20 Part 1½ Fundamentals Section 1½ Abstraction and Notation
 

M[function:primary]	Complete specification.
M [primary]	Drop the attribute "function," since it can be inferred from the value.
M.primary	Use the value outside the brackets, concatenated with a dot.
M.p	Use an explicitly given abbreviation, namely, primary\p (only if it is not ambiguous).
Mp	Drop the concatenation marker (the dot) if it is not needed to recover the two parts (all components are given by a single capital letter-here M).

Each of these rules corresponds to a natural tendency to abbreviate when redundant information is given; each has as its condition that recovery must be possible.
 
 

A PMS Example Using the DEC PDP-8

Let us now describe the PMS structure of an actual, though small, general-purpose computer, the DEC LINC-8, which is a PDP-8 with a LING processor. Figure 1 gives the detailed PMS diagram. In explaining it, we will concentrate on making the notation clear rather than on discussing substantive features of the system (which are described in Chap. 8). A simplified PMS diagram of the system shows its essential structure:

This shows the basic Mp-Pc-T-X structure of a C with the addition of a secondary memory (Ms) and two processors, one of which, Pc['LINC], has its own Ms. Two switches are used: the I/O Bus, which permits access to all the devices, and the Data Break to Mp via Pc, for high-data-rate devices. There are many other switches in the actual system, as one can see from Fig. 1; for example, Mp is really one to eight separate modules connected by a switch S to Pc. Also there are many T's connected to the input/output switch, Sio, which we collapsed as a single T, and similarly for S[ Data Break].

Consider the Mp module. The specifications assert that it is made with core technology, that its size is 4,096 words; that its operation time is 1.5 m s and that its word size is 13 bits (12 data bits plus one other with a different function). We could have written the same information as

M[function primary; technology:core; operation-time; 1.5 m s; size: 4096 w; word: (12 + 1) b]

In Fig. 1 we wrote only the values, suppressing the attributes, since moderate familiarity with memories permits an immediate inference about what attributes are involved. For example, it is common knowledge that computer memories store information in words; therefore 4,096 w must be the number of words in the memory. As another example, we did not specify the function of the additional bit in the word when we wrote (12 + 1) b. An informed reader will assume this to be a parity bit, since this is the common reason for having an extra bit in a word. If the extra bit had some unusual function, we would have needed to define it. That is, in the absence of additional information, the most common interpretation is to be assumed.

In fact, we could have been even more cryptic and still communicated with most readers:

M.core[1.5 m /s; 4 Kw; 12 b]

This corresponds to the phrase, "a 12-bit, 1.5-m s. 4K core store, which is intelligible to any computer engineer. The 4 Kw stands for 4 ´ 1,024 4,096, which again is known to computer engineers; however, if someone less informed took it to be 4 ´ 1,000 = 4,000, no real harm would be done.

Consider the magnetic tapes for Pc. Since there are eight possible tapes that make use of the same controller K through a switch 5, we label them #0 through #7. Actually, # is an abbreviation for index, which is an attribute like any other, whose values are integers. Since the attribute is a unique character, we do not have to write #:3 (although we could). The additional parameters give information about the physical attributes of the encoding. These are alternative values, and any tape has only one of them. We use a vertical bar (½ ) to indicate this (as in BNF notation for grammars). Thus, 45½ 112 in/s says that one can have a tape with a speed of 45 inches per second or one with 112 inches per second, but not a tape which can be switched dynamically to run at either speed.

For many of the components no further information is given. Thus, knowing that M.magnetic.tape is connected to a control and from there to the Pc tells generally what that K does. It is a tape controller, which evokes all the actions of the tape, such as read, write, rewind; therefore these actions do not have to be done by Pc. The fact that there is only one K for many Ms's implies that only one tape can be accessed at a time. Other information could be given, although that just provided is all that