Web-Projects/blog-static
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Finish compiler series

Browse Source
This commit is contained in:
Danila Fedorin 2020-02-10 19:18:55 -08:00
parent e5d01a4e19
commit e7f0ccfa16
5 changed files with 573 additions and 15 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

9
code/compiler/09/llvm_context.cpp
View File

@ -20,7 +20,9 @@ void llvm_context::create_types() {
gmachine_type->setBody(
stack_ptr_type,
node_ptr_type
node_ptr_type,
IntegerType::getInt64Ty(ctx),
IntegerType::getInt64Ty(ctx)
);
struct_types.at("node_base")->setBody(
IntegerType::getInt32Ty(ctx),
@ -212,11 +214,6 @@ Value* llvm_context::create_track(Function* f, Value* v) {
return builder.CreateCall(track_f, { f->arg_begin(), v });
}
Value* llvm_context::create_eval(Value* e) {
auto eval_f = functions.at("eval");
return builder.CreateCall(eval_f, { e });
}
void llvm_context::create_unwind(Function* f) {
auto unwind_f = functions.at("unwind");
builder.CreateCall(unwind_f, { f->args().begin() });

1
code/compiler/09/llvm_context.hpp
View File

@ -55,7 +55,6 @@ struct llvm_context {
void create_alloc(llvm::Function*, llvm::Value*);
llvm::Value* create_track(llvm::Function*, llvm::Value*);
llvm::Value* create_eval(llvm::Value*);
void create_unwind(llvm::Function*);
llvm::Value* unwrap_gmachine_stack_ptr(llvm::Value*);

14
code/compiler/09/runtime.c
View File

@ -170,14 +170,16 @@ void gmachine_split(struct gmachine* g, size_t n) {
struct node_base* gmachine_track(struct gmachine* g, struct node_base* b) {
g->gc_node_count++;
if(g->gc_node_count >= g->gc_node_threshold) {
gc_visit_node(b);
gmachine_gc(g);
g->gc_node_threshold *= 2;
}
b->gc_next = g->gc_nodes;
g->gc_nodes = b;
if(g->gc_node_count >= g->gc_node_threshold) {
uint64_t nodes_before = g->gc_node_count;
gc_visit_node(b);
gmachine_gc(g);
g->gc_node_threshold = g->gc_node_count * 2;
}
return b;
}

5
content/blog/08_compiler_llvm.md
View File

@ -574,5 +574,6 @@ In the next several posts, we will improve
our compiler to properly free unused memory
usign a __garbage collector__, implement
lambda functions using __lambda lifting__,
and use our Alloc instruction to implement `let/in` expressions. See
you there!
and use our Alloc instruction to implement `let/in` expressions.
We get started on the first of these tasks in
[Part 9 - Garbage Collection]({{< relref "09_compiler_garbage_collection.md" >}}).

559
content/blog/09_compiler_garbage_collection.md Normal file
View File

@ -0,0 +1,559 @@
---
title: Compiling a Functional Language Using C++, Part 9 - Garbage Collection
date: 2020-01-27T20:35:15-08:00
tags: ["C and C++", "Functional Languages", "Compilers"]
draft: true
---
> "When will you learn? When will you learn that __your actions have consequences?__"
So far, we've entirely ignored the problem of memory management. Every time
that we need a new node for our growing graph, we simply ask for more memory
from the runtime with `malloc`. But selfishly, even when we no longer require
the memory allocated for a particular node, when that node is no longer in use,
we do not `free` it. In fact, our runtime currently has no idea about
which nodes are needed and which ones are ready to be discarded.
To convince ourselves that this is a problem, let's first assess the extent of the damage.
Consider the program from `works3.txt`:
{{< rawblock "compiler/09/examples/works3.txt" >}}
Compiling and running this program through `valgrind`, we get the following output:
```
==XXXX== LEAK SUMMARY:
==XXXX== definitely lost: 288 bytes in 12 blocks
==XXXX== indirectly lost: 768 bytes in 34 blocks
==XXXX== possibly lost: 0 bytes in 0 blocks
==XXXX== still reachable: 0 bytes in 0 blocks
==XXXX== suppressed: 0 bytes in 0 blocks
```
We lost 1056 bytes of memory, just to return the length of a list
with 3 elements. The problem of leaking memory is very real.
How do we solve this issue? We can't embed memory management into our language;
We want to keep it pure, and managing memory is typically pretty far from
that goal. Instead, we will make our runtime do the work of freeing memory.
Even then, this is a nontrivial goal: our runtime manipulates graphs, each
of which can be combined with others in arbitrary ways. In general, there
will not always be a _single_ node that, when freed, will guarantee that
another node can be freed as well. Instead, it's very possible in our
graphs that two parent nodes both refer to a third, and only when both
parents are freed can we free that third node itself. Consider,
for instance, the function `square` as follows:
```
defn square x = {
x * x
}
```
This function will receive, on top of the stack, a single graph representing `x`.
It will then create two applications of a global `(+)` function, each time
to the graph of `x`. Thus, it will construct a tree with two `App` nodes, both
of which
{{< sidenote "right" "lazy-note" "must keep track of a reference to x.">}}
We later take advantage of this, by replacing the graph of <code>x</code> with the
result of evaluating it. Since both <code>App</code> nodes point to the same
graph, when we evaluate it once, each node observes this update, and is not
required to evaluate <code>x</code> again. With this, we achieve lazy evaluation.
{{< /sidenote >}} The runtime will have to wait until both `App` nodes
are freed before it can free the graph of `x`.
This seems simple enough! If there are multiple things that may reference a node
in the graph, why don't we just keep track of how many there are? Once we know
that no more things are still referencing a node, we can free it. This is
called [reference counting](https://en.wikipedia.org/wiki/Reference_counting).
Reference counting is a valid technique, but unfortunately, it will not suit us.
The reason for this is that our language may produce
[cyclic graphs](https://en.wikipedia.org/wiki/Cycle_(graph_theory)). Consider,
for example, this definition of an infinite list of the number 1:
```
defn ones = { Cons 1 ones }
```
Envisioning the graph of the tree, we can see `ones` as an application
of the constructor `Cons` to two arguments, one of which is `ones` again.
{{< sidenote "right" "recursive-note" "It refers to itself!" >}}
Things are actually more complicated than this. In our current language,
recursive definitions are only possible in function definitions (like
<code>ones</code>). In our runtime, each time there is a reference
to a function, this is done through a <em>new node</em>, which
means that functions with recursive definitions are <em>not</em> represented cyclically.
Therefore, reference counting would work. However, in the future,
our language will have more ways of creating circular definitions,
some of which will indeed create cycles in our graphs. So, to
prepare for this, we will avoid the use of reference counting.
{{< /sidenote >}} In this case, when we compute the number of nodes
that require `ones`, we will always find the number to be at least 1: `ones`
needs `ones`, which needs `ones`, and so on. It will not be possible for
us to free `ones`, then, by simply counting the number of references to it.
There's a more powerful technique than reference counting for freeing
unused memory: __mark-and-sweep garbage collection__. This technique
is conceptually pretty simple to grasp, yet will allow us to handle
cycles in our graphs. Unsurprisingly, we implement this type
of garbage collection in two stages:
1. __Mark__: We go through every node that is still needed by
the runtime, and recursively mark is, its children, and so on as "to keep".
2. __Sweep__: We go through every node we haven't yet freed, and,
if it hasn't been marked as "to keep", we free it.
This also seems simple enough. There are two main things for us
to figure out:
1. For __Mark__, what are the "nodes still needed by the runtime"?
These are just the nodes on the various G-machine stacks. If
a node is not on the stack, nor is it a child of a node
that is on the stack, why should we keep it around?
2. For __Sweep__, how do we keep track of all the nodes we haven't
yet freed? In our case, the solution is a global list of allocated
nodes, which is updated every time that a node is allocated.
Wait a minute, though. Inside of `unwind` in C, we only have
a reference to the most recent stack. Our execution model allows
for an arbitrary number of stacks: we can keep using `Eval`,
placing the current stack on the dump, and starting a new stack
from scratch to evaluate a node. How can we traverse these stacks
from inside unwind? One solution could be to have each stack
point to the "parent" stack. To find all the nodes on the
stack, then, we'd start with the current stack, mark all the
nodes on it as "required", then move on to the parent stack,
rinse and repeat. This is plausible and pretty simple, but
there's another way.
We clean up after ourselves.
### Towards a Cleaner Stack
Simon Peyton Jones wrote his G-machine semantics in a particular way. Every time
that a function is called, all it leaves behind on the stack is the graph node
that represents the function's output. Our own internal functions, however, have been less
careful. Consider, for instance, the "binary operator" function I showed you.
Its body is given by the following G-machine instructions:
```C++
instructions.push_back(instruction_ptr(new instruction_push(1)));
instructions.push_back(instruction_ptr(new instruction_eval()));
instructions.push_back(instruction_ptr(new instruction_push(1)));
instructions.push_back(instruction_ptr(new instruction_eval()));
instructions.push_back(instruction_ptr(new instruction_binop(op)));
```
When the function is called, there are at least 3 things on the stack:
1. The "outermost" application node, to be replaced with an indirection (to enable laziness).
2. The second argument to the binary operator.
3. The first argument to the binary operator.
Then, __Push__ adds another node to the stack, an __Eval__ forces
its evaluation (and leaves it on the stack). This happens again with the second argument.
Finally, we call __BinOp__, popping two values off the stack and combining them
according to the binary operator. This leaves the stack with 4 things: the 3 I described
above, and thew newly computed value. This is fine as far as `eval` is concerned: its
implementation only asks for the top value on the stack after `unwind` finishes. But
for anything more complicated, this is a very bad side effect. We want to leave the
stack as clean as we found it - with one node and no garbage.
Fortunately, the way we compile functions is a good guide for how we should
compile internal operators and constructors. The idea is captured
by the two instructions we insert at the end of a user-defined
function:
{{< codelines "C++" "compiler/09/definition.cpp" 56 57 >}}
Once a result is computed, we turn the node that represented the application
into an indirection, and point it to the computed result (as I said before,
this enables lazy evaluation). We also pop the arguments given to the function
off the stack. Let's add these two things to the `gen_llvm_internal_op` function:
{{< codelines "C++" "compiler/09/main.cpp" 70 85 >}}
Notice, in particular, the `instruction_update(2)` and `instruction_pop(2)`
instructions that were recently added. A similar thing has to be done for data
type constructors. The difference, though, is that __Pack__ removes the data
it packs from the stack, and thus, __Pop__ is not needed:
{{< codelines "C++" "compiler/09/definition.cpp" 102 117 >}}
With this done, let's run a quick test: let's print the number of things
on the stack at the end of an `eval` call (before the stack is freed,
of course). We can compare the output of runtime without the fix (`old`)
and with the fix (`current`):
```
current old
Current stack size is 0 | Current stack size: 1
Current stack size is 0 | Current stack size: 1
Current stack size is 0 | Current stack size: 1
Current stack size is 0 | Current stack size: 1
Current stack size is 0 | Current stack size: 0
Current stack size is 0 | Current stack size: 0
Current stack size is 0 | Current stack size: 3
Current stack size is 0 | Current stack size: 0
Current stack size is 0 | Current stack size: 3
Current stack size is 0 | Current stack size: 0
Current stack size is 0 | Current stack size: 3
Result: 3 | Result: 3
```
The stack is now much cleaner! Every time `eval` is called, it starts
with one node, and ends with one node (which is then popped).
### One Stack to Rule Them All
Wait a minute. If the stack is really always empty at the end, do we really need to construct
a new stack every time?
{{< sidenote "right" "arity-note" "I think not" >}}
There's some nuance to this. While it is true that for the most
part, we can get rid of the new stacks in favor of a single
one, our runtime will experience a change. The change lies
in the Unwind-Global rule, which <em>requires that the
stack has as many children as the function needs
arguments</em>. Until now, there was no way
for this condition to be accidentally satisfied: the function
we were unwinding was the only thing on the stack. Now,
though, things are different: the function being
unwound may share a stack with something else,
and just checking the stack size will not be sufficient.
<em>I believe</em> that this is not a problem for us,
since the compiler will only emit <strong>Eval</strong>
instructions for things it knows are data types or numbers,
meaning their type is not a partially applied function
that is missing arguments. However, this is a nontrivial
observation.
{{< /sidenote >}}, and Simon Peyton Jones seems to
agree. In _Implementing Functional Languages: a tutorial_, he mentions
that the dump does not need to be implemented as a real stack of stacks.
So let's try this out: instead of starting a new stack using `eval`,
let's use an existing one, by just calling `unwind` again. To do so,
all we have to do is change our `instruction_eval` instruction. When
the G-machine wants something evaluated now, it should just call
`unwind` directly!
To make this change, we have to make `unwind` available to the
compiler. We thus declare it in the `llvm_context.cpp` file:
{{< codelines "C++" "compiler/09/llvm_context.cpp" 158 163 >}}
And even create a function to construct a call to `unwind`
with the following signature:
{{< codelines "C++" "compiler/09/llvm_context.hpp" 58 58 >}}
We implement it like so:
{{< codelines "C++" "compiler/09/llvm_context.cpp" 217 220 >}}
Finally, the `instruction_eval::gen_llvm` method simply calls
`unwind`:
{{< codelines "C++" "compiler/09/instruction.cpp" 157 159 >}}
After this change, we only call `eval` from `main`. Furthermore,
since `eval` releases all the resources it allocates before
returning, we won't be able to
{{< sidenote "right" "retrieve-note" "easily retrieve" >}}
We were able to do this before, but that's because our
runtime didn't free the nodes, <em>ever</em>. Now that
it does, returning a node violates that node's lifetime.
{{< /sidenote >}}the result of the evaluation from it.
Thus, we simply merge `eval` with `main` - combining
the printing and the initialization / freeing
code.
With this, only one stack will be allocated for the entirety of
program execution. This doesn't just help us save on memory
allocations, but also __solves the problem of marking
valid nodes during garbage collection__! Instead of traversing
a dump of stacks, we can now simply traverse a single stack;
all that we need is in one place.
So this takes care, more or less, of the "mark" portion of mark-and-sweep.
Using the stack, we can recursively mark the nodes that we need. But
what about "sweeping"? How can we possibly know of every node that
we've allocated? There's some more bookkeping for us to do.
### It's All Connected
There exists a simple technique I've previously seen (and used)
for keeping track of all the allocated memory. The technique is
to __turn all the allocated nodes into elements of a linked list__.
The general process of implementing this proceeds as follows:
1. To each node, add a "next" pointer.
2. Keep a handle to the whole node chain somewhere.
3. Add each newly allocated node to the front of the whole chain.
This "somewhere" could be a global variable. However,
since we already pass a stack to almost all of our
functions, it makes more sense to make the list handle
a part of some data structure that will also contain the stack,
and pass that around, instead. This keeps all of the G-machine
data in one place, and in principle could allow for concurrent
execution of more than one G-machine in a single program. Let's
call our new data structure `gmachine`:
{{< codelines "C++" "compiler/09/runtime.h" 69 74 >}}
Here, the `stack` field holds the G-machine stack,
and the `gc_nodes` is the handle to the list of all the nodes
we've allocated and not yet freed. Don't worry about the `gc_node_count`
and `gc_threshold` fields - we'll get to them a little later.
This is going to be a significant change. First of all, since
the handle won't be global, it can't be accessed from inside the
`alloc_*` functions. Instead, we have to make sure to add
nodes allocated through `alloc_*` to a G-machine somewhere
wherever we call the allocators. To make it easier to add nodes to a G-machine
GC handle, let's make a new function, `track`:
```C
struct node_base* gmachine_track(struct gmachine*, struct node_base*);
```
This function will add the given node to the G-machine's handle,
and return that same node. This way, we can wrap nodes in
a call to `gmachine_track`. We will talk about this
function's implementation later in the post.
This doesn't get us all the way to a working runtime, though:
right now, we still pass around `struct stack*` instead of
`struct gmachine*` everywhere. However, the whole point
of adding the `gmachine` struct was to store more data in it!
Surely we need that new data somewhere, and thus, we need to
use the `gmachine` struct for _some_ functions. What functions
_do_ need a whole `gmachine*`, and which ones only need
a `stack*`?
1. {{< sidenote "right" "ownership-note" "Clearly," >}}
This might not be clear. Maybe <em>pushing</em> onto a stack will
add a node to our GC handle, and so, we need to have access
to the handle in <code>stack_push</code>. The underlying
question is that of <em>ownership</em>: when we allocate
a node, which part of the program does it "belong" to?
The "owner" of the node should do the work of managing
when to free it or keep it. Since we already agreed to
create a <code>gmachine</code> struct to house the GC
handle, it makes sense that nodes are owned by the
G-machine. Thus, the assumption in functions like
<code>stack_push</code> is that the "owner" of the node
already took care of allocating and tracking it, and
<code>stack_push</code> itself shouldn't bother.
{{< /sidenote >}} `stack_push`, `stack_pop`, and similar functions
do not require a G-machine.
2. `stack_alloc` and `stack_pack` __do__ need a G-machine,
because they must allocate new nodes. Where the nodes
are allocated, we should add them to the GC handle.
3. Since they use `stack_alloc` and `stack_pack`,
generated functions also need a G-machine.
4. Since `unwind` calls the generated functions,
it must also receive a G-machine.
As far as stack functions go, we only _need_ to update
`stack_alloc` and `stack_pack`. Everything else
doesn't require new node allocations, and thus,
does not require the GC handle. However, this makes
our code rather ugly: we have a set of mostly `stack_*`
functions, followed suddenly by two `gmachine_*` functions.
In the interest of cleanliness, let's instead do the following:
1. Make all functions associated with G-machine rules (like
__Alloc__, __Update__, and so on) require a `gmachine*`. This
way, theres a correspondence between our code and the theory.
2. Leave the rest of the functions (`stack_push`, `stack_pop`,
etc.) as is. They are not G-machine specific, and don't
require a GC handle, so there's no need to touch them.
Let's make this change. We end up with the following
functions:
{{< codelines "C" "compiler/09/runtime.h" 56 84 >}}
For the majority of the changed functions, the
updates are
{{< sidenote "right" "cosmetic-note" "cosmetic." >}}
We must also update the LLVM/C++ declarations of
the affected functions: many of them now take a
<code>gmachine_ptr_type</code> instead of <code>stack_ptr_type</code>.
This change is not shown explicitly here (it is hard to do with our
growing code base), but it is nonetheless significant.
{{< /sidenote >}} The functions
that require more significant modifications are `gmachine_alloc`
and `gmachine_pack`. In both, we must now make a call to `gmachine_track`
to ensure that a newly allocated node will be garbage collected in the future.
The updated code for `gmachine_alloc` is:
{{< codelines "C" "compiler/09/runtime.c" 140 145 >}}
Correspondingly, the updated code for `gmachine_pack` is:
{{< codelines "C" "compiler/09/runtime.c" 147 162 >}}
Note that we've secretly made one more change. Instead of
allocating `sizeof(*data) * n` bytes of memory for
the array of packed nodes, we allocate `sizeof(*data) * (n + 1)`,
and set the last element to `NULL`. This will allow other
functions (which we will soon write) to know how many elements are packed inside
a `node_data` (effectively, we've added a `NULL` terminator).
We must change our compiler to keep it up to date with this change. Importantly,
it must know that a G-machine struct exists. To give it
this information, we add a new
`llvm::StructType*` called `gmachine_type` to the `llvm_context` class,
initialize it in the constructor, and set its body as follows:
{{< codelines "C++" "compiler/09/llvm_context.cpp" 21 26 >}}
The compiler must also know that generated functions now use the G-machine
struct rather than a stack struct:
{{< codelines "C++" "compiler/09/llvm_context.cpp" 19 19 >}}
Since we still use some functions that require a stack and not a G-machine,
we must have a way to get the stack from a G-machine. To do this,
we create a new `unwrap` function, which uses LLVM's GEP instruction
to get a pointer to the G-machine's stack field:
{{< codelines "C++" "compiler/09/llvm_context.cpp" 222 225 >}}
We use this function elsewhere, such `llvm_context::create_pop`:
{{< codelines "C++" "compiler/09/llvm_context.cpp" 176 179 >}}
Finally, we want to make sure our generated functions don't allocate
nodes without tracking them with the G-machine. To do so, we modify
all the `create_*` methods to require the G-machine function argument,
and update the functions themselves to call `gmachine_track`. For
example, here's `llvm_context::create_num`:
{{< codelines "C++" "compiler/09/llvm_context.cpp" 235 239 >}}
Of course, this requires us to add a new `create_track` method
to the `llvm_context`:
{{< codelines "C++" "compiler/09/llvm_context.cpp" 212 215 >}}
This is good. Let's now implement the actual mark-and-sweep algorithm
in `gmachine_gc`:
{{< codelines "C" "compiler/09/runtime.c" 186 204 >}}
In the code above, we first iterate through the stack,
calling `gc_visit_node` on every node that we encounter. The
assumption is that once `gc_visit_node` is done, every node
that _can_ be reached has its `gc_reachable` field set to 1,
and all the others have it set to 0.
Once we reach the end of the stack, we continue to the "sweep" phase,
iterating through the linked list of nodes (held in the G-machine
GC handle `gc_nodes`). For each node, if its `gc_reachable` flag
is not set, we remove it from the linked list, and call `free_node_direct`
on it. Otherwise (that is, if the flag __is__ set), we clear it,
so that the node can potentially be garbage collected in a future
invocation of `gmachine_gc`.
`gc_visit_node` recursively marks a node and its children as reachable:
{{< codelines "C" "compiler/09/runtime.c" 51 70 >}}
This is possible with the `node_data` nodes because of the change we
made to the `gmachine_pack` instruction earlier: now, the last element
of the "packed" array is `NULL`, telling `gc_visit_node` that it has
reached the end of the list of children.
`free_node_direct` performs a non-recursive deallocation of all
the resources held by a particular node. So far, this is only
needed for `node_data` nodes, since the arrays holding their children
are dynamically allocated. Thus, the code for the function is
pretty simple:
{{< codelines "C" "compiler/09/runtime.c" 45 49 >}}
### When to Collect
When should we run garbage collection? Initially, I tried
running it after every call to `unwind`. However, this
quickly proved impractical: the performance of all
the programs in the language decreased by a spectacular
amount. Programs like `works1.txt` and `works2.txt`
would take tens of seconds to complete.
Instead of this madness, let's settle for an approach
common to many garbage collectors. Let's __perform
garbage collection every time the amount of
memory we've allocated doubles__. Tracking when the
amount of allocated memory doubles is the purpose of
the `gc_node_count` and `gc_threshold` fields in the
`gmachine` struct. The former field tracks how many
nodes have been tracked by the garbage collector, and the
latter holds the number of nodes the G-machine must
reach before triggering garbage collection.
Since the G-machine is made aware of allocations
by a call to the `gmachine_track` function, this
is where we will attempt to perform garbage collection.
We end up with the following code:
{{< codelines "C++" "compiler/09/runtime.c" 171 184 >}}
When a node is added to the GC handle, we increment the `gc_node_count`
field. If the new value of this field exceeds the threshold,
we perform garbage collection. There are cases in which
this is fairly dangerous: for instance, `gmachine_pack` first
moves all packed nodes into an array, then allocates a `node_data`
node. This means that for a brief moment, the nodes stored
into the new data node are inaccessible from the stack,
and thus susceptible to garbage collection. To prevent
situations like this, we run `gc_visit_node` on the node
being tracked, marking it and its children as "reachable".
Finally, we set the next "free" threshold to double
the number of currently allocated nodes.
This is about as much as we need to do. The change in this
post was a major one, and required updating multiple files.
As always, you're welcome to check out [the compiler source
code for this post](https://dev.danilafe.com/Web-Projects/blog-static/src/branch/master/code/compiler/09).
To wrap up, let's evaluate our change.
To especially stress the compiler, I came up with a prime number
generator. Since booleans are not in the standard library, and
since it isn't possible to pattern match on numbers, my
only option was the use Peano encoding. This effectively
means that numbers are represented as linked lists,
which makes garbage collection all the more
important. The program is quite long, but you can
[find the entire code here](https://dev.danilafe.com/Web-Projects/blog-static/src/branch/master/code/compiler/09/examples/primes.txt).
When I ran the `primes` program compiled using the
previous version of the compiler using `time`, I
got the following output:
```
Maximum resident set size (kbytes): 935764
Minor (reclaiming a frame) page faults: 233642
```
In contrast, here is the output of `time` when running
the same program compiled with the new version of
the compiler:
```
Maximum resident set size (kbytes): 7448
Minor (reclaiming a frame) page faults: 1577
```
We have reduced maximum memory usage by a factor of
125, and the number of page faults by a factor of 148.
That seems pretty good!
With this success, we end today's post. As I mentioned
before, we're not done. The language is still clunky to use,
and can benefit from `let/in` expressions and __lambda functions__.
Furthermore, our language is currently monomorphic, and would
be much better with __polymorphism__. Finally, to make our language
capable of more-than-trivial work, we may want to implement
__Input/Output__ and __strings__. I hope to see you in future posts,
where we will implement these features!