Description
1. Overview
In this assignment, you will implement a desk calculator in Ocaml, a language with strong static type checking. Your program will be a strict subset of dc(1), although it will not have all of its functions. Begin by reading the man page for dc(1) and experimenting with it. Study its input format, output format, error messages, and exit status.
Your program will read the single file (if specified) as does dc and then read stdin. Implement the following dc functions : + – * / % ^ c d f l p s. Note that all of these letters are lower case.

Implementation Notes


You may not use the Num or Big_int modules in the Ocaml library. Instead, you will implement your own version of bigint by representing an integer by a

product of a sign with a list of integers. The largest value of int in Ocaml is 4611686018427387903 = 0x3FFFFFFFFFFFFFFF = 2^{62} − 1,
which is one bit less than what you might normally expect. This is because one bit is used in each word for tagging.


The ideal representation therefore would be to use eightdigit numbers in a list. However, in order to make sure that the lists are working, which is the point of the assignment, you can store only one digit in each element of a list. This is incredibly wasteful of storage, but possible makes the representation easier. The dc utility actually uses character arrays with two decimal digits per byte.



Since arithmetic operations proceed from the lowest order digit to the highest, represent your numbers with the lowest order digit at the front of the list and the leftmost digit at the end.



Do not use any loops in your program. All iteration should be done via recursion, and whenever possible, by using higherorder functions like map.



First implement input and output of numbers. Make sure your output duplicates dc for very large numbers. Note that an underscore prefixing a number makes it negative. The minus sign is strictly for subtraction.



Next, implement addition and subtraction. To do this, you will need two functions add and sub which just compare signs and then call add’ or sub’ as appropriate to do the work on their absolute values. When you subtract, make sure that the first argument is always the larger one.



You will need a function cmp which returns a comparison value in the same way as does strcmp in C. This can move from the low order digits to the high order digits tail recursively and stop at the end of the shorter list, or by maintaining an actual comparison when the two lists turn out to be the same length.

2 of 2 



Make sure that you always canonicalize your answers by deleting leading 0 digits. This is only an issue with absolute subtraction, since addition can only lengthen the number. All other operations are implemented in terms of addition and subtraction.



To implement multiplication, you add appropriate elements of the right column. To implement division, you add appropriate elements of the left column. The remainder is just whatever is left over after finishing the division, so your division function should return two results as a tuple, namely the quotient and remainder, and the main module then ignores the one not wanted.



Exponentiation will then be trivial, since it is a simple matter to call the other functions.


Interactive Use
As with some other languages, ocaml can be used interactively for testing purposes :
bash1$ ocaml
OCaml version 4.02.1

let f x y = x + y;;
val f : int > int > int = <fun>

f 3 4;;
– : int = 7

^D
You will, of course, need to add it to your $PATH :
bash2$ which ocaml
/afs/cats.ucsc.edu/courses/cmps112wm/usr/ocaml/bin/ocaml
Unfortunately, while interacting with ocaml, the up arrow can not be used to recover earlier lines. Using it just causes ocaml to print ^[[A. To get around this, you can use rlwrap, as in
bash3$ rlwrap ocaml
Then you can use the arrow keys to navigate.
bash4$ which rlwrap
/afs/cats.ucsc.edu/courses/cmps112wm/usr/rlwrap/bin/rlwrap
4. What to Submit
Makefile, bigint.ml, bigint.mli, maindc.ml, and scanner.mll. Note that scanner.ml is a generated file and should be made by the Makefile. Also, dc.ml is a debugging tool, not to be submitted. Testing will be done on the ocamlrun script ocamldc, which should be runnable from the commandline.
Program testing : Test data will be fed to dc(1) as well as to your program and the output will be checked with diff(1).