WEBVTT 00:00:21.170 --> 00:00:24.550 PROFESSOR: Well, now that we've given you some power to 00:00:24.550 --> 00:00:28.340 make independent local state and to model objects, I 00:00:28.340 --> 00:00:31.610 thought we'd do a bit of programming of a very 00:00:31.610 --> 00:00:35.380 complicated kind, just to illustrate what you can do 00:00:35.380 --> 00:00:36.630 with this sort of thing. 00:00:40.430 --> 00:00:44.080 I suppose, as I said, we were motivated by physical systems 00:00:44.080 --> 00:00:47.200 and the ways we like to think about physical systems, which 00:00:47.200 --> 00:00:52.060 is that there are these things that the world is made out of. 00:00:52.060 --> 00:00:55.570 And each of these things has particular independent local 00:00:55.570 --> 00:00:58.830 state, and therefore it is a thing. 00:00:58.830 --> 00:01:01.280 That's what makes it a thing. 00:01:01.280 --> 00:01:04.410 And then we're going to say that in the model in the 00:01:04.410 --> 00:01:07.900 world--we have a world and a model in our minds and in the 00:01:07.900 --> 00:01:10.940 computer of that world. 00:01:10.940 --> 00:01:13.230 And what I want to make is a correspondence between the 00:01:13.230 --> 00:01:15.980 objects in the world and the objects in the computer, the 00:01:15.980 --> 00:01:18.140 relationships between the objects in the world and the 00:01:18.140 --> 00:01:21.200 relationships between those same obj...--the model objects 00:01:21.200 --> 00:01:24.890 in the computer, and the functions that relate things 00:01:24.890 --> 00:01:27.320 in the world to the functions that relate 00:01:27.320 --> 00:01:28.570 things in the computer. 00:01:30.840 --> 00:01:34.740 This buys us modularity. 00:01:34.740 --> 00:01:37.786 If we really believe the world is like that, that it's made 00:01:37.786 --> 00:01:40.120 out of these little pieces, and of course we could arrange 00:01:40.120 --> 00:01:43.085 our world to be like that, we could only model those things 00:01:43.085 --> 00:01:47.030 that are like that, then we can inherit the modularity in 00:01:47.030 --> 00:01:50.450 the world into our programming. 00:01:50.450 --> 00:01:53.150 That's why we would invent some of this object-oriented 00:01:53.150 --> 00:01:55.420 programming. 00:01:55.420 --> 00:01:58.890 Well, let's take the best kind of objects I know. 00:01:58.890 --> 00:02:03.160 They're completely--they're completely wonderful: 00:02:03.160 --> 00:02:10.270 electrical systems. Electrical systems really are the 00:02:10.270 --> 00:02:14.220 physicist's best, best objects. 00:02:14.220 --> 00:02:16.760 You see over here I have some piece of machinery. 00:02:16.760 --> 00:02:20.040 Right here's a piece of machinery. 00:02:20.040 --> 00:02:24.270 And it's got an electrical wire connecting one part of 00:02:24.270 --> 00:02:27.190 the machinery with another part of the machinery. 00:02:27.190 --> 00:02:30.450 And one of the wonderful properties of the electrical 00:02:30.450 --> 00:02:34.610 world is that I can say this is an object, and this is an 00:02:34.610 --> 00:02:36.040 object, and they're-- 00:02:36.040 --> 00:02:38.310 the connection between them is clear. 00:02:38.310 --> 00:02:41.190 In principle, there is no connection that I didn't 00:02:41.190 --> 00:02:44.740 describe with these wires. 00:02:44.740 --> 00:02:48.000 Let's say if I have light bulbs, a light bulb and a 00:02:48.000 --> 00:02:51.370 power supply that's plugged into the outlet. 00:02:51.370 --> 00:02:53.620 Then the connection is perfectly clear. 00:02:53.620 --> 00:02:56.220 There's no other connections that we know of. 00:02:56.220 --> 00:02:59.250 If I were to tie a knot in the wire that connects the light 00:02:59.250 --> 00:03:04.040 bulb to the power supply, the light remains lit up. 00:03:04.040 --> 00:03:05.290 It doesn't care. 00:03:08.300 --> 00:03:11.120 That the way the physics is arranged is such that the 00:03:11.120 --> 00:03:13.790 connection can be made abstract, at least for low 00:03:13.790 --> 00:03:15.270 frequencies and things like that. 00:03:17.840 --> 00:03:20.360 So in fact, we have captured all of the connections there 00:03:20.360 --> 00:03:22.350 really are. 00:03:22.350 --> 00:03:24.310 Well, as you can go one step further and talk about the 00:03:24.310 --> 00:03:27.830 most abstract types of electrical systems we have, 00:03:27.830 --> 00:03:30.951 digital to dual circuits. 00:03:30.951 --> 00:03:34.610 And here there are certain kinds of objects. 00:03:34.610 --> 00:03:38.240 For example, in digital circuits we 00:03:38.240 --> 00:03:41.092 have things like inverters. 00:03:41.092 --> 00:03:43.990 We have things like and-gates. 00:03:43.990 --> 00:03:47.210 We have things like or-gates. 00:03:47.210 --> 00:03:53.980 We connect them together by sort-of wires which represent 00:03:53.980 --> 00:03:55.610 abstract signals. 00:03:55.610 --> 00:03:57.390 We don't really care as physical variables whether 00:03:57.390 --> 00:04:00.190 these are voltages or currents or some combination or 00:04:00.190 --> 00:04:05.160 anything like that, or water, water pressure. 00:04:05.160 --> 00:04:09.420 These abstract variables represent certain signals. 00:04:09.420 --> 00:04:11.950 And we build systems by wiring these things 00:04:11.950 --> 00:04:14.070 together with wires. 00:04:14.070 --> 00:04:17.730 So today what I'm going to show you, right now, we're 00:04:17.730 --> 00:04:22.650 going to build up an invented language in Lisp, embedded in 00:04:22.650 --> 00:04:24.590 the same sense that Henderson's picture language 00:04:24.590 --> 00:04:29.780 was embedded, which is not the same sense as the language of 00:04:29.780 --> 00:04:32.700 pattern match and substitution was done yesterday. 00:04:32.700 --> 00:04:35.725 The pattern match/substitution language was interpreted by a 00:04:35.725 --> 00:04:38.160 Lisp program. 00:04:38.160 --> 00:04:40.920 But the embedding of Henderson's program is that we 00:04:40.920 --> 00:04:43.370 just build up more and more procedures that encapsulate 00:04:43.370 --> 00:04:45.480 the structure we want. 00:04:45.480 --> 00:04:49.280 So for example here, I'm going to have some various primitive 00:04:49.280 --> 00:04:53.026 kinds of objects, as you see, that one and that one. 00:04:53.026 --> 00:04:55.810 I'm going to use wires to combine them. 00:04:55.810 --> 00:04:58.420 The way I represent attaching-- 00:04:58.420 --> 00:04:59.870 I can make wires. 00:04:59.870 --> 00:05:01.740 So let's say A is a wire. 00:05:01.740 --> 00:05:02.690 And B is a wire. 00:05:02.690 --> 00:05:03.460 And C is a wire. 00:05:03.460 --> 00:05:04.230 And D is a wire. 00:05:04.230 --> 00:05:04.830 And E is wire. 00:05:04.830 --> 00:05:06.880 And S is a wire. 00:05:06.880 --> 00:05:12.380 Well, an or-gate that has both inputs, the inputs being A and 00:05:12.380 --> 00:05:17.940 B, and the output being Y or D, you notate like this. 00:05:17.940 --> 00:05:22.390 An and-gate, which has inputs A and B and output C, we 00:05:22.390 --> 00:05:24.820 notate like that. 00:05:24.820 --> 00:05:29.690 By making such a sequence of declarations, like this, I can 00:05:29.690 --> 00:05:32.750 wire together an arbitrary circuit. 00:05:32.750 --> 00:05:35.940 So I've just told you a set of primitives and means of 00:05:35.940 --> 00:05:40.930 combination for building digital circuits, when I need 00:05:40.930 --> 00:05:43.690 more in a real language than abstraction. 00:05:43.690 --> 00:05:46.766 And so for example, here I have--here 00:05:46.766 --> 00:05:52.240 I have a half adder. 00:05:52.240 --> 00:05:54.270 It's something you all know if you've 00:05:54.270 --> 00:05:56.930 done any digital design. 00:05:56.930 --> 00:06:00.830 It's used for adding numbers together on A and B and 00:06:00.830 --> 00:06:03.956 putting out a sum and a carry. 00:06:03.956 --> 00:06:05.710 And in fact, the wiring diagram is 00:06:05.710 --> 00:06:07.450 exactly what I told you. 00:06:07.450 --> 00:06:11.410 A half adder with things that come out of the box-- you see 00:06:11.410 --> 00:06:14.790 the box, the boundary, the abstraction is always a box. 00:06:14.790 --> 00:06:19.700 And there are things that come out of it, A, B, S, and C. 00:06:19.700 --> 00:06:24.950 Those are the declared variables--declared variables 00:06:24.950 --> 00:06:27.020 of a lambda expression, which is the one that 00:06:27.020 --> 00:06:28.270 defines half adder. 00:06:31.400 --> 00:06:36.080 And internal to that, I make up some more wires, D and E, 00:06:36.080 --> 00:06:37.760 which I'm going to use for the interconnect-- 00:06:37.760 --> 00:06:41.860 here E is this one and D is this wire, the interconnect 00:06:41.860 --> 00:06:45.100 that doesn't come through the walls of the box-- 00:06:45.100 --> 00:06:48.790 and wire things together as you just saw. 00:06:48.790 --> 00:06:51.180 And the nice thing about this that I've just shown you is 00:06:51.180 --> 00:06:53.890 this language is hierarchical in the right way. 00:06:53.890 --> 00:06:55.950 If a language isn't hierarchical in the right way, 00:06:55.950 --> 00:06:58.850 if it turns out that a compound object doesn't look 00:06:58.850 --> 00:07:00.820 like a primitive, there's something 00:07:00.820 --> 00:07:02.180 wrong with the language-- 00:07:02.180 --> 00:07:06.300 at least the way I feel about that. 00:07:06.300 --> 00:07:09.220 So here we have--here, instead of starting with mathematical 00:07:09.220 --> 00:07:10.900 functions, or things that compute mathematical 00:07:10.900 --> 00:07:13.870 functions, which is what we've been doing up until now, 00:07:13.870 --> 00:07:15.770 instead of starting with things that look like 00:07:15.770 --> 00:07:18.080 mathematical functions, or compute such things, we are 00:07:18.080 --> 00:07:21.330 starting with things that are electrical objects and we 00:07:21.330 --> 00:07:23.350 build up more electrical objects. 00:07:23.350 --> 00:07:26.590 And the glue we're using is basically the 00:07:26.590 --> 00:07:30.500 Lisp structure: lambdas. 00:07:30.500 --> 00:07:32.930 Lambda is the ultimate glue, if you will. 00:07:32.930 --> 00:07:39.000 And of course, half adder itself can be used in a more 00:07:39.000 --> 00:07:42.250 complicated abstraction called a full adder, which in fact 00:07:42.250 --> 00:07:46.670 involves two half adders, as you see here, hooked together 00:07:46.670 --> 00:07:50.600 with some extra wires, that you see here, S, C1, and C2, 00:07:50.600 --> 00:07:57.340 and an or-gate, to manufacture a full adder, which takes a 00:07:57.340 --> 00:08:01.570 input number, another input number, a carry in, and 00:08:01.570 --> 00:08:05.900 produces output, a sum and a carry out. 00:08:05.900 --> 00:08:09.820 And out of full adders, you can make real adder chains and 00:08:09.820 --> 00:08:12.990 big adders. 00:08:12.990 --> 00:08:18.870 So we have here a language so far that has primitives, means 00:08:18.870 --> 00:08:22.270 of combination, and means of abstraction to real language. 00:08:22.270 --> 00:08:25.000 Now, how are we going to implement this? 00:08:25.000 --> 00:08:27.070 Well, let's do it easily. 00:08:27.070 --> 00:08:28.610 Let's look at the primitives. 00:08:28.610 --> 00:08:31.160 The only problem is we have to implement the primitives. 00:08:31.160 --> 00:08:34.270 Nothing else has to be implemented, because we're 00:08:34.270 --> 00:08:37.640 picking up the means of combination and abstraction 00:08:37.640 --> 00:08:43.417 from Lisp, inheriting them in the embedding. 00:08:43.417 --> 00:08:45.860 OK, so let's look at a particular primitive. 00:08:45.860 --> 00:08:47.400 An inverter is a nice one. 00:08:51.540 --> 00:08:54.900 Now, inverter has two wires coming in, an in and an out. 00:08:57.440 --> 00:09:01.570 And somehow, it's going to have to know what to do when a 00:09:01.570 --> 00:09:04.300 signal comes in. 00:09:04.300 --> 00:09:07.710 So somehow it's going to have to tell its input wire-- 00:09:07.710 --> 00:09:10.756 and now we're going to talk about objects and we're going 00:09:10.756 --> 00:09:13.260 to see this in a little more detail soon-- 00:09:13.260 --> 00:09:16.660 but it's going to have to tell its input wire that when you 00:09:16.660 --> 00:09:20.120 change, tell me. 00:09:20.120 --> 00:09:22.720 So this object, the object which is the inverter has to 00:09:22.720 --> 00:09:25.070 tell the object which is the input wire, 00:09:25.070 --> 00:09:26.870 hi, my name is George. 00:09:26.870 --> 00:09:30.480 And my, my job is to do something with results when 00:09:30.480 --> 00:09:31.720 you change. 00:09:31.720 --> 00:09:34.730 So when you change, you get a change, tell me about it. 00:09:34.730 --> 00:09:37.010 Because I've got to do something with that. 00:09:37.010 --> 00:09:42.200 Well, that's done down here by adding an action on the input 00:09:42.200 --> 00:09:47.020 wire called invert-in, where invert-in is defined over here 00:09:47.020 --> 00:09:51.660 to be a procedure of no arguments, which gets the 00:09:51.660 --> 00:09:56.130 logical not of the signal on the input wire. 00:09:56.130 --> 00:09:59.720 And after some delay, which is the inverter delay, all these 00:09:59.720 --> 00:10:04.110 electrical objects have delays, we'll do the following 00:10:04.110 --> 00:10:07.140 thing-- set the signal on the output wire to the new value. 00:10:10.160 --> 00:10:12.400 A very simple program. 00:10:12.400 --> 00:10:14.820 Now, you have to imagine that the output wire has to be 00:10:14.820 --> 00:10:19.650 sensitive and know that when its signal changes, it may 00:10:19.650 --> 00:10:23.840 have to tell other guys, hey, wake up. 00:10:23.840 --> 00:10:26.050 My value has changed. 00:10:26.050 --> 00:10:29.350 So when you hook together inverter with an and-gate or 00:10:29.350 --> 00:10:31.680 something like that, there has to be a lot of communication 00:10:31.680 --> 00:10:34.040 going on in order to make sure that the 00:10:34.040 --> 00:10:36.810 signal propagates right. 00:10:36.810 --> 00:10:38.620 And down here is nothing very exciting. 00:10:38.620 --> 00:10:41.100 This is just the definition of logical not for some 00:10:41.100 --> 00:10:44.170 particular representations of the logical values-- 00:10:44.170 --> 00:10:46.240 1, 0 in this case. 00:10:46.240 --> 00:10:49.780 And we can look at things more complicated like and-gates. 00:10:49.780 --> 00:10:55.000 And-gates take two inputs, A1 and A2, we'll call them, and 00:10:55.000 --> 00:10:56.950 produce an output. 00:10:56.950 --> 00:10:59.840 But the structure of the and-gate is identical to the 00:10:59.840 --> 00:11:00.860 one we just saw. 00:11:00.860 --> 00:11:03.000 There's one called an and-action procedure that's 00:11:03.000 --> 00:11:08.570 defined, which is the thing that gets called when an input 00:11:08.570 --> 00:11:10.910 is changed. 00:11:10.910 --> 00:11:13.230 And what it does, of course, is nothing more than compute 00:11:13.230 --> 00:11:15.900 the logical and of the signals on the inputs. 00:11:15.900 --> 00:11:20.890 And after some delay, called the and-gate delay, calls this 00:11:20.890 --> 00:11:25.470 procedure, which sets a signal on the output to a new value. 00:11:25.470 --> 00:11:27.320 Now, how I implement these things 00:11:27.320 --> 00:11:28.350 is all wishful thinking. 00:11:28.350 --> 00:11:32.020 As you see here, I have an assignment operation. 00:11:32.020 --> 00:11:34.570 It's not set. 00:11:34.570 --> 00:11:36.820 It's a derived assignment operation in the same way we 00:11:36.820 --> 00:11:41.140 had functions that were derived from CAR and CDR. So 00:11:41.140 --> 00:11:46.340 I, by convention, label that with an exclamation point. 00:11:46.340 --> 00:11:50.730 And over here, you see there's an action, which is to inform 00:11:50.730 --> 00:11:57.190 the wire, called A1 locally in this and-gate, to call the 00:11:57.190 --> 00:12:00.960 and-action procedure when it gets changed, and the wire A2 00:12:00.960 --> 00:12:02.100 to call the and-action procedure 00:12:02.100 --> 00:12:03.350 when it gets changed. 00:12:06.310 --> 00:12:09.510 All very simple. 00:12:09.510 --> 00:12:12.870 Well, let's talk a little bit about this communication that 00:12:12.870 --> 00:12:18.310 must occur between these various parts. 00:12:18.310 --> 00:12:24.560 Suppose, for example, I have a very simple circuit which 00:12:24.560 --> 00:12:34.230 contains an and with wires A and B. And that connects 00:12:34.230 --> 00:12:40.580 through a wire called C to an inverter which has a wire 00:12:40.580 --> 00:12:46.310 output called D. What are the comput...--here's 00:12:46.310 --> 00:12:47.360 the physical world. 00:12:47.360 --> 00:12:49.860 It's an abstraction of the physical world. 00:12:49.860 --> 00:12:52.010 Now I can buy these out of little pieces that you get at 00:12:52.010 --> 00:12:54.880 Radio Shack for a few cents. 00:12:54.880 --> 00:12:57.680 And there are boxes that act like this, which have little 00:12:57.680 --> 00:13:01.530 numbers on them like LS04 or something. 00:13:01.530 --> 00:13:06.980 Now supposing I were to try to say what's the 00:13:06.980 --> 00:13:09.010 computational model. 00:13:09.010 --> 00:13:11.610 What is the thing that corresponds to that, that part 00:13:11.610 --> 00:13:15.850 of reality in the mind of us and in the computer? 00:13:15.850 --> 00:13:18.200 Well, I have to assign for every object in the world an 00:13:18.200 --> 00:13:22.160 object in the computer, and for every relationship in the 00:13:22.160 --> 00:13:25.750 world between them a relationship in the computer. 00:13:25.750 --> 00:13:28.560 That's my goal. 00:13:28.560 --> 00:13:30.900 So let's do that. 00:13:30.900 --> 00:13:35.401 Well, I have some sort of thing called the signal, A. 00:13:35.401 --> 00:13:37.940 This is A. It's a signal. 00:13:37.940 --> 00:13:39.900 It's a cloudy thing like that. 00:13:39.900 --> 00:13:42.390 And I have another one down here which I'm going to call 00:13:42.390 --> 00:13:49.140 B. It's another signal. 00:13:49.140 --> 00:13:52.070 Now this signal--these two signals are somehow going to 00:13:52.070 --> 00:13:56.180 have to hook together into a box, let's call it this, which 00:13:56.180 --> 00:14:00.320 is the and-gate, action procedure. 00:14:00.320 --> 00:14:02.040 That's the and-gate's action procedure. 00:14:07.660 --> 00:14:09.750 And it's going to produce--well, it's going to 00:14:09.750 --> 00:14:18.360 interact with a signal object, which we call C--a wire 00:14:18.360 --> 00:14:21.330 object, excuse me, we call C. And then the-- 00:14:21.330 --> 00:14:25.630 this is going to put out again, or connect to, another 00:14:25.630 --> 00:14:28.240 action procedure which is one associated with the inverter 00:14:28.240 --> 00:14:30.195 in the world, not. 00:14:32.860 --> 00:14:39.980 And I'm going to have another--another wire, which 00:14:39.980 --> 00:14:42.970 we'll call D. 00:14:42.970 --> 00:14:45.770 So here's my layout of stuff. 00:14:45.770 --> 00:14:47.650 Now we have to say what's inside them and what they have 00:14:47.650 --> 00:14:51.500 to know to compute. 00:14:51.500 --> 00:14:53.900 Well, every--every one of these wires has to know what 00:14:53.900 --> 00:14:57.340 the value of the signal that's on that wire is. 00:14:57.340 --> 00:14:59.430 So there's going to be some variable inside here, we'll 00:14:59.430 --> 00:15:00.680 call it signal. 00:15:02.670 --> 00:15:05.840 And he owns a value. 00:15:05.840 --> 00:15:06.870 So there must be some environment 00:15:06.870 --> 00:15:08.656 associated with this. 00:15:08.656 --> 00:15:10.550 And for each one of these, there must be an environment 00:15:10.550 --> 00:15:11.800 that binds signal. 00:15:15.400 --> 00:15:16.880 And there must be a signal here, therefore. 00:15:19.400 --> 00:15:22.920 And presumably, signal's a value that's either 1 or 0, 00:15:22.920 --> 00:15:24.170 and signal. 00:15:28.000 --> 00:15:33.140 Now, we also have to have some list of people to inform if 00:15:33.140 --> 00:15:34.390 the signal here changes. 00:15:36.660 --> 00:15:39.300 We're going to have to inform this. 00:15:39.300 --> 00:15:41.470 So I've got that list. We'll call it the 00:15:41.470 --> 00:15:44.500 Action Procedures, AP. 00:15:44.500 --> 00:15:47.590 And it's presumably a list. But the first thing on the 00:15:47.590 --> 00:15:50.500 list, in this case, is this guy. 00:15:50.500 --> 00:15:53.730 And the action procedures of this one happens to have some 00:15:53.730 --> 00:15:54.810 list of stuff. 00:15:54.810 --> 00:15:57.510 There might be other people who are sharing A, who are 00:15:57.510 --> 00:15:59.020 looking at it. 00:15:59.020 --> 00:16:02.060 So there might be other guys on this list, like somebody 00:16:02.060 --> 00:16:03.630 over there that we don't know about. 00:16:03.630 --> 00:16:07.200 It's the other guy attached to A. 00:16:07.200 --> 00:16:11.230 And the action procedure here also has to point to that, the 00:16:11.230 --> 00:16:13.070 list of action procedures. 00:16:13.070 --> 00:16:17.060 And of course, that means this one, its action procedures has 00:16:17.060 --> 00:16:18.530 to point up to here. 00:16:18.530 --> 00:16:18.770 This is the things-- 00:16:18.770 --> 00:16:21.770 the people it has to inform. 00:16:21.770 --> 00:16:24.280 And this guy has some too. 00:16:24.280 --> 00:16:25.660 But I don't know what they are because I didn't 00:16:25.660 --> 00:16:27.190 draw it in my diagram. 00:16:27.190 --> 00:16:30.320 It's the things connected to D. 00:16:30.320 --> 00:16:36.240 Now, it's also the case that when the and-action procedure 00:16:36.240 --> 00:16:41.951 is awakened, saying one of the people who know that you've 00:16:41.951 --> 00:16:44.010 told--one of the people you've told to wake you up if their 00:16:44.010 --> 00:16:48.430 signal changes, you have to go look and ask them what's their 00:16:48.430 --> 00:16:51.540 signal so you can do the and, and produce a 00:16:51.540 --> 00:16:52.790 signal for this one. 00:16:57.090 --> 00:16:59.760 So there has to be, for example, information here 00:16:59.760 --> 00:17:06.400 saying A1, my A1 is this guy, and my A2 is this guy. 00:17:08.930 --> 00:17:14.170 And not only that, when I do my and, I'm going to have to 00:17:14.170 --> 00:17:16.170 tell this guy something. 00:17:16.170 --> 00:17:17.420 So I need an output-- 00:17:19.904 --> 00:17:21.160 being this guy. 00:17:25.800 --> 00:17:29.550 And similarly, this guy's going to have a thing called 00:17:29.550 --> 00:17:37.540 the input that he interrogates to find out what the value of 00:17:37.540 --> 00:17:39.430 the signal on the input is, when the signal wakes up and 00:17:39.430 --> 00:17:42.980 says, I've changed, and sends a message this way saying, 00:17:42.980 --> 00:17:43.520 I've changed. 00:17:43.520 --> 00:17:46.900 This guy says, OK, what's your value now? 00:17:46.900 --> 00:17:50.840 When he gets that value, then he's going to have to say, OK, 00:17:50.840 --> 00:17:55.860 output changes this guy, changes this guy. 00:18:00.600 --> 00:18:02.481 And so on. 00:18:02.481 --> 00:18:06.240 And so I have to have at least that much connected-ness. 00:18:06.240 --> 00:18:10.260 Now, let's go back and look, for example, at the and-gate. 00:18:10.260 --> 00:18:13.670 Here we are back on this slide. 00:18:13.670 --> 00:18:16.040 And we can see some of these parts. 00:18:16.040 --> 00:18:18.470 For any particular and-gate, there is an A1, there is an 00:18:18.470 --> 00:18:21.030 A2, and the output. 00:18:21.030 --> 00:18:21.483 And those are, those are an environment that was created 00:18:21.483 --> 00:18:30.720 at the--those produce a frame at the time and-gate was 00:18:30.720 --> 00:18:37.200 called, a frame where A1, A2, and output are--have as their 00:18:37.200 --> 00:18:41.940 values, they're bound to the wires which, they are--which 00:18:41.940 --> 00:18:46.240 were passed in. 00:18:46.240 --> 00:18:50.890 In that environment, I constructed a procedure-- 00:18:50.890 --> 00:18:54.590 this one right there. 00:18:54.590 --> 00:18:56.810 And-action procedure was constructed in that 00:18:56.810 --> 00:18:57.780 environment. 00:18:57.780 --> 00:19:00.190 That was the result of evaluating a lambda 00:19:00.190 --> 00:19:01.620 expression. 00:19:01.620 --> 00:19:07.620 So it hangs onto the frame where these were defined. 00:19:07.620 --> 00:19:11.700 Local--part of its local state is that. 00:19:11.700 --> 00:19:15.000 The and-action procedure, therefore, has access to A1, 00:19:15.000 --> 00:19:17.310 A2, and output as we see here. 00:19:17.310 --> 00:19:19.645 A1, A2, and output. 00:19:22.360 --> 00:19:26.030 Now, we haven't looked inside of a wire yet. 00:19:26.030 --> 00:19:29.030 That's all that remains. 00:19:29.030 --> 00:19:30.280 Let's look at a wire. 00:19:33.520 --> 00:19:36.160 Like the overhead, very good. 00:19:39.500 --> 00:19:40.940 Well, the wire, again, is a, is a 00:19:40.940 --> 00:19:43.090 somewhat complicated mess. 00:19:43.090 --> 00:19:46.840 Ooh, wrong one. 00:19:46.840 --> 00:19:49.780 It's a big complicated mess, like that. 00:19:49.780 --> 00:19:54.720 But let's look at it in detail and see what's going on. 00:19:54.720 --> 00:19:57.760 Well, the wire is one of these. 00:19:57.760 --> 00:20:02.320 And it has to have two things that are part of 00:20:02.320 --> 00:20:05.010 it, that it's state. 00:20:05.010 --> 00:20:07.390 One of them is the signal we see here. 00:20:07.390 --> 00:20:10.670 In other words, when we call make-wire to make a wire, then 00:20:10.670 --> 00:20:15.300 the first thing we do is we create some variables which 00:20:15.300 --> 00:20:19.270 are the signal and the action procedures for this wire. 00:20:22.042 --> 00:20:26.540 And in that context, we define various functions--or 00:20:26.540 --> 00:20:27.840 procedures, excuse me, procedures. 00:20:27.840 --> 00:20:32.850 One of them is called set-my-signal to a new value. 00:20:32.850 --> 00:20:37.930 And what that does is takes a new value in. 00:20:37.930 --> 00:20:40.360 If that's equal to my current value of my signal, I'm done. 00:20:40.360 --> 00:20:43.460 Otherwise, I set the signal to the new value and call each of 00:20:43.460 --> 00:20:47.081 the action procedures that I've been, that I've 00:20:47.081 --> 00:20:48.331 been--what's the right word?-- 00:20:51.700 --> 00:20:54.630 introduced to. 00:20:54.630 --> 00:21:01.530 I get introduced when the and-gate was applied to me. 00:21:04.130 --> 00:21:07.410 I add action procedure at the bottom. 00:21:07.410 --> 00:21:10.440 Also, I have to define a way of accepting an action 00:21:10.440 --> 00:21:12.780 procedure-- which is what you see here--- 00:21:12.780 --> 00:21:18.530 which increments my action procedures using set to the 00:21:18.530 --> 00:21:22.060 result of CONSing up a new process--a procedure, which is 00:21:22.060 --> 00:21:25.760 passed to me, on to my actions procedures list. And for 00:21:25.760 --> 00:21:27.780 technical reasons, I have to call that procedure one. 00:21:27.780 --> 00:21:29.660 So I'm not going to tell you anything about that, that has 00:21:29.660 --> 00:21:32.610 to do with event-driven simulations and getting them 00:21:32.610 --> 00:21:36.950 started, which takes a little bit of thinking. 00:21:36.950 --> 00:21:38.690 And finally, I'm going to define a thing called the 00:21:38.690 --> 00:21:45.390 dispatcher, which is a way of passing a message to a wire, 00:21:45.390 --> 00:21:48.030 which is going to be used to extract from it various 00:21:48.030 --> 00:21:53.820 information, like what is the current signal value? 00:21:53.820 --> 00:21:57.180 What is the method of setting your signal? 00:21:57.180 --> 00:22:00.100 I want to get that out of it. 00:22:00.100 --> 00:22:02.600 How do I--how do I add another action procedure? 00:22:05.510 --> 00:22:08.280 And I'm going to return that dispatch, that 00:22:08.280 --> 00:22:09.940 procedure as a value. 00:22:09.940 --> 00:22:12.610 So the wire that I've constructed is a message 00:22:12.610 --> 00:22:16.710 accepting object which accepts a message like, like what's 00:22:16.710 --> 00:22:19.790 your method of adding action procedures? 00:22:19.790 --> 00:22:22.270 In fact, it'll give me a procedure, which is the add 00:22:22.270 --> 00:22:26.020 action procedure, which I can then apply to an action 00:22:26.020 --> 00:22:29.010 procedure to create another action procedure in the wire. 00:22:31.620 --> 00:22:32.820 So that's a permission. 00:22:32.820 --> 00:22:37.450 So it's given me permission to change your action procedures. 00:22:37.450 --> 00:22:41.710 And in fact, you can see that over here. 00:22:41.710 --> 00:22:43.278 Next slide. 00:22:43.278 --> 00:22:44.528 Ah. 00:22:47.760 --> 00:22:49.120 This is nothing very interesting. 00:22:49.120 --> 00:22:52.040 The call each of the action procedures is just a CDRing 00:22:52.040 --> 00:22:53.500 down a list. And I'm not going to even 00:22:53.500 --> 00:22:54.990 talk about that anymore. 00:22:54.990 --> 00:22:57.560 We're too advanced for that. 00:22:57.560 --> 00:23:00.280 However, if I want to get a signal from a 00:23:00.280 --> 00:23:02.250 wire, I ask the wire-- 00:23:02.250 --> 00:23:03.090 which is, what is the wire? 00:23:03.090 --> 00:23:05.860 The wire is the dispatch returned by creating the wire. 00:23:05.860 --> 00:23:06.830 It's a procedure. 00:23:06.830 --> 00:23:12.590 I call that dispatch on the message get-signal. 00:23:12.590 --> 00:23:14.770 And what I should expect to get is a method 00:23:14.770 --> 00:23:16.900 of getting a signal. 00:23:16.900 --> 00:23:19.220 Or actually, I get the signal. 00:23:19.220 --> 00:23:25.800 If I want to set a signal, I want to change a signal, then 00:23:25.800 --> 00:23:28.810 what I'm going to do is take a wire as an argument and a new 00:23:28.810 --> 00:23:31.120 value for the signal, I'm going to ask the wire for 00:23:31.120 --> 00:23:35.660 permission to set its signal and use that permission, which 00:23:35.660 --> 00:23:38.700 is a procedure, on the new value. 00:23:38.700 --> 00:23:44.156 And if we go back to the overhead here, thank you, if 00:23:44.156 --> 00:23:46.880 we go back to the overhead here, we see that the method-- 00:23:46.880 --> 00:23:49.720 if I ask for the method of setting the signal, that's 00:23:49.720 --> 00:23:54.620 over here, it's set-my-signal, a procedure that's defined 00:23:54.620 --> 00:23:59.270 inside the wire, which if we look over here is the thing 00:23:59.270 --> 00:24:02.930 that says set my internal value called the signal, my 00:24:02.930 --> 00:24:08.640 internal variable, which is the signal, to the new value, 00:24:08.640 --> 00:24:11.630 which is passed to me as an argument, and then call each 00:24:11.630 --> 00:24:13.010 of the action procedures waking them up. 00:24:16.340 --> 00:24:19.400 Very simple. 00:24:19.400 --> 00:24:24.310 Going back to that slide, we also have the one last thing-- 00:24:24.310 --> 00:24:27.810 which I suppose now you can easily work out for yourself-- 00:24:27.810 --> 00:24:30.100 is the way you add an action. 00:24:30.100 --> 00:24:36.470 You take a wire--a wire and an action procedure. 00:24:36.470 --> 00:24:40.050 And I ask the wire for permission to add an action. 00:24:40.050 --> 00:24:43.210 Getting that permission, I use that permission to give it an 00:24:43.210 --> 00:24:45.020 action procedure. 00:24:45.020 --> 00:24:48.570 So that's a real object. 00:24:48.570 --> 00:24:52.460 There's a few more details about this. 00:24:52.460 --> 00:24:58.390 For example, how am I going to control this thing? 00:24:58.390 --> 00:25:01.290 How do I do these delays? 00:25:01.290 --> 00:25:02.540 Let's look at that for a second. 00:25:05.275 --> 00:25:08.360 The next one here. 00:25:08.360 --> 00:25:09.570 Let's see. 00:25:09.570 --> 00:25:15.450 We know when we looked at the and-gate or the not-gate that 00:25:15.450 --> 00:25:18.770 when a signal changed on the input, there was a delay. 00:25:18.770 --> 00:25:22.060 And then it was going to call the procedure, which was going 00:25:22.060 --> 00:25:23.310 to change the output. 00:25:26.040 --> 00:25:28.120 Well, how are we going to do this? 00:25:28.120 --> 00:25:30.600 We're going to make up some mechanism, a fairly 00:25:30.600 --> 00:25:32.840 complicated mechanism at that, which we're going to have to 00:25:32.840 --> 00:25:34.720 be very careful about. 00:25:34.720 --> 00:25:37.390 But after a delay, we're going to do an action. 00:25:37.390 --> 00:25:40.590 A delay is a number, and an action is a procedure. 00:25:40.590 --> 00:25:41.970 What that's going to be is they're going to have a 00:25:41.970 --> 00:25:47.120 special structure called an agenda, which is a thing that 00:25:47.120 --> 00:25:49.510 organizes time and actions. 00:25:49.510 --> 00:25:50.880 And we're going to see that in a while. 00:25:50.880 --> 00:25:53.070 I don't want to get into that right now. 00:25:53.070 --> 00:25:55.745 But the agenda has a moment at which--at 00:25:55.745 --> 00:25:59.130 which something happens. 00:25:59.130 --> 00:26:03.120 We're setting up for later at some moment, which is the sum 00:26:03.120 --> 00:26:05.400 of the time, which is the delay time plus the current 00:26:05.400 --> 00:26:08.460 time, which the agenda thinks is now. 00:26:08.460 --> 00:26:11.840 We're going to set up to do this action, and add that to 00:26:11.840 --> 00:26:13.090 the agenda. 00:26:15.280 --> 00:26:18.660 And the way this machine will now run is very simple. 00:26:18.660 --> 00:26:20.800 We have a thing called propagate, which is the way 00:26:20.800 --> 00:26:22.710 things run. 00:26:22.710 --> 00:26:25.290 If the agenda is empty, we're done--if there's nothing more 00:26:25.290 --> 00:26:27.440 to be done. 00:26:27.440 --> 00:26:31.690 Otherwise, we're going to take the first item off the agenda, 00:26:31.690 --> 00:26:34.200 and that's a procedure of no arguments. 00:26:34.200 --> 00:26:36.030 So that we're going to see extra parentheses here. 00:26:36.030 --> 00:26:39.190 We call that on no arguments. 00:26:39.190 --> 00:26:42.200 That takes the action. 00:26:42.200 --> 00:26:45.050 Then we remove that first item from the agenda, and we go 00:26:45.050 --> 00:26:48.395 around the propagation loop. 00:26:48.395 --> 00:26:50.750 So that's the overall structure of this thing. 00:26:53.380 --> 00:26:57.430 Now, there's a, a few other things we can look at. 00:26:57.430 --> 00:26:59.160 And then we're going to look into the agenda a 00:26:59.160 --> 00:27:00.410 little while from now. 00:27:00.410 --> 00:27:02.800 Now the overhead again. 00:27:02.800 --> 00:27:04.980 Well, in order to set this thing going, I just want to 00:27:04.980 --> 00:27:07.410 show you some behavior out of this simulator. 00:27:07.410 --> 00:27:10.610 By the way, you may think this simulator is very simple, and 00:27:10.610 --> 00:27:12.370 probably too simple to be useful. 00:27:12.370 --> 00:27:15.730 The fact of the matter is that this simulator has been used 00:27:15.730 --> 00:27:18.680 to manufacture a fairly large computer. 00:27:18.680 --> 00:27:22.360 So this is a real live example. 00:27:22.360 --> 00:27:24.790 Actually, not exactly this simulator, because I'll tell 00:27:24.790 --> 00:27:25.560 you the difference. 00:27:25.560 --> 00:27:28.180 The difference is that there were many more different kinds 00:27:28.180 --> 00:27:29.820 of primitives. 00:27:29.820 --> 00:27:33.200 There's not just the word inverter or and-gate. 00:27:33.200 --> 00:27:37.590 There were things like edge-triggered, flip-flops, 00:27:37.590 --> 00:27:43.780 and latches, transparent latches, and adders, and 00:27:43.780 --> 00:27:45.170 things like that. 00:27:45.170 --> 00:27:48.510 And the difficulty with that is that there's pages and 00:27:48.510 --> 00:27:51.410 pages of the definitions of all these primitives with 00:27:51.410 --> 00:27:54.690 numbers like LS04. 00:27:54.690 --> 00:27:56.740 And then there's many more parameters for them. 00:27:56.740 --> 00:27:58.480 It's not just one delay. 00:27:58.480 --> 00:28:00.020 There's things like set up times and hold 00:28:00.020 --> 00:28:01.220 times and all that. 00:28:01.220 --> 00:28:03.990 But with the exception of that part of the complexity, the 00:28:03.990 --> 00:28:07.580 structure of the simulator that we use for building a 00:28:07.580 --> 00:28:12.290 real computer, that works is exactly what 00:28:12.290 --> 00:28:15.110 you're seeing here. 00:28:15.110 --> 00:28:19.270 Well in any case, what we have here is a few simple things. 00:28:19.270 --> 00:28:21.580 Like, there's inverter delays being set up and 00:28:21.580 --> 00:28:23.030 making a new agenda. 00:28:23.030 --> 00:28:26.470 And then we can make some inputs. 00:28:26.470 --> 00:28:28.220 There's input-1, input-2, a sum and a 00:28:28.220 --> 00:28:29.460 carry, which are wires. 00:28:29.460 --> 00:28:32.560 I'm going to put a special kind of object called a probe 00:28:32.560 --> 00:28:37.810 onto, onto some of the wires, onto sum and onto carry. 00:28:37.810 --> 00:28:41.590 A probe is a, can object that has the property that when you 00:28:41.590 --> 00:28:46.120 change a wire it's attached to, it types out a message. 00:28:46.120 --> 00:28:47.970 It's an easy thing to do. 00:28:47.970 --> 00:28:50.790 And then once we have that, of course, the way you put the 00:28:50.790 --> 00:28:53.040 probe on, the first thing it does, it says, the current 00:28:53.040 --> 00:28:59.400 value of the sum at time 0 is 0 because I just noticed it. 00:28:59.400 --> 00:29:02.640 And the value of the carry at time 0, this is 00:29:02.640 --> 00:29:05.556 the time, is 0. 00:29:05.556 --> 00:29:09.620 And then we go off and we build some structure. 00:29:09.620 --> 00:29:14.440 Like, we can build a structure here that says you have a 00:29:14.440 --> 00:29:18.420 half-adder on input-1, input-2, sum, and carry. 00:29:18.420 --> 00:29:20.420 And we're going to set the signal on input-1 to 1. 00:29:20.420 --> 00:29:21.880 We do some propagation. 00:29:21.880 --> 00:29:25.380 At time 8, which you could see going through this thing if 00:29:25.380 --> 00:29:29.520 you wanted to, the new value of sum became 1. 00:29:29.520 --> 00:29:31.150 And the thing says I'm done. 00:29:31.150 --> 00:29:32.630 That wasn't very interesting. 00:29:32.630 --> 00:29:34.150 But we can send it some more signals. 00:29:34.150 --> 00:29:36.590 Like, we set-signal on input-2 to be one. 00:29:36.590 --> 00:29:39.430 And at that time if we propagate, then it carried at 00:29:39.430 --> 00:29:43.280 11, the carry becomes 1, and at 16, the sum's new 00:29:43.280 --> 00:29:45.040 value becomes 0. 00:29:45.040 --> 00:29:48.060 And you might want to work out that, if you like, about the 00:29:48.060 --> 00:29:48.990 digital circuitry. 00:29:48.990 --> 00:29:50.620 It's true, and it works. 00:29:50.620 --> 00:29:51.535 And it's not very interesting. 00:29:51.535 --> 00:29:53.330 But that's the kind of behavior we 00:29:53.330 --> 00:29:54.580 get out of this thing. 00:30:01.830 --> 00:30:06.550 So what I've shown you right now is a large-scale picture, 00:30:06.550 --> 00:30:10.360 how you, at a bigger, big scale, you implement an 00:30:10.360 --> 00:30:12.952 event-driven simulation of some sort. 00:30:12.952 --> 00:30:16.010 And how you might organize it to have nice hierarchical 00:30:16.010 --> 00:30:20.220 structure allowing you to build abstract boxes that you 00:30:20.220 --> 00:30:21.225 can instantiate. 00:30:21.225 --> 00:30:23.630 But I haven't told you any of the details about how this 00:30:23.630 --> 00:30:25.780 agenda and things like that work. 00:30:25.780 --> 00:30:28.630 That we'll do next. 00:30:28.630 --> 00:30:32.040 And that's going to involve change and mutation of data 00:30:32.040 --> 00:30:34.310 and things like that. 00:30:34.310 --> 00:30:35.860 Are there any questions now, before I go on? 00:30:47.160 --> 00:30:47.550 Thank you. 00:30:47.550 --> 00:30:48.800 Let's take a break. 00:31:28.940 --> 00:31:35.060 Well, we've been making a simulation. 00:31:35.060 --> 00:31:39.360 And the simulation is an event-driven simulation where 00:31:39.360 --> 00:31:43.920 the objects in the world are the objects in the computer. 00:31:43.920 --> 00:31:46.700 And the changes of state that are happening in the world in 00:31:46.700 --> 00:31:53.520 time are organized to be time in the computer, so that if 00:31:53.520 --> 00:31:56.430 something happens after something else in the world, 00:31:56.430 --> 00:32:00.910 then we have it happen after, after the corresponding events 00:32:00.910 --> 00:32:04.420 happen in the same order in the computer. 00:32:04.420 --> 00:32:06.070 That's where we have assignments, when 00:32:06.070 --> 00:32:08.220 we make that alignment. 00:32:08.220 --> 00:32:11.860 Right now I want to show you a way of organizing time, which 00:32:11.860 --> 00:32:16.040 is an agenda or priority queue, it's sometimes called. 00:32:16.040 --> 00:32:17.990 We'll do some--we'll do a little bit of just 00:32:17.990 --> 00:32:19.980 understanding what are the things we need to be able to 00:32:19.980 --> 00:32:21.230 do to make agendas. 00:32:28.330 --> 00:32:30.310 And so we're going to have--and so right now over 00:32:30.310 --> 00:32:31.750 here, I'm going to write down a bunch of primitive 00:32:31.750 --> 00:32:35.960 operations for manipulating agendas. 00:32:35.960 --> 00:32:38.650 I'm not going to show you the code for them because they're 00:32:38.650 --> 00:32:41.300 all very simple, and you've got 00:32:41.300 --> 00:32:43.680 listings of all that anyway. 00:32:43.680 --> 00:32:44.380 So what do we have? 00:32:44.380 --> 00:32:52.880 We have things like make-agenda which produces a 00:32:52.880 --> 00:32:54.130 new agenda. 00:32:59.860 --> 00:33:10.950 We can ask--we get the current-time of an agenda, 00:33:10.950 --> 00:33:12.625 which gives me a number, a time. 00:33:16.990 --> 00:33:20.650 We can get--we can ask whether an agenda is empty, 00:33:20.650 --> 00:33:21.900 empty-agenda. 00:33:30.200 --> 00:33:32.570 And that produces either a true or a false. 00:33:42.590 --> 00:33:44.720 We can add an object to an agenda. 00:33:52.710 --> 00:33:55.230 Actually, what we add to an agenda is an operation--an 00:33:55.230 --> 00:33:56.910 action to be done. 00:33:56.910 --> 00:34:03.560 And that takes a time, the action itself, and the agenda 00:34:03.560 --> 00:34:04.810 I want to add it to. 00:34:07.850 --> 00:34:09.280 That inserts it in the appropriate 00:34:09.280 --> 00:34:10.719 place in the agenda. 00:34:10.719 --> 00:34:14.850 I can get the first item off an agenda, the first thing I 00:34:14.850 --> 00:34:23.259 have to do, which is going to give me an action. 00:34:26.085 --> 00:34:29.540 And I can remove the first item from an agenda. 00:34:29.540 --> 00:34:31.409 That's what I have to be able to do with agendas. 00:34:31.409 --> 00:34:33.020 That is a big complicated mess. 00:34:42.530 --> 00:34:43.780 From an agenda. 00:34:45.530 --> 00:34:48.040 Well, let's see how we can organize this thing as a data 00:34:48.040 --> 00:34:52.528 structure a bit. 00:34:52.528 --> 00:34:58.720 Well, an agenda is going to be some kind of list. And it's 00:34:58.720 --> 00:35:00.190 going to be a list that I'm going to have 00:35:00.190 --> 00:35:01.570 to be able to modify. 00:35:01.570 --> 00:35:05.820 So we have to talk about modifying of lists, because 00:35:05.820 --> 00:35:09.590 I'm going to add things to it, and delete things from it, and 00:35:09.590 --> 00:35:11.070 things like that. 00:35:11.070 --> 00:35:13.820 It's organized by time. 00:35:13.820 --> 00:35:15.570 It's probably good to keep it in sorted order. 00:35:18.330 --> 00:35:22.170 But sometimes there are lots of things that happen at the 00:35:22.170 --> 00:35:23.420 same time--approximate same time. 00:35:23.420 --> 00:35:26.440 What I have to do is say, group things by the time at 00:35:26.440 --> 00:35:29.040 which they're supposed to happen. 00:35:29.040 --> 00:35:32.780 So I'm going to make an agenda as a list of segments. 00:35:32.780 --> 00:35:36.780 And so I'm going to draw you a data structure for an agenda, 00:35:36.780 --> 00:35:39.620 a perfectly reasonable one. 00:35:39.620 --> 00:35:41.110 Here's an agenda. 00:35:41.110 --> 00:35:42.870 It's a thing that begins with a name. 00:35:47.630 --> 00:35:49.940 I'm going to do it right now out of list structure. 00:35:52.620 --> 00:35:53.980 It's got a header. 00:35:53.980 --> 00:35:55.840 There's a reason for the header. 00:35:55.840 --> 00:35:57.630 We're going to see the reason soon. 00:36:00.680 --> 00:36:03.750 And it will have a segment. 00:36:03.750 --> 00:36:05.620 It will have--it will be a list of segments. 00:36:08.310 --> 00:36:13.580 Supposing this agenda has two segments, they're the car's-- 00:36:13.580 --> 00:36:18.260 successive car's of this list. Each segment is 00:36:18.260 --> 00:36:20.250 going to have a time-- 00:36:24.160 --> 00:36:26.900 say for example, 10-- 00:36:26.900 --> 00:36:29.060 that says that the things that happen in this 00:36:29.060 --> 00:36:33.320 segment are at time 10. 00:36:33.320 --> 00:36:36.670 And what I'm going to have in here is another data structure 00:36:36.670 --> 00:36:39.490 which I'm not going to describe, which is a queue of 00:36:39.490 --> 00:36:42.240 things to do at time 10. 00:36:42.240 --> 00:36:43.330 It's a queue. 00:36:43.330 --> 00:36:45.130 And we'll talk about that in a second. 00:36:45.130 --> 00:36:49.530 But abstractly, the queue is just a list of things to do at 00:36:49.530 --> 00:36:50.200 a particular time. 00:36:50.200 --> 00:36:53.100 And I can add things to a queue. 00:36:53.100 --> 00:36:56.140 This is a queue. 00:36:56.140 --> 00:36:59.115 There's a time, there's a segment. 00:37:02.889 --> 00:37:06.035 Now, I may have another segment in this agenda. 00:37:08.940 --> 00:37:13.410 Supposing this is stuff that happens at time 30. 00:37:13.410 --> 00:37:18.020 It has, of course, another queue of things that are 00:37:18.020 --> 00:37:23.210 queued up to be done at time 30. 00:37:23.210 --> 00:37:24.705 Well, there are various things I have to be 00:37:24.705 --> 00:37:27.090 able to do to an agenda. 00:37:27.090 --> 00:37:30.410 Supposing I want to add to an agenda another thing to be 00:37:30.410 --> 00:37:33.030 done at time 10. 00:37:33.030 --> 00:37:34.700 Well, that's not very hard. 00:37:34.700 --> 00:37:37.480 I'm going to walk down here, looking for the 00:37:37.480 --> 00:37:39.730 segment of time 10. 00:37:39.730 --> 00:37:42.930 It is possible that there is no segment of time 10. 00:37:42.930 --> 00:37:45.420 We'll cover that case in a second. 00:37:45.420 --> 00:37:48.590 But if I find a segment of time 10, then if I want to add 00:37:48.590 --> 00:37:51.070 another thing to be done at time 10, I just 00:37:51.070 --> 00:37:53.860 increase that queue-- 00:37:53.860 --> 00:37:56.290 "just increase" isn't such an obvious idea. 00:37:56.290 --> 00:38:01.430 But I increase the things to be done at that time. 00:38:01.430 --> 00:38:02.900 Now, supposing I want to add something to be 00:38:02.900 --> 00:38:05.140 done at time 20. 00:38:05.140 --> 00:38:08.680 There is no segment for time 20. 00:38:08.680 --> 00:38:11.340 I'm going to have to create a new segment. 00:38:11.340 --> 00:38:13.960 I want my time 20 segment to exist between 00:38:13.960 --> 00:38:17.610 time 10 and time 30. 00:38:17.610 --> 00:38:20.170 Well, that takes a little work. 00:38:20.170 --> 00:38:21.525 I'm going to have to do a CONS. 00:38:24.260 --> 00:38:28.690 I'm going to have to make a new element of the agenda 00:38:28.690 --> 00:38:29.940 list--list of segments. 00:38:33.600 --> 00:38:35.400 I'm going to have to change. 00:38:35.400 --> 00:38:37.540 Here's change. 00:38:37.540 --> 00:38:42.290 I'm going to have to change the CDR of the CDR of the 00:38:42.290 --> 00:38:50.620 agenda to point that a new CONS of the new segment and 00:38:50.620 --> 00:38:56.657 the CDR of the CDR of the CDR of the agenda, the CD-D-D-DR. 00:38:56.657 --> 00:39:02.470 And this is going to have a new segment now of time 20 00:39:02.470 --> 00:39:06.290 with its own queue, which now has one element in it. 00:39:10.730 --> 00:39:13.080 If I wanted to add something at the end, I'm going to have 00:39:13.080 --> 00:39:20.770 to replace the CDR of this, of this list with something. 00:39:20.770 --> 00:39:24.040 We're going to have to change that piece of data structure. 00:39:24.040 --> 00:39:27.210 So I'm going to need new primitives for doing this. 00:39:27.210 --> 00:39:29.550 But I'm just showing you why I need them. 00:39:29.550 --> 00:39:33.390 And finally, if I wanted to add a thing to be done at time 00:39:33.390 --> 00:39:41.240 5, I'm going to have to change this one, because I'm going to 00:39:41.240 --> 00:39:44.770 have to add it in over here, which is why I planned ahead 00:39:44.770 --> 00:39:49.400 and had a header cell, which has a place. 00:39:49.400 --> 00:39:50.580 If I'm going to change things, I have to have 00:39:50.580 --> 00:39:53.420 places for the change. 00:39:53.420 --> 00:39:58.600 I have to have a place to make the change. 00:39:58.600 --> 00:40:02.540 If I remove things from the agenda, that's not so hard. 00:40:02.540 --> 00:40:04.990 Removing them from the beginning is pretty easy, 00:40:04.990 --> 00:40:07.740 which is the only case I have. I can go looking for the 00:40:07.740 --> 00:40:11.220 first, the first segment. 00:40:11.220 --> 00:40:14.510 I see if it has a non-empty queue. 00:40:14.510 --> 00:40:17.610 If it has a non-empty queue, well, I'm going to delete one 00:40:17.610 --> 00:40:20.100 element from the queue, like that. 00:40:20.100 --> 00:40:23.460 If the queue ever becomes empty, then I have to delete 00:40:23.460 --> 00:40:24.220 the whole segment. 00:40:24.220 --> 00:40:28.220 And then this, this changes to point to here. 00:40:28.220 --> 00:40:30.540 So it's quite a complicated data structure manipulation 00:40:30.540 --> 00:40:36.440 going on, the details of which are not really very exciting. 00:40:36.440 --> 00:40:38.920 Now, let's talk about queues. 00:40:38.920 --> 00:40:41.160 They're similar. 00:40:41.160 --> 00:40:44.340 Because each of these agendas has a queue in it. 00:40:44.340 --> 00:40:45.590 What's a queue? 00:40:49.079 --> 00:40:51.110 A queue is going to have the following primitive 00:40:51.110 --> 00:40:52.350 operations. 00:40:52.350 --> 00:41:02.170 To make a queue, this gives me a new queue. 00:41:07.274 --> 00:41:12.610 I'm going to have to be able to insert into 00:41:12.610 --> 00:41:16.850 a queue a new item. 00:41:24.510 --> 00:41:27.490 I'm going to have to be able to delete from a queue the 00:41:27.490 --> 00:41:28.740 first item in the queue. 00:41:39.988 --> 00:41:51.320 And I want to be able to get the first thing in the queue 00:41:51.320 --> 00:41:52.890 from some queue. 00:41:52.890 --> 00:41:55.140 I also have to be able to test whether a queue is empty. 00:42:07.110 --> 00:42:09.710 And when you invent things like this, I want you to be 00:42:09.710 --> 00:42:13.220 very careful to use the kinds of conventions I use for 00:42:13.220 --> 00:42:15.120 naming things. 00:42:15.120 --> 00:42:18.450 Notice that I'm careful to say these change something and 00:42:18.450 --> 00:42:19.870 that tests it. 00:42:19.870 --> 00:42:24.335 And presumably, I did the same thing over here. 00:42:24.335 --> 00:42:29.240 OK, and there should be an empty test over here. 00:42:29.240 --> 00:42:31.720 OK, well, how would I make a queue? 00:42:31.720 --> 00:42:35.210 A queue wants to be something I can add to at the end of, 00:42:35.210 --> 00:42:37.840 and pick up the thing at the beginning of. 00:42:37.840 --> 00:42:39.290 I should be able to delete from the beginning 00:42:39.290 --> 00:42:41.230 and add to the end. 00:42:41.230 --> 00:42:42.400 Well, I'm going to show you a very simple 00:42:42.400 --> 00:42:43.740 structure for that. 00:42:43.740 --> 00:42:47.080 We can make this out of CONSes as well. 00:42:47.080 --> 00:42:49.910 Here's a queue. 00:42:49.910 --> 00:42:55.310 It has--it has a queue header, which contains two parts-- 00:42:55.310 --> 00:42:59.610 a front pointer and a rear pointer. 00:43:02.930 --> 00:43:09.000 And here I have a queue with two items in it. 00:43:09.000 --> 00:43:12.095 The first item, I don't know, it's perhaps a 1. 00:43:12.095 --> 00:43:16.530 And the second item, I don't know, let's give it a 2. 00:43:21.160 --> 00:43:24.550 The reason why I want two pointers in here, a front 00:43:24.550 --> 00:43:27.570 pointer and a rear pointer, is so I can add to the end 00:43:27.570 --> 00:43:31.850 without having to chase down from the beginning. 00:43:31.850 --> 00:43:34.380 So for example, if I wanted to add one more item to this 00:43:34.380 --> 00:43:40.380 queue, if I want to add on another item to be worried 00:43:40.380 --> 00:43:44.060 about later, all I have to do is make a CONS, which contains 00:43:44.060 --> 00:43:47.530 that item, say a 3. 00:43:47.530 --> 00:43:51.340 That's for inserting 3 into the queue. 00:43:51.340 --> 00:44:00.100 Then I have to change this pointer here to here. 00:44:00.100 --> 00:44:04.320 And I have to change this one to point to the new rear. 00:44:09.120 --> 00:44:11.990 If I wish to take the first element of the queue, the 00:44:11.990 --> 00:44:15.130 first item, I just go chasing down the front pointer until I 00:44:15.130 --> 00:44:18.890 find the first one and pick it up. 00:44:18.890 --> 00:44:22.560 If I wish to delete the first item from the queue, 00:44:22.560 --> 00:44:25.240 delete-queue, all I do is move the front 00:44:25.240 --> 00:44:27.450 pointer along this way. 00:44:27.450 --> 00:44:31.700 The new front of the queue is now this. 00:44:31.700 --> 00:44:34.390 So queues are very simple too. 00:44:34.390 --> 00:44:39.690 So what you see now is that I need a certain number of new 00:44:39.690 --> 00:44:41.350 primitive operations. 00:44:41.350 --> 00:44:42.560 And I'm going to give them some names. 00:44:42.560 --> 00:44:45.310 And then we're going to look into how they work, and how 00:44:45.310 --> 00:44:47.350 they're used. 00:44:47.350 --> 00:44:56.970 We have set the CAR of some pair, or a thing produced by 00:44:56.970 --> 00:44:58.940 CONSing, to a new value. 00:45:02.370 --> 00:45:09.920 And set the CDR of a pair to a new value. 00:45:12.680 --> 00:45:16.030 And then we're going to look into how they work. 00:45:16.030 --> 00:45:19.720 I needed setting CAR over here to delete the first 00:45:19.720 --> 00:45:20.960 element of the queue. 00:45:20.960 --> 00:45:23.470 This is the CAR, and I had to set it. 00:45:23.470 --> 00:45:26.300 I had to be able to set the CDR to be able to move the 00:45:26.300 --> 00:45:30.160 rear pointer, or to be able to increment the queue here. 00:45:30.160 --> 00:45:33.170 All of the operations I did were made out of those that I 00:45:33.170 --> 00:45:35.515 just showed you on the, on the last blackboard. 00:45:38.230 --> 00:45:38.430 Good. 00:45:38.430 --> 00:45:40.357 Let's pause the time, and take a little break then. 00:46:38.346 --> 00:46:42.910 When we originally introduced pairs made out of CONS, made 00:46:42.910 --> 00:46:48.640 by CONS, we only said a few axioms about them, which were 00:46:48.640 --> 00:46:50.040 of the form-- 00:46:50.040 --> 00:46:52.010 what were they-- 00:46:52.010 --> 00:47:06.040 for all X and Y, the CAR of the CONS of X and Y is X and 00:47:06.040 --> 00:47:15.650 the CDR of the CONS of X and Y is Y. Now, these say nothing 00:47:15.650 --> 00:47:21.850 about whether a CONS has an identity like a person. 00:47:21.850 --> 00:47:25.730 In fact, all they say is something sort of abstract, 00:47:25.730 --> 00:47:29.740 that a CONS is the parts it's made out of. 00:47:29.740 --> 00:47:32.320 And of course, two things are made out of the same parts, 00:47:32.320 --> 00:47:34.990 they're the same, at least from the point of view of 00:47:34.990 --> 00:47:37.390 these axioms. 00:47:37.390 --> 00:47:39.920 But by introducing assignment-- 00:47:39.920 --> 00:47:43.360 in fact, mutable data is a kind of assignment, we have a 00:47:43.360 --> 00:47:45.590 set CAR and a set CDR-- 00:47:45.590 --> 00:47:48.300 by introducing those, these axioms no longer tell the 00:47:48.300 --> 00:47:49.830 whole story. 00:47:49.830 --> 00:47:53.250 And they're still true if written exactly like this. 00:47:53.250 --> 00:47:56.070 But they don't tell the whole story. 00:47:56.070 --> 00:48:01.150 Because if I'm going to set a particular CAR in a particular 00:48:01.150 --> 00:48:05.810 CONS, the questions are, well, is that setting all CARs and 00:48:05.810 --> 00:48:10.090 all CONSes of the same two things or not? 00:48:10.090 --> 00:48:12.610 If I--if we use CONSes to make up things like rational 00:48:12.610 --> 00:48:19.540 numbers, or things like 3 over 4, supposing I had two 00:48:19.540 --> 00:48:21.570 three-fourths. 00:48:21.570 --> 00:48:24.110 Are they the same one-- 00:48:24.110 --> 00:48:25.340 or are they different? 00:48:25.340 --> 00:48:27.860 Well, in the case of numbers, it doesn't matter. 00:48:27.860 --> 00:48:29.410 Because there's no meaning to changing the 00:48:29.410 --> 00:48:33.020 denominator of a number. 00:48:33.020 --> 00:48:34.670 What you could do is make a number which has a different 00:48:34.670 --> 00:48:36.840 denominator. 00:48:36.840 --> 00:48:38.980 But the concept of changing a number which has to have a 00:48:38.980 --> 00:48:41.570 different denominator is sort of a very weird, and sort of 00:48:41.570 --> 00:48:44.770 not supported by what you think of as mathematics. 00:48:44.770 --> 00:48:46.570 However, when these CONSes represent things in the 00:48:46.570 --> 00:48:50.940 physical world, then changing something like the CAR is like 00:48:50.940 --> 00:48:53.690 removing a piece of the fingernail. 00:48:53.690 --> 00:48:57.770 And so CONSes have an identity. 00:48:57.770 --> 00:49:01.280 Let me show you what I mean about identity, first of all. 00:49:01.280 --> 00:49:04.320 Let's do some little example here. 00:49:04.320 --> 00:49:15.200 Supposing I define A to the CONS of 1 and 2. 00:49:18.040 --> 00:49:22.510 Well, what that means, first of all, is that somewhere in 00:49:22.510 --> 00:49:27.590 some environment I've made a symbol A to have a value which 00:49:27.590 --> 00:49:33.300 is a pair consisting of pointers to a 1 and a pointer 00:49:33.300 --> 00:49:38.120 to a 2, just like that. 00:49:38.120 --> 00:49:47.220 Now, supposing I also say define B to be the CONS-- 00:49:53.320 --> 00:49:58.240 it doesn't matter, but I like it better, it's prettier-- 00:49:58.240 --> 00:50:03.970 of A and A. 00:50:03.970 --> 00:50:07.840 Well, first of all, I'm using the name A twice. 00:50:07.840 --> 00:50:09.100 At this moment, I'm going to think of 00:50:09.100 --> 00:50:11.300 CONSes as having identity. 00:50:11.300 --> 00:50:13.690 This is the same one. 00:50:13.690 --> 00:50:19.200 And so what that means is I make another pair, which I'm 00:50:19.200 --> 00:50:29.120 going to call B. And it contains two pointers to A. At 00:50:29.120 --> 00:50:33.260 this point, I have three names for this object. 00:50:33.260 --> 00:50:34.790 A is its name. 00:50:34.790 --> 00:50:37.230 The CAR of B is its name. 00:50:37.230 --> 00:50:39.360 And the CDR of B is its name. 00:50:39.360 --> 00:50:41.150 It has several aliases, they're called. 00:50:44.230 --> 00:51:01.860 Now, supposing I do something like set-the-CAR, the CAR of 00:51:01.860 --> 00:51:07.880 the CAR of B to 3. 00:51:12.750 --> 00:51:17.830 What that means is I find the CAR of B, that's this. 00:51:17.830 --> 00:51:20.935 I set the CAR of that to be 3, changing this. 00:51:24.760 --> 00:51:29.940 I've changed A. If I were to ask what's the 00:51:29.940 --> 00:51:35.340 CAR of A--of A now? 00:51:35.340 --> 00:51:42.250 I would get out 3, even though here we see that A was the 00:51:42.250 --> 00:51:45.290 CONS of 1 and 2. 00:51:45.290 --> 00:51:48.400 I caused A to change by changing B. 00:51:48.400 --> 00:51:52.010 There is sharing here. 00:51:52.010 --> 00:51:54.240 That's sometimes what we want. 00:51:54.240 --> 00:51:56.400 Surely in the queues and things like that, that's 00:51:56.400 --> 00:51:59.560 exactly what we defined our--organized our data 00:51:59.560 --> 00:52:01.790 structures to facilitate-- 00:52:01.790 --> 00:52:04.350 sharing. 00:52:04.350 --> 00:52:08.950 But inadvertent sharing, unanticipated interactions 00:52:08.950 --> 00:52:12.925 between objects, is the source of most of the bugs that occur 00:52:12.925 --> 00:52:17.820 in complicated programs. So by introducing this possibility 00:52:17.820 --> 00:52:22.570 of things having identity and sharing and having multiple 00:52:22.570 --> 00:52:25.190 names for the same thing, we get a lot of power. 00:52:25.190 --> 00:52:27.390 But we're going to pay for it with lots of 00:52:27.390 --> 00:52:28.640 complexity and bugs. 00:52:32.190 --> 00:52:35.430 So also, for example, if I just looked at this just to 00:52:35.430 --> 00:52:43.370 drive that home, the CADR of B, which has nothing to do 00:52:43.370 --> 00:52:46.560 with even the CAR of B, apparently. 00:52:46.560 --> 00:52:49.350 The CADR of B, what's that? 00:52:49.350 --> 00:52:53.560 Take that CDR of B and now take the CAR of that. 00:52:53.560 --> 00:52:56.480 Oh, that's 3 also. 00:52:56.480 --> 00:53:01.120 So I can have non-local interactions by sharing. 00:53:01.120 --> 00:53:02.480 And I have to be very careful of that. 00:53:06.640 --> 00:53:10.530 Well, so far, of course, it seems I've introduced several 00:53:10.530 --> 00:53:13.030 different assignment operators-- 00:53:13.030 --> 00:53:19.480 set, set CAR, set CDR. Well, maybe I should just get rid of 00:53:19.480 --> 00:53:22.820 set CAR and set CDR. Maybe they're not worthwhile. 00:53:22.820 --> 00:53:25.680 Well, the answer is that once you let the camel's nose into 00:53:25.680 --> 00:53:27.170 the tent, the rest of him follows. 00:53:30.160 --> 00:53:34.600 All I have to have is set, and I can make all of the--all of 00:53:34.600 --> 00:53:35.850 the bad things that can happen. 00:53:38.550 --> 00:53:40.690 Let's play with that a little bit. 00:53:40.690 --> 00:53:45.330 A couple of days ago, when we introduced compound data, you 00:53:45.330 --> 00:53:49.980 saw Hal show you a definition of CONS in terms 00:53:49.980 --> 00:53:52.480 of a message acceptor. 00:53:52.480 --> 00:53:57.280 I'm going to show you even a more horrible thing, a 00:53:57.280 --> 00:54:04.440 definition of CONS in terms of nothing but air, hot air. 00:54:04.440 --> 00:54:07.640 What is the definition of CONS, of the old functional 00:54:07.640 --> 00:54:13.330 kind, in terms of purely lambdic expressions, 00:54:13.330 --> 00:54:14.580 procedures? 00:54:17.190 --> 00:54:20.630 Because I'm going to then modify this definition to get 00:54:20.630 --> 00:54:25.020 assignment to be only one kind of assignment, to get rid of 00:54:25.020 --> 00:54:28.580 the set CAR and set CDR in terms of set. 00:54:28.580 --> 00:54:41.020 So what if I define CONS of X and Y to be a procedure of one 00:54:41.020 --> 00:54:44.310 argument called a message M, which calls that 00:54:44.310 --> 00:54:46.320 message on X and Y? 00:54:51.120 --> 00:54:54.080 This [? idea ?] was invented by Alonzo Church, who was the 00:54:54.080 --> 00:54:56.180 greatest programmer of the 20th century, although he 00:54:56.180 --> 00:54:57.870 never saw a computer. 00:54:57.870 --> 00:54:59.130 It was done in the 1930s. 00:54:59.130 --> 00:55:02.220 He was a logician, I suppose at Princeton at the time. 00:55:08.660 --> 00:55:15.690 Define CAR of X to be the result of applying X to that 00:55:15.690 --> 00:55:24.000 procedure of two arguments, A and D, which selects A. I will 00:55:24.000 --> 00:55:36.410 define CDR of X to be that procedure, to be the result of 00:55:36.410 --> 00:55:46.670 applying X to that procedure of A and D, which selects D. 00:55:46.670 --> 00:55:50.510 Now, you may not recognize this as CAR, CDR, and CONS. 00:55:50.510 --> 00:55:52.690 But I'm going to demonstrate to you that it satisfies the 00:55:52.690 --> 00:55:55.210 original axioms, just once. 00:55:55.210 --> 00:55:58.290 And then we're going to do some playing of games. 00:55:58.290 --> 00:56:09.695 Consider the problem CAR of CONS of, say, 35 and 47. 00:56:09.695 --> 00:56:11.120 Well, what is that? 00:56:11.120 --> 00:56:14.080 It is the result of taking car of the result of substituting 00:56:14.080 --> 00:56:19.710 35 and 47 for X and Y in the body of this. 00:56:19.710 --> 00:56:20.690 Well, that's easy enough. 00:56:20.690 --> 00:56:27.780 That's CAR of the result of substituting into lambda of M, 00:56:27.780 --> 00:56:35.750 M of 35 and 47. 00:56:35.750 --> 00:56:38.680 Well, what this is, is the result of substituting this 00:56:38.680 --> 00:56:42.830 object for X in the body of that. 00:56:42.830 --> 00:56:48.930 So that's just lambda of M-- 00:56:48.930 --> 00:56:51.090 that's substituted, because this object is being 00:56:51.090 --> 00:56:54.980 substituted for X, which is the beginning of a list, 00:56:54.980 --> 00:56:57.260 lambda of M-- 00:56:57.260 --> 00:57:07.570 M of 35 and 47, applied to that procedure of A and D, 00:57:07.570 --> 00:57:12.280 which gives me A. Well, that's the result of substituting 00:57:12.280 --> 00:57:15.840 this for M here. 00:57:15.840 --> 00:57:22.320 So that's the same thing as lambda of A, D, A, 00:57:22.320 --> 00:57:26.026 applied to 35 and 47. 00:57:26.026 --> 00:57:27.560 Oh, well that's 35. 00:57:27.560 --> 00:57:36.000 That's substituting 35 for A and for 47 for D in A. So I 00:57:36.000 --> 00:57:40.720 don't need any data at all, not even numbers. 00:57:40.720 --> 00:57:42.640 This is Alonso Church's hack. 00:57:52.420 --> 00:57:56.760 Well, now we're going to do something nasty to him. 00:57:56.760 --> 00:57:58.860 Being a logician, he wouldn't like this. 00:57:58.860 --> 00:58:03.260 But as programmers, let's look at the overhead. 00:58:03.260 --> 00:58:05.390 And here we go. 00:58:05.390 --> 00:58:09.570 I'm going to change the definition of CONS. 00:58:09.570 --> 00:58:14.520 It's almost the same as Alonzo Church's, but not quite. 00:58:14.520 --> 00:58:16.070 What do we have here? 00:58:16.070 --> 00:58:20.880 The CONS of two arguments, X and Y, is going to be that 00:58:20.880 --> 00:58:25.020 procedure of one argument M, which supplies M to X and Y as 00:58:25.020 --> 00:58:30.900 before, but also to two permissions, the permission to 00:58:30.900 --> 00:58:35.030 set X to N and the permission to set Y to N, given that I 00:58:35.030 --> 00:58:40.940 have an N. 00:58:40.940 --> 00:58:44.040 So besides the things that I had here in Church's 00:58:44.040 --> 00:58:50.990 definition, what I have is that the thing that CONS 00:58:50.990 --> 00:58:55.900 returns will apply its argument to not just the 00:58:55.900 --> 00:59:00.210 values of the X and Y that the CONS is made of, but also 00:59:00.210 --> 00:59:03.365 permissions to set X and Y to new values. 00:59:06.540 --> 00:59:09.220 Now, of course, just as before, CAR 00:59:09.220 --> 00:59:11.690 is exactly the same. 00:59:11.690 --> 00:59:14.980 The CAR of X is nothing more than applying X, as in 00:59:14.980 --> 00:59:18.110 Church's definition, to a procedure, in this case, of 00:59:18.110 --> 00:59:22.550 four arguments, which selects out the first one. 00:59:22.550 --> 00:59:28.750 And just as we did before, that will be the value of X 00:59:28.750 --> 00:59:33.470 that was contained in the procedure which is the result 00:59:33.470 --> 00:59:36.260 of evaluating this lambda expression in the environment 00:59:36.260 --> 00:59:37.920 where X and Y are defined over here. 00:59:41.940 --> 00:59:45.640 That's the value of CONS. 00:59:45.640 --> 00:59:47.730 Now, however, the exciting part. 00:59:47.730 --> 00:59:48.960 CDR, of course, is the same. 00:59:48.960 --> 00:59:54.270 The exciting part, set CAR and set CDR. Well, they're nothing 00:59:54.270 --> 00:59:55.800 very complicated anymore. 00:59:55.800 --> 01:00:02.700 Set CAR of a CONS X to a new value Y is nothing more than 01:00:02.700 --> 01:00:06.097 applying that CONS, which is the procedure of four--the 01:00:06.097 --> 01:00:09.160 procedure of one argument which applies its argument to 01:00:09.160 --> 01:00:15.950 four things, to a procedure which is of four arguments-- 01:00:15.950 --> 01:00:19.450 the value of X, the value of Y, permission to set X, the 01:00:19.450 --> 01:00:21.390 permission to set Y-- 01:00:21.390 --> 01:00:23.610 and using it--using that permission to set 01:00:23.610 --> 01:00:26.150 X to the new value. 01:00:31.650 --> 01:00:33.540 And similarly, set-cdr is the same thing. 01:00:36.120 --> 01:00:38.470 So what you've just seen is that I didn't introduce any 01:00:38.470 --> 01:00:40.470 new primitives at all. 01:00:40.470 --> 01:00:43.340 Whether or not I want to implement it this way is a 01:00:43.340 --> 01:00:45.340 matter of engineering. 01:00:45.340 --> 01:00:48.080 And the answer is of course I don't implement it this way 01:00:48.080 --> 01:00:51.680 for reasons that have to do with engineering. 01:00:51.680 --> 01:00:55.170 However in principle, logically, once I introduced 01:00:55.170 --> 01:00:57.515 one assignment operator, I've assigned--I've 01:00:57.515 --> 01:00:58.765 introduced them all. 01:01:05.420 --> 01:01:06.670 Are there any questions? 01:01:09.200 --> 01:01:12.040 Yes, David. 01:01:12.040 --> 01:01:14.860 AUDIENCE: I can follow you up until you get--I can follow 01:01:14.860 --> 01:01:15.740 all of that. 01:01:15.740 --> 01:01:19.760 But when we bring in the permissions, defining CONS in 01:01:19.760 --> 01:01:24.210 terms of the lambda N, I don't follow where N gets passed. 01:01:24.210 --> 01:01:25.100 PROFESSOR: Oh, I'm sorry. 01:01:25.100 --> 01:01:26.340 I'll show you. 01:01:26.340 --> 01:01:27.360 Let's follow it. 01:01:27.360 --> 01:01:29.180 Of course, we could do it on the blackboard. 01:01:29.180 --> 01:01:30.170 It's not so hard. 01:01:30.170 --> 01:01:32.450 But it's also easy here. 01:01:32.450 --> 01:01:38.520 Supposing I wish to set-cdr of X to Y. See that right there. 01:01:38.520 --> 01:01:43.680 set-cdr of X to Y. X is presumably a CONS, a thing 01:01:43.680 --> 01:01:46.890 resulting from evaluating CONS. 01:01:46.890 --> 01:01:54.030 Therefore X comes from a place over here, that that X is of 01:01:54.030 --> 01:01:58.110 the result of evaluating this lambda expression. 01:01:58.110 --> 01:01:59.380 Right? 01:01:59.380 --> 01:02:04.475 That when I evaluated that lambda expression, I evaluated 01:02:04.475 --> 01:02:07.700 it in an environment where the arguments 01:02:07.700 --> 01:02:08.950 to CONS were defined. 01:02:11.750 --> 01:02:14.530 That means that as free variables in this lambda 01:02:14.530 --> 01:02:18.670 expression, there is the--there are in the frame, 01:02:18.670 --> 01:02:23.860 which is the parent frame of this lambda expression, the 01:02:23.860 --> 01:02:27.470 procedure resulting from this lambda expression, X and Y 01:02:27.470 --> 01:02:29.250 have places. 01:02:29.250 --> 01:02:31.910 And it's possible to set them. 01:02:31.910 --> 01:02:35.380 I set them to an N, which is the argument of the 01:02:35.380 --> 01:02:37.010 permission. 01:02:37.010 --> 01:02:43.650 The permission is a procedure which is passed to M, which is 01:02:43.650 --> 01:02:47.940 the argument that the CONS object gets passed. 01:02:47.940 --> 01:02:54.020 Now, let's go back here in the set-cdr The CONS object, which 01:02:54.020 --> 01:02:56.230 is the first argument of set-cdr 01:02:56.230 --> 01:02:57.480 gets passed an argument. 01:03:00.260 --> 01:03:02.910 That--there's a procedure of four things, indeed, because 01:03:02.910 --> 01:03:05.780 that's the same thing as this M over here, which is applied 01:03:05.780 --> 01:03:07.920 to four objects. 01:03:07.920 --> 01:03:12.970 The object over here, SD, is, in fact, this permission. 01:03:15.470 --> 01:03:19.930 When I use SD, I apply it to Y, right there. 01:03:22.910 --> 01:03:25.740 So that comes from this. 01:03:25.740 --> 01:03:27.410 AUDIENCE: So what do you-- 01:03:27.410 --> 01:03:31.420 PROFESSOR: So to finish that, the N that was here is the Y 01:03:31.420 --> 01:03:34.160 which is here. 01:03:34.160 --> 01:03:34.810 How's that? 01:03:34.810 --> 01:03:35.750 AUDIENCE: Right, OK. 01:03:35.750 --> 01:03:40.240 Now, when you do a set-cdr, X is the value the 01:03:40.240 --> 01:03:41.970 CDR is going to become. 01:03:41.970 --> 01:03:44.742 PROFESSOR: The X over here. 01:03:44.742 --> 01:03:46.200 I'm sorry, that's not true. 01:03:46.200 --> 01:03:48.720 The X is--set-cdr has two arguments-- 01:03:48.720 --> 01:03:56.150 The CONS I'm changing and the value I'm changing it to. 01:03:56.150 --> 01:03:58.320 So you have them backwards, that's all. 01:04:01.750 --> 01:04:03.000 Are there any other questions? 01:04:07.880 --> 01:04:08.640 Well, thank you. 01:04:08.640 --> 01:04:09.890 It's time for lunch.