Stem

We call things that can be stored on the stack literals. They can be in four different forms, of which two are immediately easy to understand: strings, or basically any english phrase or list of characters that you want to store, and numbers. Strings look like this:

"this is a string!" "1234678876" "this too is a string" "asdfghjkl"

and numbers look like this:

50 3.1415 1000000

The third type of literal is called a quote. You can imagine a quote as an ordered list of other literals:

[ "hello" 50 3.14 [ "inside another quote" ] ]

between the ’[’ and the ’]’ character, you can see a list of four different literals. Because a quote is also another type of literal, quotes can store other quotes. The fourth type of literal we will talk about later, as it is not just a literal.

Now it is time to talk about the stack. The stack is what stores the literals, of course as we know, but how does it store the literals, and for what purpose? It stores the literals like a regular stack of objects, such as a stack of plates, would in real life. When something is put on the stack, it is on the top of the stack. When another object is then put on the stack, that object becomes the new top of the stack, and the previous object is under that object. This makes a natural ordering of what is considered above something else on the stack, just like a stack of plates each with some information on each of them would in real life. Note that if you had a real life arrangement of these plates, you would be able to read the top piece of information on the stack but no others, until you took that plate off the stack. Then, another plate would be on the top of the stack, and you would be able to read that plate. This is very much like how stem works, but how do you read information from the stack, when we’ve only described how to put things on the stack? This is where we introduce the full language: a language of not just literals, but words with meaning.

Words are the last type of thing that can be put on the stack, but they are special in that they can also do things. Thus far, none of the things we’ve talked about can actually add numbers, for example, only store them. Words add meaning to the language, and make it not just a place to store data, but rather, do things with the data. Here are some examples of some words:

dsc myword myword123 hello_this_is_word IAMAWORDTOO

But most of these words will actually be put on the stack as well rather than do something. In order for them to do something rather than to be interpreted as data, we must define them. Stem comes with a set of predefined words that you can combine in order to make new definitions which are defined in terms of a combination of the predefined words, just like in the english language. Next, we’ll go over some predefined words.

To follow along, I suggest after following the instructions on the github page you go into the stem project folder, find the stemlib folder, go into it with cd stemlib, and then run stem repl.stem. Here you will encounter what is known as the REPL, or the read, eval, print loop. What it is called doesn’t matter. Just know that it runs stem code interactively.

A basic word that prints out the top thing on the stack and removes it is simply a period:

# this is a comment, used to explain code but doesn't affect the outcome at all.
# comments start with a '#'.
"hello world\n" .

hello world

where the \n just signifies a newline character, basically just telling it to not print the “hello world” on the same line as the next thing printed. You can print the entire stack like so:

1 2 3 [ "some quote" ] "string!"

?

1
2
3
Q: [
some quote]
string!

Which prints the entire stack, where the bottom-most thing is the top thing on the stack. There are also some basic math operations you can do:

3 4 + .
3 4 - .
3 4 * .
3.0 4 / .

7
-1
12
0.750000

One can independently verify that these results are accurate. These basic math operations take two things off of the stack, does the operation on those two numbers, and then puts the new value back on the stack, deleting the old values. Then, the period character prints the value and pops them off the stack.

There are predefined words for other mathematical operations too, all listed here:

0.0 sin .
0.0 cos .
1.0 exp .
2.5 floor .
2.5 ceil .
2.71828 ln .

0.000000
1.000000
2.718282
2.000000
3.000000
0.999999

These operations I will assume you are familiar with, and one can independently verify their (approximate) validity. There are also comparison and logical operations:

"hi" "hi" = .
4 3 = .
3 4 < .
3 4 > .
3 4 <= .
3 4 >= .
1 1 and .
1 0 and .
0 1 or .
0 0 or .

Which compare the first number to the second number with a certain operation like “greater than or equals to”. The result is a zero or one, indicating that the statement is either true or false, with 1 being true. With these statements, you can make decisions:

3 4 < [ "3 < 4" . ] [ "3 >= 4" . ] if

3 < 4

where the word if just checks if the third thing from the top of the stack (the first thing you write) is a zero or a one, and if it is, then execute whatever’s inside the first quote, otherwise execute the second quote. Note that this wording is a little bit confusing because the first thing you write is also the last thing on the stack because adding new things to the stack puts the first thing below the second.

Now, also observe that inside the quotes we are storing valid code. This will become important later on as we introduce the concept of metaprogramming. First, though, we have to introduce a couple more important predefined words.

[ "hello world!\n" . ] eval
3 quote .
[ 1 2 ] [ 3 4 ] compose .
1 [ 2 3 ] curry .

hello world!
Q: [
3
]
Q: [
1
2
3
4
]
Q: [
1
2
3
]

eval evaluates the top of the stack as if it were a piece of code; quote puts the top of the stack in a quote and then pushes it back to the top of the stack; compose combines two quotes into one; and curry puts a value in the front of the quote. Note that some of these operations work for strings as well:

"hello " "world\n" compose .

hello world

And some other words that we use to operate on quotes and strings are here:

[ 1 2 3 4 ] 1 cut . .
0 [ 5 6 7 8 ] vat .
"hello\nworld\n" 6 cut . .
1 "asdfghjkl;" vat .

Q: [
3
4
]
Q: [
1
2
]
5
world
hello
s

cut cuts a string or quote into two, where the number in front tells cut where to cut. Note that normally in programming numbering starts at 0, so 1 is actually the second element of the quote. vat gets the nth element, where n is the first value passed into vat. It also returns the quote or string on the stack back after, with the value at that index on top. There are two more words that we have to define:

1 2 swap . .
1 2 . .
"hello\n" dup . .
1 2 5 [ + ] dip . .

1
2
2
1
hello
hello
5
3

swap just swaps the top two numbers on the stack, dup just duplicates the top of the stack, and dip is just eval except it does the operation one layer below. In this example, it adds 1 and 2 instead of 2 and 5, thus you see a 5 and a 3 printed instead. Note that there are more words, but we won’t need them for now. Now, we are ready to investigate how to define words in terms of other words, or so-called compound words.

Compound words, or words made up of other words (and literals), are created with yet another word, def. def takes an undefined word (all undefined words are just put on the stack) and a quote, and then from there on the word in question is defined as that quote, where whenever stem sees that word in the future, it immediately eval’s that quote. undef undefines a word, which is self explanatory.

hello [ "hello world\n" . ] def
hello
\hello undef
hello .

hello world
W: hello

In order to put words on the stack instead of calling them, just escape them:

\def .

W: def

Now, so far, we have discussed making decisions with if, doing various operations and evaluating quotes in a multitude of ways. What we haven’t covered is executing the same code some amount of times, or looping. In this language, all looping is done by defining words that call themselves, or what’s called recursion.

We can loop in stem by defining a word that calls itself:

loop-forever [ "hello world\n" . loop-forever ] def

Now, we don’t actually want to run this because it will just keep on printing hello world forever, without stopping, and we might want to constrain how much it loops. We can do this by only looping under some condition:

loop-some [ dup 0 <= [  ] [ dup . 1 - loop-some ] if ] def
4 loop-some

4
3
2
1

and we can see that it actually loops. You can modify the code to do more complex looping, and in the standard library (the stemlib folder), there is a loop function that loops any code any amount of times, written by Matthew Hinton.