The usual suspects

In this part, we will go beyond the simple numerical operations, and dive into stack manipulation. And while the title of this section refers to the 1995 movie, we are not going to deal with Keyser Söze this time.

Dup

The first one is dup. Its “stack signature” can be expressed as dup ( n -- n n ), as it duplicates the top element of the stack.
This means that given the following program

1 2 3 dup <- Top

we will get the following stack as result:

1 2 3 3 <- Top

To add this capability to our interpreter, we need to do two things: The first one is to add this keyword to our process function’s pattern-matching, and the second one is to actually implement it. Let’s get to it.

process :: Stack -> Text -> Stack
process stack "+"    = add stack
process stack "-"    = subtraction stack
process stack "dup"  = dup  stack

-- ...

dup :: Stack -> Stack
dup stack = push (V.head (getStack stack)) stack

As you can seen, this implementation of dup doesn’t rely on a pop function. While this is certainly a questionable choice, I wanted to show what some naïve implementation could look like.

Next in line are, as advertised…

Drop, Swap, Over and Rot

drop’s stack signature is the following: drop ( n -- ). In itself, this does not tell us much about its actual purpose: dropping the top element of the stack.

As an example,

1 2 3 drop <- Top
1 2 <- Top

In the case of swap, the signature is swap ( n1 n2 -- n2 n1 ). In plain words, it means that the top two elements of the stack are swapped.

For instance:

1 2 3 4 swap <- Top
1 2 4 3 <- Top

The next one is over. It duplicates the second topmost element, but puts the new element on the top of the stack. Its signature is over ( n1 n2 -- n1 n2 n1 ), and we can see it action here:

1 2 3 over <- Top
1 2 3 2 <- Top

And finally, rot. This one is slightly more messy. It pushes the third topmost element of the stack to the top, and by doing that pushes the other two down. Its stack signature is rot ( n1 n2 n3 -- n2 n3 n1 ), and it gives you:

1 2 3 rot <- Top
2 3 1 <- Top

Implementing

Let’s get to it.

drop is fairly simple to implement, as an operation on a vector.

drop :: Stack -> Stack
drop stack = Stack \$ V.drop 1 (getStack stack)

We drop the first element of the stack, which returns a new stack.

swap is a bit more sophisticated. Since we do not have any kind of abstraction on our stack, it looks like this:

swap :: Stack -> Stack
swap stack = Stack \$ (V.reverse elems) <> newStack
where
(elems, newStack) = V.splitAt 2 (getStack stack)

We get the first two elements of the stack, by effectively splitting the stack at the second position. From this operation, we get a Vector of size two, that we reverse before concatenating it with the (<>) operator.
If you know some Ruby or Elixir, it is akin to their, respectively, (<<) and (<>) operators for Strings, except that in Haskell any data structure can implement concatenation with (<>). Even Vector.

over’s implementation is a bit more explicit.

over :: Stack -> Stack
over stack = Stack \$ V.concat [e2, e1, e2, newStack]
where
(elems, newStack) = V.splitAt 2 (getStack stack)
(e1, e2)          = V.splitAt 1 elems

By splitting the stack at the right places, we can reorder the elements in a final concatenation.

In the same vein, here is rot’s implementation.

rot :: Stack -> Stack
rot stack = Stack \$ V.concat [newHead, newStack]
where
(elems, newStack) = V.splitAt 3 (getStack stack)
[e1, e2, e3]      = V.toList elems
newHead           = V.fromList [e3, e1, e2]

And finally, here is the final form of our process function:

process :: Stack -> Text -> Stack
process stack "+"    = add stack
process stack "-"    = subtraction stack
process stack "dup"  = dup  stack
process stack "drop" = drop stack
process stack "swap" = swap stack
process stack "over" = over stack
process stack "rot"  = rot  stack
process stack a      = push item stack
where
item = either (error . pack) fst (parseInt a)

And here we are! Let’s meet in part 03 to make our interpreter evolve into something more useful and less clumsy regarding stack operations.