PL/I - Language features 1

Let's look at the PL/I language in more details. Before we start, PL/I is a big language, and we are going to need two posts to even scratch the surface.

Format

PL/I is free format, but the IBM implementation requires use of upper case letters for keywords and identifiers. By default, characters after the 72nd column are ignored by the IBM compiler but this can be changed by a command line switch.

Comments are introduced with /* and ended with */ like in C.

Keywords are not reserved words, so you can do things like the below, where IF is an identifier; this will print 4. Also note that = is used for assignment or comparison, depending on context.

TEST: PROCEDURE OPTIONS(MAIN);  
  DECLARE IF FIXED BINARY(16);
  IF = 3;
  IF IF = 3 THEN IF = 4; ELSE IF = 5;
  PUT FILE (SCARDS) LIST(IF);
END TEST;  

Variables and constants

Arithmetic data

Arithmetic data can be either fixed point or floating, both using in decimal or binary as its base. An example of each of these combinations:

TEST: PROCEDURE OPTIONS(MAIN);  
  DECLARE XB FIXED BINARY(16);
  DECLARE XD FIXED DECIMAL(8,2);
  DECLARE FB FLOAT BINARY(8);
  DECLARE FD FLOAT DECIMAL(5);
  XB = 42;
  XD = 123.45;
  FB = 10110.01B;
  FD = 123.45678;
  PUT FILE (SCARDS) LIST(XB, XD, FB, FD);
END TEST;  

which will print

42      123.45  2.22E+01  1.2345E+02  

Note that for the binary items, the number in brackets specifies the number of bits to be used for storage; for decimals, it is the precision, so FD has been truncated.

In the above, you can see that B can be used as a suffix for binary constants. There is also a L suffix for pre-decimalisation British currency where the elements designate pounds, shillings and pence. This is converted into pence for storage.

TEST: PROCEDURE OPTIONS(MAIN);  
  DECLARE AMT FIXED BINARY(16);
  AMT = 1.5.2L;
  PUT FILE (SCARDS) LIST(AMT);
END TEST;  

I think no other language has this, and it may reflect that PL/I was originally designed at IBM's labs in England.

You can also declare complex variables and use the I suffix in constants, and there are PICTURE definitions for string representations of numeric data similar to COBOL.

Strings

Strings can be defined with either a fixed length or maximum length (with the VARYING keyword). A repeating constant can be introduced with a prefix number, as the below:

TEST: PROCEDURE OPTIONS(MAIN);  
  DECLARE A CHARACTER(20);
  DECLARE B CHARACTER(20) VARYING;
  A = 'HELLO';
  B = (3)'PL1 ';
  PUT FILE (SCARDS) LIST(A,B);
END TEST;  

which prints:

'HELLO               ' 'PL1 PL1 PL1 '  

There are also bit strings, eg DECLARE C BIT(8); C = '1010'B.

Arrays and structures

Arrays can be defined by adding dimensions after the variable name, eg DECLARE TABLE(10,20) FIXED DECIMAL(16);

Structures are collections of variables using a hierarchical format, for example

TEST: PROCEDURE OPTIONS(MAIN);  
  DECLARE 1 MEAL,
            2 NAME CHARACTER(20) VARYING,
            2 CUISINE CHARACTER(20) VARYING,
            2 RESTAURANT,
              3 NAME CHARACTER(20) VARYING,
              3 ADDRESS CHARACTER(80) VARYING,
            2 COST FIXED DECIMAL(5,2);
  MEAL.NAME = 'Dinner';
  MEAL.CUISINE = 'Italian';
  MEAL.RESTAURANT.NAME = 'Alfredo';
  MEAL.ADDRESS = '123 Foo Road';
  MEAL.COST = 123.45;
  PUT FILE (SCARDS) LIST(MEAL);
END TEST;  

Note that when qualifying a structure member we can omit levels if it is not ambiguous, eg MEAL.ADDRESS.

Once a structure has been set up, other variables can be instantiated with the same type using LIKE, eg DECLARE PARTY LIKE MEAL;.

Other types and attributes

As well as statement labels, which can be used for GO TO targets, there are special types for multitasking called events and tasks, but these are not supported by MTS.

An alias to another variable can be set up with DEFINED, eg DECLARE A FIXED BINARY(16); DECLARE B DEFINED A; means B and A point at the same variable.

Other attributes on types include ALIGNED and UNALIGNED and an initial value set at declaration with INITIAL;

Not covered here are variable lifetimes and pointers, which I will come back to in the next part.

Expressions

Expressions work mostly as expected, with conversions allowed implicitly between types - which leads to some complex rules given the number of built in types. || can be used as the string concatenation operator. Whole arrays or structures can be used as parameters to an expression.

Statements

Multiple assignments can be made on the left hand side of an expression, eg A,B = 2*21.

Control flow statements include IF ... THEN ... ELSE and looping via DO, which allows variable and condition testing as in the below:

TEST: PROCEDURE OPTIONS(MAIN);  
  DECLARE I FIXED BINARY(16);
  DECLARE S FIXED BINARY(16);

  DO I = 1 TO 5, 10 TO 15;
    PUT FILE (SCARDS) LIST(I);
  END;
  PUT FILE (SCARDS) SKIP;

  S = 0;
  DO WHILE (S < 10);
    S = S + 1;
    PUT FILE (SCARDS) LIST(S);
  END;
  PUT FILE (SCARDS) SKIP;

  S = 0;
  DO I = 2 TO 10 BY 2 WHILE (S < 10);
    S = S + I;
    PUT FILE (SCARDS) LIST(S);
  END;
  PUT FILE (SCARDS) SKIP;
END TEST;  

while will print

          1         2         3         4         5        10        11  
         13        14        15 

          1         2         3         4         5         6         7  
          9        10 

          2         6        12 

The STOP and EXIT statements can be used to terminate program execution immediately. There is also exception support for a set of predefined cases, such as end of file, using ON, eg ON ENDFILE(SCARDS) GO TO DONE;

In the next post we will look at pointers, block structure and the pre-processor along with other topics.

Further information

The original IBM documentation for the PL/I language and PL/I F compiler can be found at bitsavers.

PL/I - Introduction

In this series we'll look at PL/I, or Programming Language 1, an ambitious multi-purpose language developed by IBM.

PL/I overview

PL/I was intended to be a programming language for all users - scientific, business and systems. It was originally developed by IBM in the mid '60s and spread to other mainframes, Multics and DEC systems. A subset of the language was used to create CP/M and IBM produced a version for OS/2 on PCs that was competitive with C. A standardised specification was produced by ECMA and ANSI from the early '70s. Although it gained some popularity (it was even used as a teaching language at some universities) it never really took off in any of the fields it was intended for.

Language-wise, it is a procedural imperative language drawing inspiration from FORTRAN, COBOL and ALGOL. Due to its intended wide coverage, it is a very large language with a number of interesting features, some of which were incorporated into later languages such as C.

PL/I on MTS

There were three PL/I environments originally available on MTS:

  • *PL1F was derived from the IBM OS/360 F version 5 compiler with modifications for MTS. This is the only version available on the D6.0 tapes today and the one we will look at here. The MTS docuimentation refers to this as *PL1 but this name is not available; use *PL1F.

  • *PL1OPT was the IBM optimising compiler for PL/I and is not available due to copyright reasons. It took many of the compiler optimisation techniques developed for the FORTRAN H compiler and also offered a checkout facility for improved debugging.

  • *PLC was a load-and-go processor developer at Cornell; according to the MTS Archive the source and object code for this has been lost. It had the unique feature that any input would compile (but maybe not produce the desired results) due to automatic substitution of syntax errors.

There are also a number of utility programs for PL/I *PL1SCAN does a quick syntax check of a program and *PL1TIDY formats a PL/I source file.

Prerequisites

No special installation instructions to get PL/I running - just do the standard D6.0 setup as described in this guide and then sign on as a regular user such as ST01.

Using *PLIF

*PLIF will read source from scards (by default *source* ie standard input) and will write object files to spunch. Unlike some other MTS compilers you need to provide a filename for spunch as there is no default. You should destroy or empty the contents of the object file before recompiling.

Other compilation parameters are listed in MTS Volume 7.

To run PL/I programs you need to concatenate the runtime library *PL1LIB with the object file.

Hello world

Here's a transcript of a session where we run a Hello world program. This assumes the source code is contained in the file hello.pl1.

# $list hello.pl1

      1     /* Hello world program in PL/I */
      2     HELLO: PROCEDURE OPTIONS(MAIN);
      3       DECLARE I FIXED BINARY(16);
      4       DO I = 1 TO 5;
      5           PUT FILE (SCARDS) LIST('Hello, world!');
      6           PUT FILE (SCARDS) SKIP;
      7     END HELLO;

# $destroy -load
 File "-LOAD" has been destroyed.

# $run *pl1f scards=hello.pl1 spunch=-load
# Execution begins   12:18:31


  PROCEDURE HELLO: SYNTAX CHECK COMPLETED. COMPILATION CONTINUES.


  NO ERRORS OR WARNINGS DETECTED.
# Execution terminated   12:18:31  T=0.087

# $run -load+*pl1lib
# Execution begins   12:18:34
 'Hello, world!'
 'Hello, world!'
 'Hello, world!'
 'Hello, world!'
 'Hello, world!'

# Execution terminated   12:18:34  T=0.002

Further information

MTS Volume 7 describes the PL/I compilers available on MTS.

The original IBM documentation for the PL/I language and PL/I F compiler can be found at bitsavers.

A good introduction to PL/I is the PL/I Primer.

The Wikipedia article gives an extensive history and list of implementations.

The great FORTRAN-LISP shootout

One of the reasons LISP did not become more popular for scientific computing was the perception that it was slower than FORTRAN. In this post I will compare the performance of the LISP and FORTRAN implementations on MTS using a simple problem.

The problem and some caveats

We'll use the finding emirp primes problem introduced in the FORTRAN posts on this blog as the subject. To make it simpler we will just look at the third test, finding the 10,000th emirp.

So some caveats before we start. Benchmarks are notoriously difficult to get right and this is only a single sample. I'm not an expert at optimising LISP or FORTRAN so there may well be better ways of implementing this. Finally, the UTILISP implementation is from the 1980s, MTS LISP is from the 1970s and the FORTRAN G and H compilers date from at least the 1960s so this is not a historically accurate recreation.

Having said that, it'll be interesting to see how they stack up, so let's start.

FORTRAN

We'll use the source code for the FORTRAN emirp implementation discussed before, taking out the first and second test.

We compile without optimisations first (ie using FORTRAN G) and then try again with FORTRAN H. The results look like this:

# run *ftn scards=emirp3.f
# Execution begins   11:39:08 
  No errors in PRIME 
  No errors in REVRSE 
  No errors in EMIRP 
  No errors in SHOW 
  No errors in TEST3 
  No errors in MAIN 
# Execution terminated   11:39:08  T=0.045 
# run -load
# Execution begins   11:39:10 
     948349
# Execution terminated   11:39:19  T=9.05 
#
# $run *ftn scards=emirp3.f par=opt=h
# Execution begins   11:39:49 

  **** No errors for  PRIME ****      SAT MAY 09/15 11:39:49 

  **** No errors for REVRSE ****      SAT MAY 09/15 11:39:49 

  **** No errors for  EMIRP ****      SAT MAY 09/15 11:39:49 

  **** No errors for   SHOW ****      SAT MAY 09/15 11:39:49 

  **** No errors for  TEST3 ****      SAT MAY 09/15 11:39:49 

  **** No errors for   MAIN ****      SAT MAY 09/15 11:39:49 
# Execution terminated   11:39:49  T=0.074 
# run -load
# Execution begins   11:39:54 
     948349
# Execution terminated   11:39:59  T=4.281 

So 9.05s for FORTRAN G and 4.28s for FORTRAN H.

MTS LISP

Let's try the original MTS LISP first. It's fairly easy to translate using the (GO) form to do looping.

;; Checks if n is prime using a simple division test
(DEFUN PRIME-P (N)
  (COND
   ;; Deal with numbers <= 3
   ((LESS N 2) NIL)
   ((LESS N 4) T)
   ;; Check if divisible by 2 or 3
   ((EQUAL (REMAIN N 2) 0) NIL)
   ((EQUAL (REMAIN N 3) 0) NIL)
   ;; See if divisible by 5, 7, ..., up to approx sqrt(n)
   (T (PROG (I RESULT)
            (SETQ I 5)
A           (SETQ RESULT (COND ((GREATER (TIMES I I) N) 'PRIME)  
                               ((EQUAL (REMAIN N I) 0) 'NOT-PRIME)
                               (T (SETQ I (ADD I 2)) NIL)))
            (COND ((NOT RESULT) (GO A)))
            (EQ RESULT 'PRIME)))))

;; Return a number that has the reversed digits in n
(DEFUN REVERSE-DIGITS (N)
  (PROG (REVERSED)
        (SETQ REVERSED 0)
        ;; Take last digit from n and append to reversed
        (PROG ()
B             (SETQ REVERSED (TIMES REVERSED 10))  
              (SETQ REVERSED (ADD REVERSED (REMAIN N 10)))
              (SETQ N (IDIVIDE N 10))
              (COND ((GREATER N 0) (GO B))))
        ;; CAR needed to evaluate REVERSED otherwise PROG will return
        ;; the symbol REVERSED
        (CAR REVERSED)))

;; Check if a number is an emirp, ie both it and its reversed digits
;; are prime.
(DEFUN EMIRP-P (N)
  (PROG (REVERSED)
        (SETQ REVERSED (REVERSE-DIGITS N))
        (AND (NOT (EQUAL N REVERSED)) (PRIME-P N) (PRIME-P REVERSED))))

(DEFUN EMIRP-10K ()
  (PROG (N COUNT LAST)
        (SETQ N 0)
        (SETQ COUNT 0)
        (SETQ LAST 0)
C       (COND ((EMIRP-P N)  
               (SETQ COUNT (ADD COUNT 1)) (SETQ LAST N)))
        (SETQ N (ADD N 1))
        (COND ((LESS COUNT 10000) (GO C)))
        (CAR LAST)))

(EMIRP-10K)
(STOP)

We'll first execute it through the interpreter:

# $run *lisp scards=emirp.l
# Execution begins   12:41:27
      WELCOME TO LISP/MTS
 >    PRIME-P
 >    REVERSE-DIGITS
 >    EMIRP-P
 >    EMIRP-10K
* GC: COLLECTED 23370 CELLS
...
* GC: COLLECTED 23370 CELLS
>    948349
# Execution terminated   12:47:15  T=347.517 

Next we'll compile the functions. Add (COMPILE PRIME-P) and so on for all the functions and rerun

# $run *lisp scards=emirp.l
     WELCOME TO LISP/MTS
>    PRIME-P
>    REVERSE-DIGITS
>    EMIRP-P
>    EMIRP-10K
* COMPILE        04-17-79 RESTORED
>    (PRIME-P)
>    (REVERSE-DIGITS)
>    (EMIRP-P)
>    (EMIRP-10K)
* GC: COLLECTED 23370 CELLS
...
* GC: COLLECTED 23370 CELLS
>    948349
# Execution terminated   12:56:39  T=72.347 

OK, so we are down from 348s to 72s (the compilation itself takes less than 0.5s). Not bad, but still 17 times slower than FORTRAN H.

UTILISP

Let's see how UTILISP compares. We do need to change the program in quite a few places to match the different built in functions (eg + instead of ADD) but at least we can now use the do macro to create more expressive loops.

;; Checks if n is prime using a simple division test
(defun prime-p (n)
  (cond
   ;; Deal with numbers <= 3
   ((<= n 1) nil)
   ((<= n 3) t)
   ;; Check if divisible by 2 or 3
   ((= (remainder n 2) 0) nil)
   ((= (remainder n 3) 0) nil)
   ;; See if divisible by 5, 7, ..., up to approx sqrt(n)
   (t (do ((i 5 (+ i 2)) (result nil))
          (result (eq result 'prime))
          (setq result (cond ((> (* i i) n) 'prime)
                             ((= (remainder n i) 0) 'not-prime)
                             (t nil)))))))


;; Return a number that has the reversed digits in n
(defun reverse-digits (n)
  (do ((reversed 0) (m n (// m 10)))
      ((< m 1) reversed)
      ;; Take last digit from n and append to reversed
      (setq reversed (* reversed 10))
      (setq reversed (+ reversed (remainder m 10)))))


;; Check if a number is an emirp, ie both it and its reversed digits
;; are prime.
(defun emirp-p (n)
  (let ((reversed (reverse-digits n)))
    (and (neq n reversed) (prime-p n) (prime-p reversed))))


;; Return the 10,000th emirp
(defun emirp-10k ()
  (do ((n 0 (+ n 1)) (count 0) (last 0))
      ((eq count 10000) last)
      (cond ((emirp-p n) (setq count (+ count 1)) (setq last n)))))

;; Run the test
(print (emirp-10k))
(quit)

And let's run it through the interpreter.

# $run *utilisp 0=emirp.ul
# Execution begins   18:18:02 
  948349
# Execution terminated   18:21:30  T=208.35 

So that's 40% quicker than the MTS LISP interpreted version. Let's try compiling the forms, which we can just do by putting

(compile prime-p reverse-digits emirp-p emirp-10k)

after the definitions and then adding the fix parameter to the command line to reserve memory for the compiler (again compilation takes less than 0.5s of the total):

$ run *utilisp 0=emirp.ul par=fix=100
# Execution begins   18:32:27 
  ; Loading Utilisp Compiler System Version(82-11-09)
  948349
# Execution terminated   18:32:54  T=27.788 

Much better - 3 times faster than the MTS LISP compiled version but 7 times slower still than FORTRAN H.

Summary of results and final thoughts

Program Time (s)
FORTRAN G 9.05
FORTRAN H 4.28
MTS LISP interpreted 347.52
MTS LISP compiled 72.35
UTILISP interpreted 208.35
UTILISP compiled 27.79

Compiled UTILISP puts up a good showing and it's definitely usable for light numerical tasks but in the end FORTRAN wins on pure performance. The UTILISP implementation is much faster than MTS LISP for both interpreted and compiled code, which you'd expect given the amount of knowledge creating fast LISP implementations that was built up between the release of the two programs.

Another factor evident from this test was the lack of LISP standardisation (pre-Common Lisp) makes porting programs between implementations a chore, whereas FORTRAN was relatively standardised.

Any suggestions for optimising the code? Please let me know in the comments.

In the next post, in a couple of weeks, we'll look at PL/1.

Further information

Full source code for the programs shown here is on github.

UTILISP - Language features

Let's look at some of the language features in UTILISP compared to the original MTS LISP.

Strings

UTILISP brings support for strings, which can also be treated as a sequence of bytes that can be accessed independently.

> (setq s "hello world")
  "hello world"
> (string-length s)
  11
> (sref s 1)
  133
> (sset s 1 134)
  134
> s
  "hfllo world"
> (string-search "world" s)
  6
> (cutout s 0 2)
  34950

In the last expression, we take the first two bytes of s and extract it as an integer. There's also bref and bset which can be used to access individual bits in a string.

Numbers

UTILISP has both fixed and floating point numbers; arithmetic operators for floating point numbers have $ at the end of the keyword to distinguish them.

> (setq f 0.0)
  +0.0000000?+00
> (setq i 0)
  0
> (0= i)
  T
> (0= f)

  @@@ ILLEGAL ARGUMENT TYPE
  +0.0000000?+00 -- C#/0=
> (0=$ f)
  T

Vectors and references

Vectors are implemented as a primitive data type: they are created with vector and addressed with vref and vset. Vectors can contain any LISP data types. Here we create a four element vector, initially filled with the number 42 in each slot.

> (setq v (vector 4 42))
  V#-8057044
> v
  V#-8057044
> (vector-length v)
  4
> (vref v 0)
  42
> (vset v 0 43)
  43
> (vset v 1 "hello")
  "hello"

You can set references, which are pointers to elements of the vector which can then be dereferenced or updated through the reference.

> (setq r (reference v 3))
  R#-8057028
> (deref r)
  42
> (setref r 99)
  99
> (vref v 3)
  99

mapv can be used to operate on each element of a vector; it passes a reference to each element.

> (mapv v (function (lambda (r) (print (deref r)))))
  43
  "hello"
  42
  99
  V#-8057044

There is also a hash function that could be used to build efficient lookup tables using vectors.

> (hash 32)
  32
> (hash "hello")
  373277

Macros

UTILISP has macro support similar to modern LISPs, with selective quoting and evaluation via backtick and comma. Here we define a macro that will change a variable to nil if it is currently t.

> (defmacro t-to-nil (v) 
      `(cond ((eq ,v t) (setq ,v nil))))
  T-TO-NIL
> (setq a 1)
  1
> (setq b t)
  T
> (t-to-nil a)
  NIL
> (t-to-nil b)
  NIL
> a
  1
> b
  NIL

Scope and closures

UTILISP has dynamic scope and no lexical-let. There also seems to be no funarg implementation although this was available in Maclisp. It is possible to mimic closures with macros:

> (defun make-adder (init)
   (let ((sym (gensym)))
     (set sym init)
     `(lambda ( val) (cond (val (setq ,sym (+ ,sym val))) (t ,sym)))))
  MAKE-ADDER
> (setq aa (make-adder 40))
  (LAMBDA (VAL) (COND (VAL ?) (T G0002)))
> (funcall aa 1)
  41
> (funcall aa 2)
  43

INFANT

One interesting macro package that comes with UTILISP is INFANT (Infix Antidote), which allows infix notation for arithmetic expressions via !:

> (! 2 + 3 * 4)
  14

Further information

MTS Volume 22 describes the UTILISP implementation and how to run it on MTS.

UTILISP - Introduction

Let's look at the other LISP implementation on MTS, University of Tokyo Lisp or UTILISP.

UTILISP overview

UTILISP was originally developed at the University of Tokyo in 1980 for S/360 compatible mainframes. It was worked on there by students and staff for the following decade, moving to 68000 and SPARC processors along the way. It was distributed to several sites in Japan and the rest of the world and was used for AI research. One reason for its popularity was the speed of its compiled code.

Language wise, it is similar to Maclisp; it uses dynamic scope and has macro facilities.

UTILISP on MTS

UTILISP was made available on MTS at UM in 1984 as *UTILISP: it has some light customisation to make it work with MTS and an initial version of an MTS Volume was produced based on the original UTILISP documentation.

One key program produced using UTILISP was a Prolog implementation, PROLOG/KR; this is also available on MTS and I will look at this later.

Prerequisites

No special installation instructions to get UTILISP running - just do the standard D6.0 setup as described in this guide and then sign on as a regular user such as ST01.

Using *UTILISP

UTILISP is an interpreted environment. Running *UTILISP on its own will allow you to start entering expressions which will be immediately evaluated. It's possible to load expressions from a text file by providing it as the 0 parameter to *UTILISP; after the file is read you will remain in the LISP expression reader. To run a complete program and return to MTS afterwards, make the last expression be (quit).

There is an editor available via (edit fn) but it's easier to do this outside of UTILISP.

One improvement over *LISP is that there is online help, though not using the MTS help system: as an example, type (help car) to view a brief description of how the car function works.

Like *LISP, it's possible to compile expressions to machine code with (compile fn); note that you have to provide some fixed space memory to UTILISP at startup by setting FIX, eg with the command $run *utilisp par=fix=100. There does not seem to be a way to write the current system state or compiled functions back to disk, however.

Hello world

Here's a transcript of a session where we run a Hello world program. This assumes the source code is contained in the file hello.ul.

# $list hello.ul

       1     ;; Hello world program for UTILISP
       2     (do ((i 0 (1+ i)))
       3         ((= i 5))
       4         (print "Hello, world!"))
       5     (quit)

# $run *utilisp 0=hello.ul
# Execution begins   12:01:48 
  "Hello, world!"
  "Hello, world!"
  "Hello, world!"
  "Hello, world!"
  "Hello, world!"
# Execution terminated   12:01:48  T=0.035 

Further information

MTS Volume 22 describes the UTILISP implementation and how to run it on MTS.

This paper describes the history of UTILISP.

LISP - 4 bit adder

The problem

For this sample program we will simulate a four bit adder chip by constructing it from a series of AND, OR and NOT gates. See Rosetta Code for full details.

Constructing the solution

LISP provides AND, OR and NOT functions and we can use T and NIL to represent true and false. First task is to make an XOR gate:

(DEFUN XOR (A B)
  (OR (AND A (NOT B))
      (AND B (NOT A))))

Next we make a half-bit and single bit adder. These return a result and a carry bit which can be fed into the next stage of the full adder. We create a cons cell containing the result and carry bit for the return type.

(DEFUN HALF-ADDER (A B)
  (CONS (XOR A B) (AND A B)))

(DEFUN ADDER (A B C0)
  (PROG (S1 S2)
        (SETQ S1 (HALF-ADDER C0 A))
        (SETQ S2 (HALF-ADDER (CAR S1) B))
        (CONS (CAR S2) (OR (CDR S1) (CDR S2)))))

We then connect the adders together to form a four bit adder. As this version of LISP's NTH returns the remainder of the list from the given position, we need a convenience function BIT to access individual values.

(DEFUN BIT (L N)
  (CAR (NTH L (ADD1 N))))

(DEFUN ADDER-4 (A B)
  (PROG (X1 X2 X3 X4)
        (SETQ X1 (ADDER (BIT A 3) (BIT B 3) NIL))
        (SETQ X2 (ADDER (BIT A 2) (BIT B 2) (CDR X1)))
        (SETQ X3 (ADDER (BIT A 1) (BIT B 1) (CDR X2)))
        (SETQ X4 (ADDER (BIT A 0) (BIT B 0) (CDR X3)))
        (CONS (MAPCAR 'CAR (LIST X4 X3 X2 X1)) (CDR X4))))

The adder takes as input, and returns, a list of binary values, eg (NIL T NIL T) for 5. It would be convenient to have a function that can convert an integer into such a list: we can do this recursively.

(DEFUN DEC-BIN (X)
  (PROG (BIT)
        (SETQ BIT (NOT (ZERO (LAND X 1))))  
        (COND ((LESS X 2) (LIST BIT))
              (T (APPEND (DEC-BIN (SHIFT X -1)) BIT)))))

;; Pad binary list L to length N by adding NILs in front
(DEFUN PAD (N L)
  (COND ((LESS (LENGTH L) N) 
         (REPEAT '(SETQ L (CONS NIL L)) (SUB N (LENGTH L))))
        (T L)))

Finally, we write a test function to take two integers (assuming each is between 0 and 15) and add them, printing the sum:

(DEFUN TEST-ADDER-4 (A B)
  (PROG (AB BB RES)
        (SETQ AB (PAD 4 (DEC-BIN A)))
        (SETQ BB (PAD 4 (DEC-BIN B)))
        (SETQ RES (ADDER-4 AB BB))
        (PRIN1 AB) (PRIN1 '+) (PRIN1 BB)
        (PRIN1 '=) (PRIN1 (CAR RES))
        (PRIN1 'carry)  (PRIN1 (CDR RES))
        (TERPRI)))

(TEST-ADDER-4 3 2)

Here PRIN1 prints a single item and a space; TERPRI ends the current line.

Getting it working

The LISP REPL helps here, as you can revise functions and test them until they work; this was fairly simple to get working, though DEC-BIN was tricky until I separated out PAD into its own function. I struggled with the LISP editor and found it easier to apply changes back to the file using *EDIT as each was done.

Let's see it in action:

# $run *lisp scards=4bitadd.l
# Execution begins   20:02:38 
     WELCOME TO LISP/MTS
>    XOR
>    HALF-ADDER
>    ADDER
>    BIT
>    ADDER-4
>    DEC-BIN
>    PAD
>    TEST-ADDER-4
>    (NIL NIL T T) + (NIL NIL T NIL) = (NIL T NIL T) carry NIL
>    NIL
# Execution terminated   20:02:38  T=0.007 

Final thoughts on MTS LISP

I like Lisp a lot and even though this is a very basic Lisp compared to Common Lisp (or even Emacs Lisp) it still feels a lot higher level than the ALGOL/FORTRAN family of languages we have seen so far. One issue that we don't have, as we are running on fast modern computers, is speed: LISP was much slower than FORTRAN for numeric work and garbage collection was very slow.

In the next post, which will be in mid-April, we'll look at the other LISP in MTS - UTILISP.

Further information

Full source code for this program is on github.