00:19:11,030 --> 00:19:12,280
using the queries?

320
00:19:12,280 --> 00:19:15,120


321
00:19:15,120 --> 00:19:18,280
Or do they become--

322
00:19:18,280 --> 00:19:23,220
do they stay someplace in space
like the database does?

323
00:19:23,220 --> 00:19:24,980
Are these temporary items?

324
00:19:24,980 --> 00:19:28,030
PROFESSOR: They're created
temporarily in the matcher.

325
00:19:28,030 --> 00:19:29,880
Really, they're someplace
in storage.

326
00:19:29,880 --> 00:19:32,430
Initially, someone creates
a thing called the empty

327
00:19:32,430 --> 00:19:36,740
dictionary that gets initially
fed to this match procedure,

328
00:19:36,740 --> 00:19:39,150
and then the match procedure
builds some dictionaries, and

329
00:19:39,150 --> 00:19:40,950
they get passed on and on.

330
00:19:40,950 --> 00:19:43,526
AUDIENCE: OK, so they'll
go way after the match?

331
00:19:43,526 --> 00:19:44,680
PROFESSOR: They'll go
away when no one

332
00:19:44,680 --> 00:19:45,930
needs them again, yeah.

333
00:19:45,930 --> 00:19:51,900


334
00:19:51,900 --> 00:19:54,230
AUDIENCE: It appears that the
AND performs some redundant

335
00:19:54,230 --> 00:19:56,050
searches of the database.

336
00:19:56,050 --> 00:19:58,660
If the first clause matched,
let's say, the third element

337
00:19:58,660 --> 00:20:01,820
and not on the first two
elements, the second clause is

338
00:20:01,820 --> 00:20:04,890
going to look at those first two
elements again, discarding

339
00:20:04,890 --> 00:20:06,700
them because they don't match.

340
00:20:06,700 --> 00:20:10,000
The match is already
in the dictionary.

341
00:20:10,000 --> 00:20:12,920
Would it makes sense to carry
the data element from the

342
00:20:12,920 --> 00:20:14,450
database along with
the dictionary?

343
00:20:14,450 --> 00:20:17,120


344
00:20:17,120 --> 00:20:18,550
PROFESSOR: Well, in general,
there are other ways to

345
00:20:18,550 --> 00:20:21,220
arrange this search, and
there's some analysis

346
00:20:21,220 --> 00:20:21,740
that you can do.

347
00:20:21,740 --> 00:20:24,600
I think there's a problem in the
book, which talks about a

348
00:20:24,600 --> 00:20:27,680
different way that you can
cascade AND to eliminate

349
00:20:27,680 --> 00:20:29,850
various kinds of redundancies.

350
00:20:29,850 --> 00:20:31,380
This one is meant to be--

351
00:20:31,380 --> 00:20:33,910
was mainly meant to be very
simple so you can see how they

352
00:20:33,910 --> 00:20:34,650
fit together.

353
00:20:34,650 --> 00:20:35,380
But you're quite right.

354
00:20:35,380 --> 00:20:38,370
There are redundancies here
that you can get rid of.

355
00:20:38,370 --> 00:20:41,190
That's another reason why this
language is somewhat slow.

356
00:20:41,190 --> 00:20:42,930
There are a lot smarter
things you can do.

357
00:20:42,930 --> 00:20:45,590
We're just trying to show you
a very simple, in principle,

358
00:20:45,590 --> 00:20:46,840
implementation.

359
00:20:46,840 --> 00:20:51,220


360
00:20:51,220 --> 00:20:53,716
AUDIENCE: Did you model this
language on Prolog, or did it

361
00:20:53,716 --> 00:20:55,150
just come out looking
like Prolog?

362
00:20:55,150 --> 00:21:04,960


363
00:21:04,960 --> 00:21:06,380
PROFESSOR: Well, Jerry insulted
a whole bunch of

364
00:21:06,380 --> 00:21:08,750
people yesterday, so I might
as well say that the MIT

365
00:21:08,750 --> 00:21:11,460
attitude towards Prolog is
something that people did in

366
00:21:11,460 --> 00:21:15,030
about 1971 and decided that it
wasn't really the right thing

367
00:21:15,030 --> 00:21:16,120
and stopped.

368
00:21:16,120 --> 00:21:22,640
So we modeled this on the sort
of natural way that this thing

369
00:21:22,640 --> 00:21:26,655
was done in about 1971, except
at that point, we didn't do it

370
00:21:26,655 --> 00:21:33,020
with streams. After we were
using it for about six months,

371
00:21:33,020 --> 00:21:35,360
we discovered that it had all
these problems, some of which

372
00:21:35,360 --> 00:21:37,330
I'll talk about later.

373
00:21:37,330 --> 00:21:40,310
And we said, gee, Prolog must
have fixed those, and then we

374
00:21:40,310 --> 00:21:41,250
found out that it didn't.

375
00:21:41,250 --> 00:21:43,460
So this does about the
same thing as Prolog.

376
00:21:43,460 --> 00:21:44,950
AUDIENCE: Does Prolog
use streams?

377
00:21:44,950 --> 00:21:46,200
PROFESSOR: No.

378
00:21:46,200 --> 00:21:48,540


379
00:21:48,540 --> 00:21:51,040
In how it behaves, it behaves
a lot like Prolog.

380
00:21:51,040 --> 00:21:53,800
Prolog uses a backtracking
strategy.

381
00:21:53,800 --> 00:21:55,910
But the other thing that's
really good about Prolog that

382
00:21:55,910 --> 00:21:59,950
makes it a usable thing is that
there's a really very,

383
00:21:59,950 --> 00:22:04,830
very well-engineered compiler
technology that makes it run

384
00:22:04,830 --> 00:22:09,260
fast. So although you saw the
merge spitting out these

385
00:22:09,260 --> 00:22:13,080
answers very, very slowly, a
real Prolog will run very,

386
00:22:13,080 --> 00:22:16,800
very fast. Because even though
it's sort of doing this, the

387
00:22:16,800 --> 00:22:19,600
real work that went into
Prolog is a very, very

388
00:22:19,600 --> 00:22:20,850
excellent compiler effort.

389
00:22:20,850 --> 00:22:24,460


390
00:22:24,460 --> 00:22:25,710
Let's take a break.

391
00:22:25,710 --> 00:23:16,650


392
00:23:16,650 --> 00:23:20,410
We've looked at the primitive
queries and the ways that

393
00:23:20,410 --> 00:23:24,300
streams are used to implement
the means of combination: AND

394
00:23:24,300 --> 00:23:26,950
and OR and NOT.

395
00:23:26,950 --> 00:23:29,580
Now, let go on to the means
of abstraction.

396
00:23:29,580 --> 00:23:31,280
Remember, the means of
abstraction in this

397
00:23:31,280 --> 00:23:32,570
language are rules.

398
00:23:32,570 --> 00:23:35,150


399
00:23:35,150 --> 00:23:42,580
So z is a boss in division d
if there's some x who has a

400
00:23:42,580 --> 00:23:48,900
job in division d and z is
the supervisor of x.

401
00:23:48,900 --> 00:23:52,260
That's what it means for
someone to be a boss.

402
00:23:52,260 --> 00:23:54,780
And in effect, if you think
about what we're doing with

403
00:23:54,780 --> 00:23:58,660
relation to this, there's the
query we wrote-- the job of x

404
00:23:58,660 --> 00:24:02,150
is in d and the supervisor
of x is z--

405
00:24:02,150 --> 00:24:05,330
what we in effect want to do
is take this whole mess and

406
00:24:05,330 --> 00:24:24,070
draw a box around it and say
this whole thing inside the

407
00:24:24,070 --> 00:24:33,900
box is boss of z
in division d.

408
00:24:33,900 --> 00:24:35,250
That's in effect what
we want to do.

409
00:24:35,250 --> 00:24:38,720


410
00:24:38,720 --> 00:24:45,690
So, for instance, if we've
done that, and we want to

411
00:24:45,690 --> 00:24:49,410
check whether or not it's true
that Ben Bitdiddle is a boss

412
00:24:49,410 --> 00:25:00,730
in the computer division, so if
I want to say boss of Ben

413
00:25:00,730 --> 00:25:05,850
Bitdiddle in the computer
division, imagine typing that

414
00:25:05,850 --> 00:25:10,860
in as query to the system, in
effect what we want to do is

415
00:25:10,860 --> 00:25:28,920
set up a dictionary here, which
has z to Ben Bitdiddle

416
00:25:28,920 --> 00:25:33,045
and d to computer.

417
00:25:33,045 --> 00:25:37,340


418
00:25:37,340 --> 00:25:38,720
Where did that dictionary
come from?

419
00:25:38,720 --> 00:25:40,710
Let's look at the slide
for one second.

420
00:25:40,710 --> 00:25:44,750
That dictionary came from
matching the query that said

421
00:25:44,750 --> 00:25:47,720
boss of Ben Bitdiddle and
computer onto the conclusion

422
00:25:47,720 --> 00:25:51,650
of the rule: boss of z and d.

423
00:25:51,650 --> 00:25:54,190
So we match the query to the
conclusion of the rule.

424
00:25:54,190 --> 00:26:00,330
That gives us a dictionary, and
that's the thing that we

425
00:26:00,330 --> 00:26:03,180
would now like to put into
this whole big thing and

426
00:26:03,180 --> 00:26:06,670
process and see if anything
comes out the other side.

427
00:26:06,670 --> 00:26:11,330
If anything comes out,
it'll be true.

428
00:26:11,330 --> 00:26:12,370
That's the basic idea.

429
00:26:12,370 --> 00:26:17,020
So in general, the way we
implement a rule is we match

430
00:26:17,020 --> 00:26:21,860
the conclusion of the rule
against something we might

431
00:26:21,860 --> 00:26:23,580
want to check it's true.

432
00:26:23,580 --> 00:26:26,790
That match gives us a
dictionary, and with respect

433
00:26:26,790 --> 00:26:36,470
to that dictionary, we process
the body of the rule.

434
00:26:36,470 --> 00:26:40,110
Well, that's really all
there is, except for

435
00:26:40,110 --> 00:26:43,070
two technical points.

436
00:26:43,070 --> 00:26:46,580
The first technical point is
that I might have said

437
00:26:46,580 --> 00:26:47,510
something else.

438
00:26:47,510 --> 00:26:52,490
I might have said who's the boss
in the computer division?

439
00:26:52,490 --> 00:26:56,270
So I might say boss of who
in computer division.

440
00:26:56,270 --> 00:27:00,329


441
00:27:00,329 --> 00:27:03,920
And if I did that, what I would
really like to do in

442
00:27:03,920 --> 00:27:09,280
effect is start up this
dictionary with a match that

443
00:27:09,280 --> 00:27:17,370
sort of says, well, d
is computer and z is

444
00:27:17,370 --> 00:27:18,620
whatever who is.

445
00:27:18,620 --> 00:27:21,700


446
00:27:21,700 --> 00:27:23,220
And our matcher won't
quite do that.

447
00:27:23,220 --> 00:27:28,580
That's not quite matching
a pattern against data.

448
00:27:28,580 --> 00:27:31,310
It's matching two patterns and
saying are they consistent or

449
00:27:31,310 --> 00:27:33,480
not or what ways make
them consistent.

450
00:27:33,480 --> 00:27:35,940
In other words, what we need
is not quite a pattern

451
00:27:35,940 --> 00:27:38,450
matcher, but something
a little bit more

452
00:27:38,450 --> 00:27:39,740
general called a unifier.

453
00:27:39,740 --> 00:27:44,420


454
00:27:44,420 --> 00:27:47,190
And a unifier is a slight
generalization

455
00:27:47,190 --> 00:27:49,530
of a pattern matcher.

456
00:27:49,530 --> 00:27:55,390
What a unifier does is take two
patterns and say what's

457
00:27:55,390 --> 00:27:59,020
the most general thing you can
substitute for the variables

458
00:27:59,020 --> 00:28:04,060
in those two patterns to make
them satisfy the pattern

459
00:28:04,060 --> 00:28:05,680
simultaneously?

460
00:28:05,680 --> 00:28:08,900
Let me give you an example.

461
00:28:08,900 --> 00:28:13,940
If I have the pattern
two-element list, which is x

462
00:28:13,940 --> 00:28:18,220
and x, so I have a two-element
list where both elements are

463
00:28:18,220 --> 00:28:20,670
the same and otherwise I don't
care what they are, and I

464
00:28:20,670 --> 00:28:23,790
unify that against the pattern
that says there's a

465
00:28:23,790 --> 00:28:27,010
two-element list, and the first
one is a and something

466
00:28:27,010 --> 00:28:33,830
in c and the second one is a
and b and z, then what the

467
00:28:33,830 --> 00:28:36,960
unifier should tell me is, oh
yeah, in that dictionary, x

468
00:28:36,960 --> 00:28:43,440
has to be a, b, c, and y has
to be d and z has to be c.

469
00:28:43,440 --> 00:28:45,660
Those are the restrictions I'd
have to put on the values of

470
00:28:45,660 --> 00:28:48,880
x, y, and z to make these two
unify, or in other words, to

471
00:28:48,880 --> 00:28:55,420
make this match x and
make this match x.

472
00:28:55,420 --> 00:28:58,540
The unifier should be
able to deduce that.

473
00:28:58,540 --> 00:28:59,730
But the unifier may--

474
00:28:59,730 --> 00:29:01,080
there are more complicated
things.

475
00:29:01,080 --> 00:29:03,810
I might have said something a
little bit more complicated.

476
00:29:03,810 --> 00:29:07,170
I might have said there's a list
with two elements, and

477
00:29:07,170 --> 00:29:10,080
they're both the same, and
they should unify against

478
00:29:10,080 --> 00:29:12,650
something of this form.

479
00:29:12,650 --> 00:29:16,890
And the unifier should be able
to deduce from that.

480
00:29:16,890 --> 00:29:19,570
Like that y would have to be
b. y would have to be b.

481
00:29:19,570 --> 00:29:24,340
Because these two are the same,
so y's got to be b.

482
00:29:24,340 --> 00:29:28,940
And v here would have to be a.

483
00:29:28,940 --> 00:29:31,450
And z and w can be anything,
but they have

484
00:29:31,450 --> 00:29:32,700
to be the same thing.

485
00:29:32,700 --> 00:29:35,710


486
00:29:35,710 --> 00:29:40,680
And x would have to be b,
followed by a, followed by

487
00:29:40,680 --> 00:29:44,680
whatever w is or whatever
z is, which is the same.

488
00:29:44,680 --> 00:29:48,260
So you see, the unifier somehow
has to deduce things

489
00:29:48,260 --> 00:29:50,880
to unify these patterns.

490
00:29:50,880 --> 00:29:52,880
So you might think there's some
kind of magic deduction

491
00:29:52,880 --> 00:29:55,850
going on, but there's not.

492
00:29:55,850 --> 00:29:59,100
A unifier is basically a very
simple modification of a

493
00:29:59,100 --> 00:30:00,150
pattern matcher.

494
00:30:00,150 --> 00:30:02,530
And if you look in the book,
you'll see something like

495
00:30:02,530 --> 00:30:05,350
three or four lines of code
added to the pattern matcher

496
00:30:05,350 --> 00:30:08,280
you just saw to handle
the symmetric case.

497
00:30:08,280 --> 00:30:11,920
Remember, the pattern matcher
has a place where it says is

498
00:30:11,920 --> 00:30:14,980
this variable matching
a constant.

499
00:30:14,980 --> 00:30:16,420
And if so, it checks
in the dictionary.

500
00:30:16,420 --> 00:30:18,970
There's only one other clause in
the unifier, which says is

501
00:30:18,970 --> 00:30:22,760
this variable matching a
variable, in which case you go

502
00:30:22,760 --> 00:30:24,740
look in the dictionary and see
if that's consistent with

503
00:30:24,740 --> 00:30:27,030
what's in the dictionary.

504
00:30:27,030 --> 00:30:31,450
So all the, quote, deduction
that's in this language, if

505
00:30:31,450 --> 00:30:33,780
you sort of look at it, sort
of sits in the rule

506
00:30:33,780 --> 00:30:37,220
applications, which, if you
look at that, sits in the

507
00:30:37,220 --> 00:30:42,500
unifier, which, if you look at
that under a microscope, sits

508
00:30:42,500 --> 00:30:45,260
essentially in the
pattern matcher.

509
00:30:45,260 --> 00:30:47,410
There's no magic at all
going on in there.

510
00:30:47,410 --> 00:30:51,930
And the, quote, deduction that
you see is just the fact that

511
00:30:51,930 --> 00:30:54,610
there's this recursion,
which is unwinding the

512
00:30:54,610 --> 00:30:56,030
matches bit by bit.

513
00:30:56,030 --> 00:30:58,670
So it looks like this thing is
being very clever, but in

514
00:30:58,670 --> 00:31:02,140
fact, it's not being
very clever at all.

515
00:31:02,140 --> 00:31:03,420
There are cases where a unifier

516
00:31:03,420 --> 00:31:04,880
might have to be clever.

517
00:31:04,880 --> 00:31:06,130
Let me show you one more.

518
00:31:06,130 --> 00:31:11,070


519
00:31:11,070 --> 00:31:17,530
Suppose I want to unify a list
of two elements, x and x, with

520
00:31:17,530 --> 00:31:24,370
a thing that says it's y
followed by a dot y.

521
00:31:24,370 --> 00:31:27,120
Now, if you think of what that
would have to mean, it would

522
00:31:27,120 --> 00:31:32,230
have to mean that x had better
be the same as y, but also x

523
00:31:32,230 --> 00:31:35,160
had better be the same as a list
whose first element is a

524
00:31:35,160 --> 00:31:37,330
and whose rest is y.

525
00:31:37,330 --> 00:31:42,460
And if you think about what that
would have to mean, it

526
00:31:42,460 --> 00:31:44,710
would have to mean that y is
the infinite list of a's.

527
00:31:44,710 --> 00:31:47,500


528
00:31:47,500 --> 00:31:53,100
In some sense, in order to do
that unification, I have to

529
00:31:53,100 --> 00:32:01,840
solve the fixed-point equation
cons of a to y is equal to y.

530
00:32:01,840 --> 00:32:04,570


531
00:32:04,570 --> 00:32:07,290
And in general, I wrote
a very simple one.

532
00:32:07,290 --> 00:32:11,260
Really doing unification might
have to solve an arbitrary

533
00:32:11,260 --> 00:32:15,530
fixed-point equation:
f of y equals y.

534
00:32:15,530 --> 00:32:18,750
And basically, you can't do that
and make the thing finite

535
00:32:18,750 --> 00:32:20,570
all the time.

536
00:32:20,570 --> 00:32:25,140
So how does the logic language
handle that?

537
00:32:25,140 --> 00:32:26,850
The answer is it doesn't.

538
00:32:26,850 --> 00:32:28,730
It just punts.

539
00:32:28,730 --> 00:32:32,280
And there's a little check in
the unifier, which says, oh,

540
00:32:32,280 --> 00:32:35,520
is this one of the hard cases
which when I go to match

541
00:32:35,520 --> 00:32:38,650
things would involve solving
a fixed-point equation?

542
00:32:38,650 --> 00:32:42,840
And in this case, I will
throw up my hands.

543
00:32:42,840 --> 00:32:47,990
And if that check were not in
there, what would happen?

544
00:32:47,990 --> 00:32:50,590
In most cases is that the
unifier would just go into an

545
00:32:50,590 --> 00:32:53,740
infinite loop.

546
00:32:53,740 --> 00:32:56,800
And other logic programming
languages work like that.

547
00:32:56,800 --> 00:32:58,220
So there's really no magic.

548
00:32:58,220 --> 00:33:00,100
The easy case is done
in a matcher.

549
00:33:00,100 --> 00:33:02,960
The hard case is not
done at all.

550
00:33:02,960 --> 00:33:05,115
And that's about the state
of this technology.

551
00:33:05,115 --> 00:33:12,840


552
00:33:12,840 --> 00:33:15,250
Let me just say again formally
how rules work now that I

553
00:33:15,250 --> 00:33:17,390
talked about unifiers.

554
00:33:17,390 --> 00:33:25,260
So the official definition is
that to apply a rule, we--

555
00:33:25,260 --> 00:33:28,270
well, let's start using some
words we've used before.

556
00:33:28,270 --> 00:33:33,280
Let's talk about sticking
dictionaries into these big

557
00:33:33,280 --> 00:33:40,090
boxes of query things as
evaluating these large queries

558
00:33:40,090 --> 00:33:43,850
relative to an environment
or a frame.

559
00:33:43,850 --> 00:33:45,350
So when you think of that
dictionary, what's the

560
00:33:45,350 --> 00:33:46,720
dictionary after all?

561
00:33:46,720 --> 00:33:48,180
It's a bunch of meanings
for symbols.

562
00:33:48,180 --> 00:33:51,800
That's what we've been calling
frames or environments.

563
00:33:51,800 --> 00:33:55,430
What does it mean to do some
processing relevant to an

564
00:33:55,430 --> 00:33:55,970
environment?

565
00:33:55,970 --> 00:33:58,310
That's what we've been
calling evaluation.

566
00:33:58,310 --> 00:34:03,030
So we can say the way that you
apply a rule is to evaluate

567
00:34:03,030 --> 00:34:07,730
the rule body relative to an
environment that's formed by

568
00:34:07,730 --> 00:34:13,230
unifying the rule conclusion
with the given query.

569
00:34:13,230 --> 00:34:16,340
And the thing I want you to
notice is the complete formal

570
00:34:16,340 --> 00:34:20,760
similarity to the net of
circular evaluator or the

571
00:34:20,760 --> 00:34:21,630
substitution model.

572
00:34:21,630 --> 00:34:27,100
To apply a procedure, we
evaluate the procedure body

573
00:34:27,100 --> 00:34:31,040
relative to an environment
that's formed by blinding the

574
00:34:31,040 --> 00:34:34,560
procedure parameters
to the arguments.

575
00:34:34,560 --> 00:34:36,760
There's a complete formal
similarity here between the

576
00:34:36,760 --> 00:34:40,870
rules, rule application, and
procedure application even

577
00:34:40,870 --> 00:34:43,650
though these things are
very, very different.

578
00:34:43,650 --> 00:34:47,290
And again, you have the
EVAL APPLY loop.

579
00:34:47,290 --> 00:34:49,445
EVAL and APPLY.

580
00:34:49,445 --> 00:34:53,360


581
00:34:53,360 --> 00:34:57,050
So in general, I might be
processing some combined

582
00:34:57,050 --> 00:35:01,050
expression that will turn into a
rule application, which will

583
00:35:01,050 --> 00:35:03,090
generate some dictionaries or
frames or environments--

584
00:35:03,090 --> 00:35:05,360
whatever you want to call them--
from match, which will

585
00:35:05,360 --> 00:35:08,660
then be the input to some big
compound thing like this.

586
00:35:08,660 --> 00:35:13,580
This has pieces of it and may
have other rule applications.

587
00:35:13,580 --> 00:35:16,220
And you have essentially the
same cycle even though there's

588
00:35:16,220 --> 00:35:19,680
nothing here at all that
looks like procedures.

589
00:35:19,680 --> 00:35:22,120
It really has to do with the
fact you've built a language

590
00:35:22,120 --> 00:35:24,150
whose means of combination
and abstraction

591
00:35:24,150 --> 00:35:25,490
unwind in certain ways.

592
00:35:25,490 --> 00:35:28,770


593
00:35:28,770 --> 00:35:33,840
And then in general, what
happens at the very top level,

594
00:35:33,840 --> 00:35:37,280
you might have rules in your
database also, so things in

595
00:35:37,280 --> 00:35:40,460
this database might be rules.

596
00:35:40,460 --> 00:35:42,920
There are ways to check
that things are true.

597
00:35:42,920 --> 00:35:46,750
So it might come in here and
have to do a rule check.

598
00:35:46,750 --> 00:35:48,580
And then there's some control
structure which says, well,

599
00:35:48,580 --> 00:35:50,130
you look at some rules, and
you look at some data

600
00:35:50,130 --> 00:35:51,965
elements, and you look at some
rules and data elements, and

601
00:35:51,965 --> 00:35:53,350
these fan out and out and out.

602
00:35:53,350 --> 00:35:56,520
So it becomes essentially
impossible to say what order

603
00:35:56,520 --> 00:35:59,300
it's looking at these things in,
whether it's breadth first

604
00:35:59,300 --> 00:36:00,245
or depth first or anything.

605
00:36:00,245 --> 00:36:03,650
And it's even more impossible
because the actual order is

606
00:36:03,650 --> 00:36:08,900
somehow buried in the delays of
the streams. So what's very

607
00:36:08,900 --> 00:36:11,270
hard to tell from this is the
order in which it's scanned.

608
00:36:11,270 --> 00:36:13,330
But what's true, because you're
looking at the stream

609
00:36:13,330 --> 00:36:15,820
view, is that all of them
eventually get looked at.

610
00:36:15,820 --> 00:36:24,980


611
00:36:24,980 --> 00:36:28,150
Let me just mention one tiny
technical problem.

612
00:36:28,150 --> 00:36:37,530


613
00:36:37,530 --> 00:36:44,960
Suppose I tried saying boss of
y is computer, then a funny

614
00:36:44,960 --> 00:36:45,780
thing would happen.

615
00:36:45,780 --> 00:36:53,680
As I stuck a dictionary with
y in here, I might get--

616
00:36:53,680 --> 00:36:59,350
this y is not the same as that
y, which was the other piece

617
00:36:59,350 --> 00:37:01,580
of somebody's job description.

618
00:37:01,580 --> 00:37:04,380
So if I really only did
literally what I said, we'd

619
00:37:04,380 --> 00:37:09,990
get some variable conflict
problems. So I lied to you a

620
00:37:09,990 --> 00:37:10,930
little bit.

621
00:37:10,930 --> 00:37:12,900
Notice that problem is
exactly a problem

622
00:37:12,900 --> 00:37:14,360
we've run into before.

623
00:37:14,360 --> 00:37:20,505
It is precisely the need for
local variables in a language.

624
00:37:20,505 --> 00:37:22,490
When I have the sum of
squares, that x had

625
00:37:22,490 --> 00:37:24,960
better not be that x.

626
00:37:24,960 --> 00:37:28,620
That's exactly the same
as this y had

627
00:37:28,620 --> 00:37:31,800
better not be that y.

628
00:37:31,800 --> 00:37:33,100
And we know how to solve that.

629
00:37:33,100 --> 00:37:34,730
That was this whole environment
model, and we

630
00:37:34,730 --> 00:37:37,710
built chains of frames and all
sorts of things like that.

631
00:37:37,710 --> 00:37:39,270
There's a much more brutal
way to solve it.

632
00:37:39,270 --> 00:37:41,730
In the query language, we
didn't even do that.

633
00:37:41,730 --> 00:37:43,540
We did something completely
brutal.

634
00:37:43,540 --> 00:37:48,520
We said every time you apply a
rule, rename consistently all

635
00:37:48,520 --> 00:37:51,100
the variables in the rule to
some new unique names that

636
00:37:51,100 --> 00:37:55,720
won't conflict with anything.

637
00:37:55,720 --> 00:37:58,150
That's conceptually simpler,
but really brutal and not

638
00:37:58,150 --> 00:37:59,970
particularly efficient.

639
00:37:59,970 --> 00:38:03,700
But notice, we could have
gotten rid of all of our

640
00:38:03,700 --> 00:38:08,030
environment structures if we
defined for procedures in Lisp

641
00:38:08,030 --> 00:38:09,180
the same thing.

642
00:38:09,180 --> 00:38:10,580
If every time we applied
a procedure and did the

643
00:38:10,580 --> 00:38:13,410
substitution model we renamed
all the variables in the

644
00:38:13,410 --> 00:38:15,830
procedure, then we never would
have had to worry about local

645
00:38:15,830 --> 00:38:19,040
variables because they
would never arise.

646
00:38:19,040 --> 00:38:21,240
OK, well, that would be
inefficient, and it's

647
00:38:21,240 --> 00:38:23,870
inefficient here in the query
language, too, but we did it

648
00:38:23,870 --> 00:38:25,610
to keep it simple.

649
00:38:25,610 --> 00:38:26,860
Let's break for questions.

650
00:38:26,860 --> 00:38:30,880


651
00:38:30,880 --> 00:38:34,870
AUDIENCE: When you started this
section, you emphasized

652
00:38:34,870 --> 00:38:40,390
how powerful our APPLY EVAL
model was that we could use it

653
00:38:40,390 --> 00:38:41,170
for any language.

654
00:38:41,170 --> 00:38:42,790
And then you say we're going to
have this language which is

655
00:38:42,790 --> 00:38:43,950
so different.

656
00:38:43,950 --> 00:38:46,440
It turns out that this language,
as you just pointed

657
00:38:46,440 --> 00:38:47,880
out, is very much the same.

658
00:38:47,880 --> 00:38:49,710
I'm wondering if you're arguing
that all languages end

659
00:38:49,710 --> 00:38:53,810
up coming down to this you can
apply a rule or apply a

660
00:38:53,810 --> 00:38:57,030
procedure or some
kind of apply?

661
00:38:57,030 --> 00:38:59,150
PROFESSOR: I would say that
pretty much any language where

662
00:38:59,150 --> 00:39:03,210
you really are building up these
means of combination and

663
00:39:03,210 --> 00:39:06,120
giving them simpler names and
you're saying anything of the

664
00:39:06,120 --> 00:39:10,430
sort, like here's a general kind
of expression, like how

665
00:39:10,430 --> 00:39:13,180
to square something, almost
anything that you

666
00:39:13,180 --> 00:39:14,880
would call a procedure.

667
00:39:14,880 --> 00:39:16,360
If that's got to have
parts, you have to

668
00:39:16,360 --> 00:39:18,020
unwind those parts.

669
00:39:18,020 --> 00:39:20,830
You have to have some kind of
organization which says when I

670
00:39:20,830 --> 00:39:24,892
look at the abstract variables
or tags or whatever you want

671
00:39:24,892 --> 00:39:28,490
to call them that might stand
for particular things, you

672
00:39:28,490 --> 00:39:29,720
have to keep track of that,
and that's going to be

673
00:39:29,720 --> 00:39:31,720
something like an environment.

674
00:39:31,720 --> 00:39:34,670
And then if you say this part
can have parts which I have to

675
00:39:34,670 --> 00:39:37,440
unwind, you've got to have
something like this cycle.

676
00:39:37,440 --> 00:39:39,970


677
00:39:39,970 --> 00:39:44,000
And lots and lots of languages
have that character when they

678
00:39:44,000 --> 00:39:45,590
sort of get put together
in this way.

679
00:39:45,590 --> 00:39:47,610
This language again really is
different because there's

680
00:39:47,610 --> 00:39:50,690
nothing like procedures
on the outside.

681
00:39:50,690 --> 00:39:52,080
When you go below the surface
and you see the

682
00:39:52,080 --> 00:39:54,870
implementation, of course, it
starts looking the same.

683
00:39:54,870 --> 00:39:56,950
But from the outside, it's a
very different world view.

684
00:39:56,950 --> 00:39:58,650
You're not computing functions
of inputs.

685
00:39:58,650 --> 00:40:03,970


686
00:40:03,970 --> 00:40:07,920
AUDIENCE: You mentioned earlier
that when you build

687
00:40:07,920 --> 00:40:10,660
all of these rules in pattern
matcher and with the delayed

688
00:40:10,660 --> 00:40:13,900
action of streams, you really
have no way to know in what

689
00:40:13,900 --> 00:40:15,495
order things are evaluated.

690
00:40:15,495 --> 00:40:15,940
PROFESSOR: Right.

691
00:40:15,940 --> 00:40:19,470
AUDIENCE: And that would
indicate then that you should

692
00:40:19,470 --> 00:40:21,850
only express declarative
knowledge that's true for

693
00:40:21,850 --> 00:40:23,950
all-time, no-time sequence
built into it.

694
00:40:23,950 --> 00:40:27,440
Otherwise, these things
get all--

695
00:40:27,440 --> 00:40:28,490
PROFESSOR: Yes.

696
00:40:28,490 --> 00:40:28,820
Yes.

697
00:40:28,820 --> 00:40:32,100
The question is this really is
set up for doing declarative

698
00:40:32,100 --> 00:40:37,190
knowledge, and as I presented
it-- and I'll show you some of

699
00:40:37,190 --> 00:40:40,830
the ugly warts under this
after the break.

700
00:40:40,830 --> 00:40:43,070
As I presented it, it's
just doing logic.

701
00:40:43,070 --> 00:40:45,720
And in principle, if it were
logic, it wouldn't matter what

702
00:40:45,720 --> 00:40:48,840
order it's getting done.

703
00:40:48,840 --> 00:40:52,840
And it's quite true when you
start doing things where you

704
00:40:52,840 --> 00:40:55,380
have side effects like adding
things to the database and

705
00:40:55,380 --> 00:40:59,990
taking things out, and we'll see
some others, you use that

706
00:40:59,990 --> 00:41:01,290
kind of control.

707
00:41:01,290 --> 00:41:02,940
So, for example, contrasting
with Prolog.

708
00:41:02,940 --> 00:41:05,720
Say Prolog has various features
where you really

709
00:41:05,720 --> 00:41:09,640
exploit the order
of evaluation.

710
00:41:09,640 --> 00:41:11,770
And people write Prolog
programs that way.

711
00:41:11,770 --> 00:41:14,420
That turns out to be very
complicated in Prolog,

712
00:41:14,420 --> 00:41:15,940
although if you're
an expert Prolog

713
00:41:15,940 --> 00:41:18,590
programmer, you can do it.

714
00:41:18,590 --> 00:41:20,210
However, here I don't think
you can do it at all.

715
00:41:20,210 --> 00:41:22,890
It's very complicated because
you really are giving up

716
00:41:22,890 --> 00:41:27,150
control over any prearranged
order of trying things.

717
00:41:27,150 --> 00:41:29,210
AUDIENCE: Now, that would
indicate then that you have a

718
00:41:29,210 --> 00:41:30,670
functional mapping.

719
00:41:30,670 --> 00:41:34,870
And when you started out this
lecture, you said that we

720
00:41:34,870 --> 00:41:36,635
express the declarative
knowledge which is a relation,

721
00:41:36,635 --> 00:41:38,810
and we don't talk about the
inputs and the outputs.

722
00:41:38,810 --> 00:41:41,390


723
00:41:41,390 --> 00:41:43,370
PROFESSOR: Well, there's a
pun on functional, right?

724
00:41:43,370 --> 00:41:46,560
There's function in the sense
of no side effects and not

725
00:41:46,560 --> 00:41:48,700
depending on what order
is going on.

726
00:41:48,700 --> 00:41:50,720
And then there's functional in
the sense of mathematical

727
00:41:50,720 --> 00:41:52,220
function, which means
input and output.

728
00:41:52,220 --> 00:41:56,510
And it's just that pun that
you're making, I think.

729
00:41:56,510 --> 00:41:58,520
AUDIENCE: I'm a little unclear
on what you're doing with

730
00:41:58,520 --> 00:42:01,270
these two statements, the
two boss statements.

731
00:42:01,270 --> 00:42:06,416
Is the first one building up
the database and the second

732
00:42:06,416 --> 00:42:09,150
one a query or--

733
00:42:09,150 --> 00:42:12,440
PROFESSOR: OK, I'm sorry.

734
00:42:12,440 --> 00:42:14,130
What I meant here, if I
type something like

735
00:42:14,130 --> 00:42:16,200
this in as a query--

736
00:42:16,200 --> 00:42:19,470
I should have given an example
way at the very beginning.

737
00:42:19,470 --> 00:42:25,100
If I type in job, Ben Bitdiddle,
computer wizard,

738
00:42:25,100 --> 00:42:28,570
what the processing will do is
if it finds a match, it'll

739
00:42:28,570 --> 00:42:31,600
find a match to that exact
thing, and it'll type out a

740
00:42:31,600 --> 00:42:34,220
job, Ben Bitdiddle,
computer wizard.

741
00:42:34,220 --> 00:42:37,400
If it doesn't find a match,
it won't find anything.

742
00:42:37,400 --> 00:42:40,100
So what I should have said is
the way you use the query

743
00:42:40,100 --> 00:42:43,610
language to check whether
something is true, remember,

744
00:42:43,610 --> 00:42:45,130
that's one of the things
you want to do in logic

745
00:42:45,130 --> 00:42:47,990
programming, is you type in
your query and either that

746
00:42:47,990 --> 00:42:50,680
comes out or it doesn't.

747
00:42:50,680 --> 00:42:52,940
So what I was trying to
illustrate here, I wanted to

748
00:42:52,940 --> 00:42:55,220
start with a very simple
example before

749
00:42:55,220 --> 00:42:57,480
talking about unifiers.

750
00:42:57,480 --> 00:43:00,260
So what I should have said, if I
just wanted to check whether

751
00:43:00,260 --> 00:43:02,820
this is true, I could type that
in and see if anything

752
00:43:02,820 --> 00:43:04,854
came out

753
00:43:04,854 --> 00:43:06,290
AUDIENCE: And then
the second one--

754
00:43:06,290 --> 00:43:07,830
PROFESSOR: The second one
would be a real query.

755
00:43:07,830 --> 00:43:10,770
AUDIENCE: A real query, yeah.

756
00:43:10,770 --> 00:43:12,380
PROFESSOR: What would come out,
see, it would go in here

757
00:43:12,380 --> 00:43:17,480
say with FOO, and in would go
frame that says z is bound to

758
00:43:17,480 --> 00:43:19,560
who and d is bound
to computer.

759
00:43:19,560 --> 00:43:21,400
And this will pass through, and
then by the time it got

760
00:43:21,400 --> 00:43:23,250
out of here, who would
pick up a binding.

761
00:43:23,250 --> 00:43:26,950


762
00:43:26,950 --> 00:43:31,950
AUDIENCE: On the unifying thing
there, I still am not

763
00:43:31,950 --> 00:43:36,460
sure what happens
with who and z.

764
00:43:36,460 --> 00:43:37,850
If the unifying--

765
00:43:37,850 --> 00:43:39,490
the rule here says--

766
00:43:39,490 --> 00:43:42,070


767
00:43:42,070 --> 00:43:44,920
OK, so you say that you can't
make question mark equal to

768
00:43:44,920 --> 00:43:46,260
question mark who.

769
00:43:46,260 --> 00:43:46,410
PROFESSOR: Right.

770
00:43:46,410 --> 00:43:48,360
That's what the matcher
can't do.

771
00:43:48,360 --> 00:43:52,550
But what this will mean to a
unifier is that there's an

772
00:43:52,550 --> 00:43:53,800
environment with three
variables.

773
00:43:53,800 --> 00:43:56,690


774
00:43:56,690 --> 00:43:58,520
d here is computer.

775
00:43:58,520 --> 00:44:01,830
z is whatever who is.

776
00:44:01,830 --> 00:44:09,180
So if later on in the matcher
routine it said, for example,

777
00:44:09,180 --> 00:44:14,110
who has to be 3, then when I
looked up in the dictionary,

778
00:44:14,110 --> 00:44:18,360
it will say, oh, z is 3 because
it's the same as who.

779
00:44:18,360 --> 00:44:20,500
And that's in some sense the
only thing you need to do to

780
00:44:20,500 --> 00:44:22,640
extend the unifier
to a matcher.

781
00:44:22,640 --> 00:44:23,830
AUDIENCE: OK, because it looked
like when you were

782
00:44:23,830 --> 00:44:26,000
telling how to unify it, it
looked like you would put the

783
00:44:26,000 --> 00:44:27,955
things together in such a way
that you'd actually solve and

784
00:44:27,955 --> 00:44:29,770
have a value for both of them.

785
00:44:29,770 --> 00:44:32,230
And what it looks like now is
that you're actually pass a

786
00:44:32,230 --> 00:44:34,860
dictionary with two variables
and the variables are linked.

787
00:44:34,860 --> 00:44:35,130
PROFESSOR: Right.

788
00:44:35,130 --> 00:44:37,580
It only looks like you're
solving for both of them

789
00:44:37,580 --> 00:44:40,540
because you're sort of looking
at the whole solution at once.

790
00:44:40,540 --> 00:44:42,790
If you sort of watch the thing
getting built up recursively,

791
00:44:42,790 --> 00:44:44,980
it's merely this.

792
00:44:44,980 --> 00:44:46,620
AUDIENCE: OK, so you
do pass off that

793
00:44:46,620 --> 00:44:48,400
dictionary with two variables?

794
00:44:48,400 --> 00:44:49,110
PROFESSOR: That's right.

795
00:44:49,110 --> 00:44:50,190
AUDIENCE: And link?

796
00:44:50,190 --> 00:44:50,560
PROFESSOR: Right.

797
00:44:50,560 --> 00:44:54,055
It just looks like an
ordinary dictionary.

798
00:44:54,055 --> 00:44:57,450
AUDIENCE: When you're talking
about the unifier, is it that

799
00:44:57,450 --> 00:45:02,785
there are some cases or some
points that you are not able

800
00:45:02,785 --> 00:45:04,725
to use by them?

801
00:45:04,725 --> 00:45:05,220
PROFESSOR: Right.

802
00:45:05,220 --> 00:45:10,100
AUDIENCE: Can you just by
building the rules or writing

803
00:45:10,100 --> 00:45:15,582
the forms know in advance if
you are going to be able to

804
00:45:15,582 --> 00:45:18,540
solve to get the unification
or not?

805
00:45:18,540 --> 00:45:23,560
Can you add some properties
either to the rules itself or

806
00:45:23,560 --> 00:45:26,730
to the formula that you're
writing so that you avoid the

807
00:45:26,730 --> 00:45:30,090
problem of not finding
unification?

808
00:45:30,090 --> 00:45:32,870
PROFESSOR: I mean, you can
agree, I think, to write in a

809
00:45:32,870 --> 00:45:35,390
fairly restricted way where
you won't run into it.

810
00:45:35,390 --> 00:45:36,870
See, because what
you're getting--

811
00:45:36,870 --> 00:45:39,760
see, the place where you get
into problems is when you--

812
00:45:39,760 --> 00:45:45,020
well, again, you're trying to
match things like that against

813
00:45:45,020 --> 00:45:47,600
things where these
have structure,

814
00:45:47,600 --> 00:45:55,300
where a, y, b, y something.

815
00:45:55,300 --> 00:45:58,980


816
00:45:58,980 --> 00:46:00,570
So this is the kind of
place where you're

817
00:46:00,570 --> 00:46:03,070
going to get into trouble.

818
00:46:03,070 --> 00:46:06,370
AUDIENCE: So you can do
that syntactically?

819
00:46:06,370 --> 00:46:09,320
PROFESSOR: So you can kind of
watch your rules in the kinds

820
00:46:09,320 --> 00:46:11,561
of things that your writing.

821
00:46:11,561 --> 00:46:14,460
AUDIENCE: So that's the problem
that the builder of

822
00:46:14,460 --> 00:46:16,310
the database has to
be concerned?

823
00:46:16,310 --> 00:46:17,560
PROFESSOR: That's a problem.

824
00:46:17,560 --> 00:46:19,930


825
00:46:19,930 --> 00:46:21,580
It's a problem either-- not
quite the builder of the

826
00:46:21,580 --> 00:46:24,270
database, the person who is
expressing the rules, or the

827
00:46:24,270 --> 00:46:25,800
builder of the database.

828
00:46:25,800 --> 00:46:29,230
What the unifier actually does
is you can check at the next

829
00:46:29,230 --> 00:46:32,710
level down when you actually get
to the unifier and you'll

830
00:46:32,710 --> 00:46:34,940
see in the code where it looks
up in the dictionary.

831
00:46:34,940 --> 00:46:37,260
If it sort of says what
does y have to be?

832
00:46:37,260 --> 00:46:40,690
Oh, does y have to be something
that contains a y as

833
00:46:40,690 --> 00:46:41,960
its expression?

834
00:46:41,960 --> 00:46:45,120
At that point, the unifier and
say, oh my God, I'm trying to

835
00:46:45,120 --> 00:46:46,240
solve a fixed-point equation.

836
00:46:46,240 --> 00:46:49,220
I'll give it up here.

837
00:46:49,220 --> 00:46:50,940
AUDIENCE: You make the
distinction between the rules

838
00:46:50,940 --> 00:46:51,910
in the database.

839
00:46:51,910 --> 00:46:56,950
Are the rules added
to the database?

840
00:46:56,950 --> 00:46:57,870
PROFESSOR: Yes.

841
00:46:57,870 --> 00:46:58,870
Yes, I should have said that.

842
00:46:58,870 --> 00:47:01,540
One way to think about rules
is that they're just other

843
00:47:01,540 --> 00:47:03,890
things in the database.

844
00:47:03,890 --> 00:47:06,050
So if you want to check the
things that have to be checked

845
00:47:06,050 --> 00:47:08,935
in the database, they're kind
of virtual facts that are in

846
00:47:08,935 --> 00:47:09,445
the database.

847
00:47:09,445 --> 00:47:12,510
AUDIENCE: But in that
explanation, you made the

848
00:47:12,510 --> 00:47:18,230
differentiation between database
and the rules itself.

849
00:47:18,230 --> 00:47:20,490
PROFESSOR: Yeah, I probably
should not have done that.

850
00:47:20,490 --> 00:47:22,440
The only reason to do that
is in terms of the

851
00:47:22,440 --> 00:47:23,540
implementation.

852
00:47:23,540 --> 00:47:25,220
When you look at the
implementation, there's a part

853
00:47:25,220 --> 00:47:28,120
which says check either
primitive assertions in the

854
00:47:28,120 --> 00:47:30,470
database or check rules.

855
00:47:30,470 --> 00:47:33,510
And then the real reason why
you can't tell what order

856
00:47:33,510 --> 00:47:38,010
things are going to come out
in and is that the rules

857
00:47:38,010 --> 00:47:42,240
database and the data database
sort of get merged in a kind

858
00:47:42,240 --> 00:47:44,600
of delayed evaluation way.

859
00:47:44,600 --> 00:47:46,320
And so that's what makes the
order very complicated.

860
00:47:46,320 --> 00:47:55,440


861
00:47:55,440 --> 00:47:56,690
OK, let's break.

862
00:47:56,690 --> 00:48:33,160


863
00:48:33,160 --> 00:48:35,520
We've just seen how the
logic language works

864
00:48:35,520 --> 00:48:37,230
and how rules work.

865
00:48:37,230 --> 00:48:40,120
Now, let's turn to a more
profound question.

866
00:48:40,120 --> 00:48:43,180
What do these things mean?

867
00:48:43,180 --> 00:48:47,240
That brings us to the subtlest,
most devious part of

868
00:48:47,240 --> 00:48:51,420
this whole query language
business, and that is that

869
00:48:51,420 --> 00:48:53,570
it's not quite what
it seems to be.

870
00:48:53,570 --> 00:48:59,750
AND and OR and NOT and the
logical implication of rules

871
00:48:59,750 --> 00:49:05,400
are not really the AND and
OR and NOT and logical

872
00:49:05,400 --> 00:49:07,690
implication of logic.

873
00:49:07,690 --> 00:49:09,910
Let me give you an
example of that.

874
00:49:09,910 --> 00:49:12,960
Certainly, if we have two things
in logic, it ought to

875
00:49:12,960 --> 00:49:22,225
be the case that AND of P and Q
is the same as AND of Q and

876
00:49:22,225 --> 00:49:28,920
P and that OR of P and Q is the
same as OR of Q and P. But

877
00:49:28,920 --> 00:49:30,100
let's look here.

878
00:49:30,100 --> 00:49:32,180
Here's an example.

879
00:49:32,180 --> 00:49:38,200
Let's talk about somebody
outranking somebody else in

880
00:49:38,200 --> 00:49:40,140
our little database
organization.

881
00:49:40,140 --> 00:49:47,890
We'll say s is outranked by b or
if either the supervisor of

882
00:49:47,890 --> 00:49:51,100
this is b or there's some middle
manager here, that

883
00:49:51,100 --> 00:49:55,640
supervisor of s is m, and
m is outranked by b.

884
00:49:55,640 --> 00:49:59,830


885
00:49:59,830 --> 00:50:02,310
So there's one way to define
rule outranked by.

886
00:50:02,310 --> 00:50:06,300
Or we can write exactly the
same thing, except at the

887
00:50:06,300 --> 00:50:11,630
bottom here, we reversed the
order of these two clauses.

888
00:50:11,630 --> 00:50:14,180
And certainly if this were
logic, those ought to mean the

889
00:50:14,180 --> 00:50:16,690
same thing.

890
00:50:16,690 --> 00:50:20,060
However, in our particular
implementation, if you say

891
00:50:20,060 --> 00:50:23,800
something like who's outranked
by Ben Bitdiddle, what you'll

892
00:50:23,800 --> 00:50:27,870
find is that this rule will
work perfectly well and

893
00:50:27,870 --> 00:50:31,030
generate answers, whereas
this rule will go

894
00:50:31,030 --> 00:50:34,110
into an infinite loop.

895
00:50:34,110 --> 00:50:37,230
And the reason for that is that
this will come in and

896
00:50:37,230 --> 00:50:39,400
say, oh, who's outranked
by Ben Bitdiddle?

897
00:50:39,400 --> 00:50:41,920


898
00:50:41,920 --> 00:50:45,790
Find an s which is outranked
by b, where b is Ben

899
00:50:45,790 --> 00:50:50,330
Bitdiddle, which is going to
happen in it a subproblem.

900
00:50:50,330 --> 00:50:55,710
Oh gee, find an m such as m is
outranked by Ben Bitdiddle

901
00:50:55,710 --> 00:50:58,560
with no restrictions on m.

902
00:50:58,560 --> 00:51:01,910
So this will say in order to
solve this problem, I solve

903
00:51:01,910 --> 00:51:04,570
exactly the same problem.

904
00:51:04,570 --> 00:51:06,010
And then after I've solved
that, I'll check for a

905
00:51:06,010 --> 00:51:08,000
supervisory relationship.

906
00:51:08,000 --> 00:51:10,290
Whereas this one won't get into
that, because before it

907
00:51:10,290 --> 00:51:14,010
tries to find this outranked by,
it'll already have had a

908
00:51:14,010 --> 00:51:15,260
restriction on m here.

909
00:51:15,260 --> 00:51:18,560


910
00:51:18,560 --> 00:51:21,190
So these two things which ought
to mean the same, in

911
00:51:21,190 --> 00:51:22,860
fact, one goes into
an infinite loop.

912
00:51:22,860 --> 00:51:26,720
One does not.

913
00:51:26,720 --> 00:51:30,630
That's a very extreme case of
a general thing that you'll

914
00:51:30,630 --> 00:51:35,970
find in logic programming that
if you start changing the

915
00:51:35,970 --> 00:51:39,910
order of the things in the
ANDs or ORs, you'll find

916
00:51:39,910 --> 00:51:42,240
tremendous differences
in efficiency.

917
00:51:42,240 --> 00:51:45,860
And we just saw an infinitely
big difference in efficiency

918
00:51:45,860 --> 00:51:47,110
and an infinite loop.

919
00:51:47,110 --> 00:51:49,190


920
00:51:49,190 --> 00:51:52,220
And there are similar things
having to do with the order in

921
00:51:52,220 --> 00:51:54,070
which you enter rules.

922
00:51:54,070 --> 00:51:55,980
The order in which it happens
to look at rules in the

923
00:51:55,980 --> 00:51:59,140
database may vastly change the
efficiency with which it gets

924
00:51:59,140 --> 00:52:01,860
out answers or, in fact, send
it into an infinite loop for

925
00:52:01,860 --> 00:52:03,840
some orderings.

926
00:52:03,840 --> 00:52:08,370
And this whole thing has to do
with the fact that you're

927
00:52:08,370 --> 00:52:10,950
checking these rules
in some order.

928
00:52:10,950 --> 00:52:13,690
And some rules may lead to
really long paths of

929
00:52:13,690 --> 00:52:15,180
implication.

930
00:52:15,180 --> 00:52:16,440
Others might not.

931
00:52:16,440 --> 00:52:18,480
And you don't know a priori
which ones are good and which

932
00:52:18,480 --> 00:52:19,300
ones are bad.

933
00:52:19,300 --> 00:52:21,270
And there's a whole bunch of
research having to do with

934
00:52:21,270 --> 00:52:24,840
that, mostly having to do with
thinking about making parallel

935
00:52:24,840 --> 00:52:26,970
implementations of logic
programming languages.

936
00:52:26,970 --> 00:52:29,330
And in some sense, what you'd
like to do is check all rules

937
00:52:29,330 --> 00:52:31,870
in parallel and whichever
ones get answers,

938
00:52:31,870 --> 00:52:32,620
you bubble them up.

939
00:52:32,620 --> 00:52:34,600
And if some go down
infinite deductive

940
00:52:34,600 --> 00:52:36,290
changed, well, you just--

941
00:52:36,290 --> 00:52:38,440
you know, memory is cheap and
processors are cheap, and you

942
00:52:38,440 --> 00:52:40,550
just let them buzz for as
for as long as you want.

943
00:52:40,550 --> 00:52:43,510


944
00:52:43,510 --> 00:52:47,660
There's a deeper problem,
though, in comparing this

945
00:52:47,660 --> 00:52:50,870
logic language to real logic.

946
00:52:50,870 --> 00:52:54,260
The example I just showed you,
it went into an infinite loop

947
00:52:54,260 --> 00:52:58,370
maybe, but at least it didn't
give the wrong answer.

948
00:52:58,370 --> 00:53:02,980
There's an actual deeper
problem when we start

949
00:53:02,980 --> 00:53:07,460
comparing, seriously comparing
this logic language with real

950
00:53:07,460 --> 00:53:09,490
classical logic.

951
00:53:09,490 --> 00:53:14,030
So let's sort of review
real classical logic.

952
00:53:14,030 --> 00:53:22,140
All humans are mortal.

953
00:53:22,140 --> 00:53:24,390
That's pretty classical logic.

954
00:53:24,390 --> 00:53:26,410
Then maybe we'll continue
in the very

955
00:53:26,410 --> 00:53:29,120
best classical tradition.

956
00:53:29,120 --> 00:53:31,010
We'll say all--

957
00:53:31,010 --> 00:53:32,740
let's make it really
classical.

958
00:53:32,740 --> 00:53:41,690
All Greeks are human, which
has the syllogism that

959
00:53:41,690 --> 00:53:48,060
Socrates is a Greek.

960
00:53:48,060 --> 00:53:49,210
And then what do
you write here?

961
00:53:49,210 --> 00:53:51,890
I think three dots,
classical logic.

962
00:53:51,890 --> 00:54:01,360
Therefore, then the syllogism,
Socrates is mortal.

963
00:54:01,360 --> 00:54:05,880
So there's some real honest
classical logic.

964
00:54:05,880 --> 00:54:12,570
Let's compare that with our
classical logic database.

965
00:54:12,570 --> 00:54:16,270
So here's a classical
logic database.

966
00:54:16,270 --> 00:54:18,030
Socrates is a Greek.

967
00:54:18,030 --> 00:54:19,600
Plato is a Greek.

968
00:54:19,600 --> 00:54:24,120
Zeus is a Greek, and
Zeus is a god.

969
00:54:24,120 --> 00:54:30,780
And all humans are mortal.

970
00:54:30,780 --> 00:54:32,880
To show that something is
mortal, it's enough to show

971
00:54:32,880 --> 00:54:34,650
that it's human.

972
00:54:34,650 --> 00:54:35,900
All humans are fallible.

973
00:54:35,900 --> 00:54:38,900


974
00:54:38,900 --> 00:54:40,980
And all Greeks are humans
is not quite right.

975
00:54:40,980 --> 00:54:45,920
This says that all Greeks who
are not gods are human.

976
00:54:45,920 --> 00:54:47,820
So to show something's human,
it's enough to show it's a

977
00:54:47,820 --> 00:54:49,320
Greek and not a god.

978
00:54:49,320 --> 00:54:54,470
And the address of any Greek
god is Mount Olympus.

979
00:54:54,470 --> 00:54:57,390
So there's a little classical
logic database.

980
00:54:57,390 --> 00:54:59,490
And indeed, that would
work fairly well.

981
00:54:59,490 --> 00:55:05,420
If we type that in and say is
Socrates mortal or Socrates

982
00:55:05,420 --> 00:55:06,910
fallible or mortal?

983
00:55:06,910 --> 00:55:07,690
It'll say yes.

984
00:55:07,690 --> 00:55:09,710
Is Plato mortal and fallible.

985
00:55:09,710 --> 00:55:10,680
It'll say yes.

986
00:55:10,680 --> 00:55:12,210
If we say is Zeus mortal?

987
00:55:12,210 --> 00:55:14,900
It won't find anything.

988
00:55:14,900 --> 00:55:16,640
And it'll work perfectly well.

989
00:55:16,640 --> 00:55:20,120
However, suppose we want
to extend this.

990
00:55:20,120 --> 00:55:25,070
Let's define what it means for
someone to be a perfect being.

991
00:55:25,070 --> 00:55:27,020
Let's say rule: a
perfect being.

992
00:55:27,020 --> 00:55:34,050


993
00:55:34,050 --> 00:55:35,480
And I think this is right.

994
00:55:35,480 --> 00:55:38,570
If you're up on your medieval
scholastic philosophy, I

995
00:55:38,570 --> 00:55:41,350
believe that perfect beings
are ones who were neither

996
00:55:41,350 --> 00:55:44,100
mortal nor fallible.

997
00:55:44,100 --> 00:55:59,300
AND NOT mortal x,
NOT fallible x.

998
00:55:59,300 --> 00:56:03,340
So we'll define this system
to teach it what a

999
00:56:03,340 --> 00:56:05,790
perfect being is.

1000
00:56:05,790 --> 00:56:09,110
And now what we're going to do
is he ask for the address of

1001
00:56:09,110 --> 00:56:11,750
all the perfect beings.

1002
00:56:11,750 --> 00:56:23,680
AND the address of x is
y and x is perfect.

1003
00:56:23,680 --> 00:56:26,590
And so what we're generating
here is the world's most

1004
00:56:26,590 --> 00:56:32,050
exclusive mailing list. For the
address of all the perfect

1005
00:56:32,050 --> 00:56:33,830
things, we might have
typed this in.

1006
00:56:33,830 --> 00:56:36,240
Or we might type in this.

1007
00:56:36,240 --> 00:56:52,140
We'll say AND perfect of x and
the address of x is y.

1008
00:56:52,140 --> 00:56:55,190
Well, suppose we type all that
in and we try this query.

1009
00:56:55,190 --> 00:56:57,650
This query is going to
give us an answer.

1010
00:56:57,650 --> 00:56:59,745
This query will say, yeah,
Mount Olympus.

1011
00:56:59,745 --> 00:57:04,230


1012
00:57:04,230 --> 00:57:06,740
This query, in fact, is going
to give us nothing.

1013
00:57:06,740 --> 00:57:11,640
It will say no addresses
of perfect beings.

1014
00:57:11,640 --> 00:57:12,510
Now, why is that?

1015
00:57:12,510 --> 00:57:14,230
Why is there a difference?

1016
00:57:14,230 --> 00:57:15,690
This is not an infinite
loop question.

1017
00:57:15,690 --> 00:57:19,145
This is a different
answer question.

1018
00:57:19,145 --> 00:57:21,790
The reason is that if you
remember the implementation of

1019
00:57:21,790 --> 00:57:25,880
NOT, NOT acted as a filter.

1020
00:57:25,880 --> 00:57:29,040
NOT said I'm going to take some
possible dictionaries,

1021
00:57:29,040 --> 00:57:32,480
some possible frames, some
possible answers, and filter

1022
00:57:32,480 --> 00:57:35,070
out the ones that happened to
satisfy some condition, and

1023
00:57:35,070 --> 00:57:36,520
that's how I implement NOT.

1024
00:57:36,520 --> 00:57:40,730
If you think about what's going
on here, I'll build this

1025
00:57:40,730 --> 00:57:46,470
query box where the output of an
address piece gets fed into

1026
00:57:46,470 --> 00:57:47,720
a perfect piece.

1027
00:57:47,720 --> 00:57:50,290


1028
00:57:50,290 --> 00:57:52,880
What will happen is the address
piece will set up some

1029
00:57:52,880 --> 00:57:55,290
things of everyone whose
address I know.

1030
00:57:55,290 --> 00:57:59,880
Those will get filtered by the
NOTs inside perfect here.

1031
00:57:59,880 --> 00:58:03,230
So it will throw out the ones
which happened to be either

1032
00:58:03,230 --> 00:58:04,910
mortal or fallible.

1033
00:58:04,910 --> 00:58:07,700
In the other order what happens
is I set this up,

1034
00:58:07,700 --> 00:58:09,520
started up with an
empty frame.

1035
00:58:09,520 --> 00:58:12,000
The perfect in here doesn't find
anything for the NOTs to

1036
00:58:12,000 --> 00:58:13,920
filter, so nothing comes
out here at all.

1037
00:58:13,920 --> 00:58:18,830


1038
00:58:18,830 --> 00:58:20,940
And there's sort of nothing
there that gets fed into the

1039
00:58:20,940 --> 00:58:21,940
address thing.

1040
00:58:21,940 --> 00:58:24,260
So here, I don't
get an answer.

1041
00:58:24,260 --> 00:58:25,620
And again, the reason
for that is NOT

1042
00:58:25,620 --> 00:58:27,440
isn't generating anything.

1043
00:58:27,440 --> 00:58:28,800
NOT's only throwing
out things.

1044
00:58:28,800 --> 00:58:31,160
And if I never started up with
anything, there's nothing for

1045
00:58:31,160 --> 00:58:32,020
it to throw out.

1046
00:58:32,020 --> 00:58:33,770
So out of this thing, I
get the wrong answer.

1047
00:58:33,770 --> 00:58:37,200


1048
00:58:37,200 --> 00:58:37,970
How can you fix that?

1049
00:58:37,970 --> 00:58:39,070
Well, there are ways
to fix that.

1050
00:58:39,070 --> 00:58:41,410
So you might say, well,
that's sort of stupid.

1051
00:58:41,410 --> 00:58:43,700
Why are you just doing
all your NOT

1052
00:58:43,700 --> 00:58:44,900
stuff at the beginning?

1053
00:58:44,900 --> 00:58:48,220
The right way to implement NOT
is to realize that when you

1054
00:58:48,220 --> 00:58:51,360
have conditions like NOT, you
should generate all your

1055
00:58:51,360 --> 00:58:54,140
answers first, and then with
each of these dictionaries

1056
00:58:54,140 --> 00:58:58,560
pass along until at the very
end I'll do filtering.

1057
00:58:58,560 --> 00:59:01,560
And there are implementations
of logic languages that work

1058
00:59:01,560 --> 00:59:04,050
like that that solve this
particular problem.

1059
00:59:04,050 --> 00:59:06,660


1060
00:59:06,660 --> 00:59:10,030
However, there's a more profound
problem, which is

1061
00:59:10,030 --> 00:59:12,530
which one of these is
the right answer?

1062
00:59:12,530 --> 00:59:15,320
Is it Mount Olympus
or is it nothing?

1063
00:59:15,320 --> 00:59:19,420
So you might say it's Mount
Olympus, because after all,

1064
00:59:19,420 --> 00:59:23,220
Zeus is in that database,
and Zeus was

1065
00:59:23,220 --> 00:59:24,805
neither mortal nor fallible.

1066
00:59:24,805 --> 00:59:29,550


1067
00:59:29,550 --> 00:59:43,310
So you might say Zeus wants to
satisfy NOT mortal Zeus or NOT

1068
00:59:43,310 --> 00:59:44,120
fallible Zeus.

1069
00:59:44,120 --> 00:59:47,638
But let's actually look
at that database.

1070
00:59:47,638 --> 00:59:49,320
Let's look at it.

1071
00:59:49,320 --> 00:59:51,275
There's no way--

1072
00:59:51,275 --> 00:59:54,810
how does it know that Zeus
is not fallible?

1073
00:59:54,810 --> 00:59:57,930
There's nothing in
there about that.

1074
00:59:57,930 --> 00:59:59,410
What's in there is that
humans are fallible.

1075
00:59:59,410 --> 01:00:02,390


1076
01:00:02,390 --> 01:00:04,430
How does it know that
Zeus is not mortal?

1077
01:00:04,430 --> 01:00:07,980
There's nothing in
there about that.

1078
01:00:07,980 --> 01:00:12,000
It just said I don't have
any rule, which--

1079
01:00:12,000 --> 01:00:13,820
the only way I can deduce
something's mortal is if it's

1080
01:00:13,820 --> 01:00:16,690
human, and that's all it really
knows about mortal.

1081
01:00:16,690 --> 01:00:20,060
And in fact, if you remember
your classical mythology, you

1082
01:00:20,060 --> 01:00:25,300
know that the Greek gods were
not mortal but fallible.

1083
01:00:25,300 --> 01:00:30,850
So the answer is not
in the rules there.

1084
01:00:30,850 --> 01:00:32,100
See, why does it deduce that?

1085
01:00:32,100 --> 01:00:34,710


1086
01:00:34,710 --> 01:00:37,330
See, Socrates would certainly
not have made

1087
01:00:37,330 --> 01:00:40,080
this error of logic.

1088
01:00:40,080 --> 01:00:43,370
What NOT needs in this
language is not NOT.

1089
01:00:43,370 --> 01:00:44,930
It's not the NOT of logic.

1090
01:00:44,930 --> 01:00:48,950
What NOT needs in this language
is not deducible from

1091
01:00:48,950 --> 01:00:55,140
things in the database as
opposed to not true.

1092
01:00:55,140 --> 01:00:57,300
That's a very big difference.

1093
01:00:57,300 --> 01:00:59,250
Subtle, but big.

1094
01:00:59,250 --> 01:01:03,080
So, in fact, this is perfectly
happy to say not anything that

1095
01:01:03,080 --> 01:01:04,610
it doesn't know about.

1096
01:01:04,610 --> 01:01:06,900
So if you ask it is it not
true that Zeus likes

1097
01:01:06,900 --> 01:01:07,830
chocolate ice cream?

1098
01:01:07,830 --> 01:01:10,251
It will say sure,
it's not true.

1099
01:01:10,251 --> 01:01:12,850
Or anything else or anything
it doesn't know about.

1100
01:01:12,850 --> 01:01:18,280
NOT means not deducible from
the things you've told me.

1101
01:01:18,280 --> 01:01:22,760
In a world where you're
identifying not deducible

1102
01:01:22,760 --> 01:01:25,800
with, in fact, not true, this
is called the closed world

1103
01:01:25,800 --> 01:01:27,050
assumption.

1104
01:01:27,050 --> 01:01:36,870


1105
01:01:36,870 --> 01:01:38,320
The closed world assumption.

1106
01:01:38,320 --> 01:01:43,550
Anything that I cannot deduce
from what I know

1107
01:01:43,550 --> 01:01:46,500
is not true, right?

1108
01:01:46,500 --> 01:01:49,290
If I don't know anything about
x, the x isn't true.

1109
01:01:49,290 --> 01:01:51,420
That's very dangerous.

1110
01:01:51,420 --> 01:01:52,860
From a logical point of view,
first of all, it doesn't

1111
01:01:52,860 --> 01:01:54,480
really makes sense.

1112
01:01:54,480 --> 01:01:58,860
Because if I don't know anything
about x, I'm willing

1113
01:01:58,860 --> 01:02:00,240
to say not x.

1114
01:02:00,240 --> 01:02:03,850
But am I willing to
say not not x?

1115
01:02:03,850 --> 01:02:04,500
Well, sure, I don't
know anything

1116
01:02:04,500 --> 01:02:06,470
about that either maybe.

1117
01:02:06,470 --> 01:02:09,450
So not not x is not necessarily
the same as x and

1118
01:02:09,450 --> 01:02:13,120
so on and so on and so on, so
there's some sort of funny

1119
01:02:13,120 --> 01:02:15,970
bias in there.

1120
01:02:15,970 --> 01:02:17,290
So that's sort of funny.

1121
01:02:17,290 --> 01:02:22,840
The second thing, if you start
building up real reasoning

1122
01:02:22,840 --> 01:02:27,210
programs based on this, think
how dangerous that is.

1123
01:02:27,210 --> 01:02:33,420
You're saying I know I'm in a
position to deduce everything

1124
01:02:33,420 --> 01:02:37,780
true that's relevant
to this problem.

1125
01:02:37,780 --> 01:02:41,590
I'm reasoning, and built into my
reasoning mechanism is the

1126
01:02:41,590 --> 01:02:45,160
assumption that anything that I
don't know can't possibly be

1127
01:02:45,160 --> 01:02:48,860
relevant to this
problem, right?

1128
01:02:48,860 --> 01:02:52,350
There are a lot of big
organizations that work like

1129
01:02:52,350 --> 01:02:54,720
that, right?

1130
01:02:54,720 --> 01:02:56,830
Most corporate marketing
divisions work like that.

1131
01:02:56,830 --> 01:03:00,560
You know the consequences
to that.

1132
01:03:00,560 --> 01:03:04,490
So it's very dangerous to start
really typing in these

1133
01:03:04,490 --> 01:03:08,750
big logical implication systems
and going on what they

1134
01:03:08,750 --> 01:03:10,500
say, because they have
this really limiting

1135
01:03:10,500 --> 01:03:12,600
assumption built in.

1136
01:03:12,600 --> 01:03:14,905
So you have to be very, very
careful about that.

1137
01:03:14,905 --> 01:03:16,560
And that's a deep problem.

1138
01:03:16,560 --> 01:03:19,570
That's not a problem about we
can make a little bit cleverer

1139
01:03:19,570 --> 01:03:22,360
implementation and do the
filters and organize the

1140
01:03:22,360 --> 01:03:23,840
infinite loops to make
them go away.

1141
01:03:23,840 --> 01:03:25,920
It's a different kind
of problem.

1142
01:03:25,920 --> 01:03:27,060
It's a different semantics.

1143
01:03:27,060 --> 01:03:31,910
So I think to wrap this up, it's
fair to say that logic

1144
01:03:31,910 --> 01:03:34,650
programming I think is a
terrifically exciting idea,

1145
01:03:34,650 --> 01:03:38,010
the idea that you can bridge
this gap from the imperative

1146
01:03:38,010 --> 01:03:42,300
to the declarative, that you
can start talking about

1147
01:03:42,300 --> 01:03:46,900
relations and really get
tremendous power by going

1148
01:03:46,900 --> 01:03:48,570
above the abstraction
of what's my input

1149
01:03:48,570 --> 01:03:50,560
and what's my output.

1150
01:03:50,560 --> 01:03:55,160
And linked to logic, the problem
is it's a goal that I

1151
01:03:55,160 --> 01:03:58,080
think has yet to be realized.

1152
01:03:58,080 --> 01:04:02,740
And probably one of the very
most interesting research

1153
01:04:02,740 --> 01:04:06,530
questions going on now in
languages is how do you

1154
01:04:06,530 --> 01:04:09,460
somehow make a real
logic language?

1155
01:04:09,460 --> 01:04:11,940
And secondly, how do you bridge
the gap from this world

1156
01:04:11,940 --> 01:04:16,020
of logic and relations to the
worlds of more traditional

1157
01:04:16,020 --> 01:04:18,680
languages and somehow combine
the power of both.

1158
01:04:18,680 --> 01:04:19,930
OK, let's break.

1159
01:04:19,930 --> 01:04:23,750


1160
01:04:23,750 --> 01:04:25,675
AUDIENCE: Couldn't you solve
that last problem by having

1161
01:04:25,675 --> 01:04:27,430
the extra rules that imply it?

1162
01:04:27,430 --> 01:04:30,060
The problem here is you have the
definition of something,

1163
01:04:30,060 --> 01:04:32,210
but you don't have the
definition of its opposite.

1164
01:04:32,210 --> 01:04:35,890
If you include in the database
something that says something

1165
01:04:35,890 --> 01:04:38,780
implies mortal x, something
else implies not mortal x,

1166
01:04:38,780 --> 01:04:40,370
haven't you basically
solved the problem?

1167
01:04:40,370 --> 01:04:43,370


1168
01:04:43,370 --> 01:04:45,660
PROFESSOR: But the issue
is do you put a finite

1169
01:04:45,660 --> 01:04:46,910
number of those in?

1170
01:04:46,910 --> 01:04:50,740


1171
01:04:50,740 --> 01:04:54,980
AUDIENCE: If things are
specified always in pairs--

1172
01:04:54,980 --> 01:04:55,970
PROFESSOR: But the impression
is then what do

1173
01:04:55,970 --> 01:04:57,220
you do about deduction?

1174
01:04:57,220 --> 01:05:00,200


1175
01:05:00,200 --> 01:05:03,400
You can't specify NOTs.

1176
01:05:03,400 --> 01:05:05,930
But the problem is, in a big
system, it turns out that

1177
01:05:05,930 --> 01:05:07,960
might not be a finite
number of things.

1178
01:05:07,960 --> 01:05:12,820


1179
01:05:12,820 --> 01:05:15,290
There are also sort
of two issues.

1180
01:05:15,290 --> 01:05:16,690
Partly it might not be finite.

1181
01:05:16,690 --> 01:05:21,510
Partly it might be that's
not what you want.

1182
01:05:21,510 --> 01:05:23,790
So a good example would be
suppose I want to do

1183
01:05:23,790 --> 01:05:25,120
connectivity.

1184
01:05:25,120 --> 01:05:28,050
I want a reason about
connectivity.

1185
01:05:28,050 --> 01:05:32,100
And I'm going to tell you
there's four things: a and b

1186
01:05:32,100 --> 01:05:35,480
and c and d.

1187
01:05:35,480 --> 01:05:39,740
And I'll tell you a is connected
to b and c's

1188
01:05:39,740 --> 01:05:43,200
connected to d.

1189
01:05:43,200 --> 01:05:45,260
And now I'll tell you
is a connected to d?

1190
01:05:45,260 --> 01:05:46,780
That's the question.

1191
01:05:46,780 --> 01:05:49,360
There's an example where I would
like something like the

1192
01:05:49,360 --> 01:05:50,610
closed world assumption.

1193
01:05:50,610 --> 01:05:54,200


1194
01:05:54,200 --> 01:05:57,630
That's a tiny toy, but a lot of
times, I want to be able to

1195
01:05:57,630 --> 01:05:59,800
say something like anything
that I haven't told you,

1196
01:05:59,800 --> 01:06:01,340
assume is not true.

1197
01:06:01,340 --> 01:06:04,260


1198
01:06:04,260 --> 01:06:06,990
So it's not as simple as you
only want to put in explicit

1199
01:06:06,990 --> 01:06:09,470
NOTs all over the place.

1200
01:06:09,470 --> 01:06:11,200
It's that sometimes it
really isn't clear

1201
01:06:11,200 --> 01:06:14,150
what you even want.

1202
01:06:14,150 --> 01:06:17,160
That having to specify both
everything and not everything

1203
01:06:17,160 --> 01:06:20,960
is too precise, and then you get
down into problems there.

1204
01:06:20,960 --> 01:06:24,420
But there are a lot of
approaches that explicitly put

1205
01:06:24,420 --> 01:06:26,510
in NOTs and reason
based on that.

1206
01:06:26,510 --> 01:06:28,070
So it's a very good idea.

1207
01:06:28,070 --> 01:06:31,620
It's just that then it starts
becoming a little cumbersome

1208
01:06:31,620 --> 01:06:33,490
in the very large problems
you'd like to use.

1209
01:06:33,490 --> 01:06:43,460


1210
01:06:43,460 --> 01:06:45,410
AUDIENCE: I'm not sure how
directly related to the

1211
01:06:45,410 --> 01:06:48,840
argument this is, but one of
your points was that one of

1212
01:06:48,840 --> 01:06:51,100
the dangers of the closed rule
is you never really know all

1213
01:06:51,100 --> 01:06:53,840
the things that are there.

1214
01:06:53,840 --> 01:06:55,930
You never really know
all the parts to it.

1215
01:06:55,930 --> 01:06:58,160
Isn't that a major problem
with any programming?

1216
01:06:58,160 --> 01:07:01,110
I always write programs where I
assume that I've got all the

1217
01:07:01,110 --> 01:07:04,430
cases, and so I check for them
all or whatever, and somewhere

1218
01:07:04,430 --> 01:07:05,750
down the road, I find
out that I didn't

1219
01:07:05,750 --> 01:07:07,390
check for one of them.

1220
01:07:07,390 --> 01:07:08,540
PROFESSOR: Well, sure,
it's true.

1221
01:07:08,540 --> 01:07:14,630
But the problem here is it's
that assumption which is the

1222
01:07:14,630 --> 01:07:16,610
thing that you're making if you
believe you're identifying

1223
01:07:16,610 --> 01:07:19,600
this with logic.

1224
01:07:19,600 --> 01:07:20,510
So you're quite right.

1225
01:07:20,510 --> 01:07:22,220
It's a situation you're
never in.

1226
01:07:22,220 --> 01:07:24,420
The problem is if you're
starting to believe that what

1227
01:07:24,420 --> 01:07:27,305
this is doing is logic and you
look at the rules you write

1228
01:07:27,305 --> 01:07:30,200
down and say what can I deduce
from them, you have to be very

1229
01:07:30,200 --> 01:07:33,470
careful to remember that NOT
means something else.

1230
01:07:33,470 --> 01:07:35,510
And it means something else
based on an assumption which

1231
01:07:35,510 --> 01:07:39,030
is probably not true.

1232
01:07:39,030 --> 01:07:41,170
AUDIENCE: Do I understand you
correctly that you cannot fix

1233
01:07:41,170 --> 01:07:44,510
this problem without killing
off all possibilities of

1234
01:07:44,510 --> 01:07:47,990
inference through
altering NOT?

1235
01:07:47,990 --> 01:07:49,370
PROFESSOR: No, that's
not quite right.

1236
01:07:49,370 --> 01:07:50,620
There are other--

1237
01:07:50,620 --> 01:07:52,710


1238
01:07:52,710 --> 01:07:56,340
there are ways to do logic
with real NOTs.

1239
01:07:56,340 --> 01:07:58,540
There are actually
ways to do that.

1240
01:07:58,540 --> 01:08:01,610
But they're very inefficient
as far as anybody knows.

1241
01:08:01,610 --> 01:08:02,860
And they're much more--

1242
01:08:02,860 --> 01:08:05,390


1243
01:08:05,390 --> 01:08:09,240
the, quote, inference in here is
built into this unifier and

1244
01:08:09,240 --> 01:08:11,980
this pattern matching
unification algorithm.

1245
01:08:11,980 --> 01:08:16,590
There are ways to automate
real logical reasoning.

1246
01:08:16,590 --> 01:08:19,460
But it's not based on that,
and logic programming

1247
01:08:19,460 --> 01:08:21,420
languages don't tend to do
that because it's very

1248
01:08:21,420 --> 01:08:23,850
inefficient as far
as anybody knows.

1249
01:08:23,850 --> 01:08:29,390


1250
01:08:29,390 --> 01:08:30,640
All right, thank you.

1251
01:08:30,640 --> 01:08:43,903