Tag Archives: Functional Programming

Erlangers! USE LABELS! (aka “Stop Writing Punched-in-the-Face Code Blocks”)

Do you write lambdas directly inline in the argument list of various list functions or list comprehensions? Do you ever do it even though the fun itself, or the other arguments or return assignment/assertion for the call are too long and force you to scrunch that lambda’s definition up into an inline-multiline ball of wild shit? YOU DO? WTF?!?!? AHHHH!

First off, realize this makes you look like a douchebag for not being polite to other people or your future self whenever you do it. There is a big difference for the human reading between:

%%% From shitty_inline.erl

do_whatever(Keys, SomeParameter) ->
    lists:foreach(fun(K) -> case external_lookup(K) of
                  {ok, V} -> do_side_effecty_thing(V, SomeParameter);
                  {error, R} -> report_some_failure(R)
                end
          end, Keys
    ).

and

%%% From shitty_listcomp.erl

do_whatever(Keys, SomeParameter) ->
    [fun(K) -> case external_lookup(K) of
        {ok, V} -> do_side_effecty_thing(V, SomeParameter);
        {error, R} -> report_some_failure(R) end end(Key) || Key <- Keys],
    ok.

and

%%% From less_shitty_listcomp.erl

do_whatever(Keys, SomeParameter) ->
    ExecIfFound = fun(K) -> case external_lookup(K) of
            {ok, V} -> do_side_effecty_thing(V, SomeParameter);
            {error, R} -> report_some_failure(R)
        end
    end,
    [ExecIfFound(Key) || Key <- Keys],
    ok.

and

%%% From labeled_lambda.erl

do_whatever(Keys, SomeParameter) ->
    ExecIfFound =
        fun(Key) ->
            case external_lookup(Key) of
                {ok, Value}     -> do_side_effecty_thing(Value, SomeParameter);
                {error, Reason} -> report_some_failure(Reason)
            end
        end,
    lists:foreach(ExecIfFound, Keys).

and

%%% From isolated_functions.erl

-spec do_whatever(Keys, SomeParameter) -> ok
    when Keys          :: [some_kind_of_key()],
         SomeParameter :: term().

do_whatever(Keys, SomeParameter) ->
    ExecIfFound = fun(Key) -> maybe_do_stuff(Key, SomeParameter) end,
    lists:foreach(ExecIfFound, Keys).

maybe_do_stuff(Key, Param) ->
    case external_lookup(Key) of
        {ok, Value}     -> do_side_effecty_thing(Value, Param);
        {error, Reason} -> report_some_failure(Reason)
    end.

Which versions force your eyes to do less jumping around? How about which version lets you most naturally understand each component of the code independently? Which is more universal? What does code like this translate to after erlc has a go at it?

Are any of these difficult to read? No, of course not. Every version of this is pretty darn basic and common — you need a listy operation by require a closure over some in-scope state to make it work right, so you really do need a lambda instead of being able to look all suave with a fun some_function/1 type thing. So we agree, taken by itself, any version of this is easy to comprehend. But when you are reading through hundreds of these sort of things at once to understand wtf is going on in a project while also remembering a bunch of other shit code that is laying around and has side effects while trying to recall some detail of a standard while the phone is ringing… things change.

Do I really care which way you do it? In a toy case like this, no. In actual code I have to care about forever and ever — absolutely, yes I do. The fifth version is my definite preference, but the fourth will do just fine also.

(Or even the third, maybe. I tend to disagree with the semantic confusion of using a list comprehension to effect a loop over a list of values only for the side effects without returning a value – partly because this is semantically ambiguous, and also because whenever possible I like every expression of my code to either be an assignment or an assertion (so every line should normally have a = on it). In other words, use lists:foreach/2 in these cases, not a list comp. I especially disagree with using a listcomp when we the main utility of using a list comprehension is normally to achieve a closure over local state, but here we are just calling another closure — so semantic fail there, twice.)

But what about my lolspeed?!?

I don’t know, but let’s see. I’ve created five modules, based on the above examples:

  1. shitty_inline.erl
  2. shitty_listcomp.erl
  3. less_shitty_listcomp.erl
  4. labeled_lambda.erl
  5. isolated_functions.erl

These all call the same helpers that do basically nothing important other than having actual side effects when called (they call io:format/2). What we are interested in here is the generated assembler. What is the cost of introducing these labels that help the humans out VS leaving things all messy the way we imagine might be faster for the runtime?

It turns out that just like with using assignments to document your code, there is zero cost to label functions. For example, here is the assembler for shitty_inline.erl side-by-side with labeled_lambda.erl:

Oooh, look. The exact same stuff!

(This is a screenshot, a text file with the contents shown is here: label_example_comparison.txt)

See? All that annoying-to-read inline lambdaness buys you absolutely nothing. You’re not helping the compiler, you’re not helping the runtime, and you are hurting your future self and anyone you want to work with on the same code later. (Note: You can generate precompiler output with erlc -P and erlc -E, and assembler output with erlc -S. Here is the manpage. Play around with it a bit, BEAM and EVM are amazing platforms, wide open for exploration!)

So use labels.

As for execution speed… all of these perform basically the same, except for the last one, isolated_functions.erl. Here is the assembler for that one: isolated_functions.S. This outperforms the others, though to a relatively insignificant degree. Of course, it is only an “insignificant degree” until that part of the program is the most critical part of whatever your program does — then even a 10% difference may be a really huge win for you. In those cases it is worth it to refactor to test the speed of different representations against each version of the runtime you happen to be using — and all thoughts on mere style have to take a backseat. But this is never the case for the vast majority of our code.

(I’ve read reports in the past that indicate 99% of our performance bottlenecks tend to reside in less than 1% of our code by line count — but I can’t recall the names of any just now. If you happen to find a reference, let me know so I can update this little parenthetical blurb with some hard references.)

My point here is that breaking every lambda out into a separate named functions isn’t always worth it — sometimes an in-place lambda really is more idiomatic and easier to understand simply because you can see everything right there in the same function body. What you don’t want to see is multi-line lambdas squashed into argument lists that make things hard to read and give you the exact same result once compiled as labeling that lambda with a meaningful variable name on another line in the code and then referring to it where it is invoked later.

Pure Declarations in Erlang

Over the last year or so I’ve gone back and forth in my mind and in discussions with other Erlangers about type systems in Erlang, or rather, I’ve been going back and forth about its lack of one and the way Dialyzer acts as our bandaid in this area. Types are useful enough that we need Dialyzer, but the pursuit of functional puritanism gets insane enough that its simply not worth it in a language intended for real-world production use, especially in the messy, massively concurrent, let-it-crash, side-effecty, message-centric world of Erlang.

But… types and pure functions are still really useful and setting a goal of making as much of a program as possible into provable, bounded, typed, pure functions tends to result in easy to understand, test and maintain code. So there is obviously some stress here.

What I would like to do is add a semantic that the compiler (or Dialyzer, but would prefer this be a compiler check, tbh) be aware of what functions are pure and which are not. The way I would do this is by using a different “arrow”, in particular the Prolog-style declaration indicator: :-

[Edit after further discussion…] What I would like to do is add a directive that Dialyzer can interpret according to a simply purity rule. Adding this to Dialyzer makes more sense than putting it in the compiler — Dialyzer is already concerned with checking; the compiler is already concerned with compiling.

The directive would be -pure(Name/Arity) (a compliment to -spec). The rule would be very simple: only guard-permissible BIFs and other pure functions are legal from within the body of a pure function. This is basically just an extension of the current guard rule (actually, I wonder why this version isn’t already the guard rule… other than the fact that unless something like this is implemented the compiler itself wouldn’t have any way of checking for purity, so currently it must blindly accept a handful of BIFs known to be pure and nothing else).

For example, here is a pure function in Erlang, but neither the compiler nor Dialyzer can currently know this:

-spec increment(integer()) -> integer().
increment(A) ->
    A + 1.

Here is the same function declared to be pure:

-pure(increment/1).
-spec increment(integer()) -> integer().
increment(A) ->
    A + 1.

Pretty simple change.

“ZOMG! The whold standard library!” And yes, this is true — the whole thing is out. Except that the most important bits of it (the data structures like lists, dict, maps, etc.) could be easily converted to pure functions with little more than changing -> to :- adding a single line to the definition.

Any pure function could be strongly typed and Dialyzer could adhere to strong types instead of looser “success types” in these cases. Some code that is currently written to take an input from a side-effecty function, pass it through a chain of non-returning and possible side-effecty functions as a way to process or act on the value, and ultimately then call some side-effecty final output function would instead change to a form where the side-effects are limited to a single function that does both the input and output, and all the processing in-between would be done in pure functions.

This makes code inherently more testable. In the first case any test of the code is essentially an integration test — as to really know how things will work requires knowing at least one step into side effects (and very often we litter our code with side-effects without a second thought, something prayer-style monadisms assist greatly with). In the second case, though, the majority of the program is pure and independently testable, with no passthrough chain of values that have to be checked. I would argue that in many cases such passthrough is either totally unnecessary, or when it really is beneficial passing through in functions is not as useful as passing through in processes — that is to say, that when transformational passthrough is desired it is easier to reason about an Erlang program as a series of signal transformations over a message stream than a chain of arbitrarily side-effecty function calls that collectively make a recursive tail-call (and that’s a whole different ball of wax, totally orthogonal to the issue of functional purity).

Consider what we can know about a basic receive loop:

loop(State) ->
  receive
    {process, Data} ->
        {ok, NewState} = do_process(Data, State),
        loop(NewState);
    {send_state, From} ->
        From ! State,
        loop(State);
    halt ->
        exit(normal);
    Message ->
        ok = log(unexpected, Unexpected),
        loop(State)
  end.

-spec do_process(term(), #state{}) -> {ok, #state{}} | {error, term()}.
do_process(Data, State) :-
    % Do purely functional stuff
    Result.

-spec log(category(), term()) -> ok.
log(Cat, Data) ->
    % Do side-effecty stuff
    ok.

We can see exactly what cases result in another iteration and which don’t. Compare that with this:

loop(State) ->
  receive
    {process, Data}     -> do_process(Data, State);
    {send_state, Asker} -> tell(Asker, State);
    quit                -> exit(normal);
    Message             -> handle_unexpected(Message, State)
  end.

do_process(Data, State) ->
    % Do stuff.
    % Mutually recursive tail call; no return type.
    loop(NewState).

tell(Asker, State) ->
    % Do stuff; another tail call...
    loop(State).

handle_unexpected(Message, State) ->
    ok = log(unexpected, Message),
    % Do whatever else; end with tail call to loop/1...
    loop(NewState).

I like the way the code lines up visually in the last version of loop/1, sure, but I can’t know nearly as much about it as a process. Both styles are common, but the former lends itself to readability and testing while the latter is a real mixed bag. Pure functions would keep us conscious of what we are doing and commit our minds in ways to the definite-return form of code where our pure functions and our side-effecty ones are clearly separated. Of course, anyone could also continue to write Erlang any old way they used to — this would just be one more tool to assist with breaking complexity down and adding some compile-time checking in large systems.

I would love to see this sort of thing happen within Erlang eventually, but I am pretty certain that its the sort of change that won’t happen if I don’t roll up my sleeves and do it myself. We’ve got bigger fish to fry, in my opinion, (and I’ve certainly got higher priorities personally right now!) but perhaps someday…

Iterators? We Don’t NEED No Stinking Iterators!

Every so often a request for “implementation of iterators for maps” over hashes/maps/dicts or some other K-V data structure appears on mailing list for a functional langauge. I’ve spent years making heavy use of iterators in imperative languages, and the way they fit into Python is really great. For Python. I totally understand where some of these folks are coming from, they just don’t realize that functional languages are not where they came from.

So… “Is this post the result of some actual event”? Yeah, you got me. It is. On the erlang-questions mailing list someone asked “Are maps ever going to get an iterator?” Again.

Erlang is definitely not Kansas, but people thinking either that it is or (more dangerously) that it should be and then trying to influence the maintainers to make it that way (and then the powers-that-be getting in a panic over “market share” and doing horrible things to the language…) worries me a bit.

There is no faster way to paint a functional language into a corner than to try making it occasionally imperative. Conversely, consider the syntactic corner C++ and Java have painted themselves into by trying to include functional features as after-thoughts where they really didn’t belong.

(I know, I know, death-by-kitchen-sink is a proud C++ tradition. It is becoming one for Java. Even though I hate Java there is no sense in making it worse by cluttering its syntax and littering it with gotchas and newbie-unfriendly readability landmines in the interest of providing features few Java coders understand the point of, especially when the whole concept of state management in a bondage-and-discipline OOP language like Java is to keep everything in structs with legs (not anonymous closures over state that is temporarily in scope…). The lack of such problems were previously one of the main points that favored Java over C++… well, that and actual encapsulation. Hopefully Rust and D can resist this temptation.)

This frustrates me. It is almost as if instead of picking a tool that matches a given job, people learn one tool and then try over time to make a super-powered Swiss Army knife of it. This never turns out well. The result is more Frankenstein’s Monster than Swiss Army knife and in the best case it winds up being hard to learn, confusing to document and crap at everything.

What’s worse, people assume that the first tool they learned well is the standard by which everything else should be judged (if so, then why are they learning anything else?). It follows, then, that if a newly studied LangX does not have a feature of previously used LangY then it must be introduced because it is “missing”. (I do admit, though, to wishing other languages had pattern matching in function heads… but I don’t bring this up on mailing lists as if its a “missing feature”; I do, however, cackle insanely when overloading is compared with matching.)

Let’s say we did include iterators for maps into Erlang — whatever an “iterator” is supposed to mean in a list-are-conses type functional language. What would that enable?

-spec foreach(fun(), map()) -> ok.

That sort of looks pointless. Its exactly the same as lists:foreach(Fun, maps:to_list(Map)) or maybe lists:foreach(Fun, maps:values(Map)). Without knowing whether we’re trying to build a new map based on the old one or get some side effect out of Fun then its hard to know what the point is.

Maybe:

-spec map(fun(), OldMap :: map()) -> {ok, NewMap :: map()}.

But… wait, isn’t that just maps:map/2 all over again?

I think I know where this is going, though. These people really wish maps were ordered dictionaries, because they want keys to be ordered. So they want something like this:

-spec side_effects_in_order_dammit(fun(), map()) -> ok.
side_effects_in_order_dammit(F, M) ->
    Ordered = [{K, maps:get(K, M)} || K <- lists:sort(maps:keys(M))],
    ok = lists:foreach(F, Ordered).

But wait, what order should the keys be in, anyway?

This is a slow, steady march to insanity. “Give me iterators” begets “Let’s have ordered maps” begets “Let’s have ordered iterators for maps” and so on, and eventually you wind up with most of the Book of Genesis in the Devil’s Bible of Previously Decent Functional Languages. All the while, totally forgetting that these things already exist in another form. There are more data structures than just maps for a reason.

This just gets ridiculous, and it isn’t even what hashes are about to begin with.

Why OTP? Why “pure” and not “raw” Erlang?

I’ve been working on my little instructional project for the last few days and today finally got around to putting a very minimal, but working, chat system into the ErlMUD “scaffolding” code. (The commit with original comment is here. Note the date. By the time this post makes its way into Google things will probably be a lot different.)

I commented the commit on GitHub, but felt it was significant enough to reproduce here (lightly edited and linked). The state of the “raw Erlang” ErlMUD codebase as of this commit is significant because it clearly demonstrates the need for many Erlang community conventions, and even more significantly why OTP was written in the first place. Not only does it demonstrate the need for them, the non-trivial nature of the problem being handled has incidentally given rise to some very clear patterns which are already recognizable as proto-OTP usage patterns (without the important detail of having written any behaviors just yet). Here is the commit comment:

Originally chanman had been written to monitor, but not link or trap exits of channel processes [example]. At first glance this appears acceptable, after all the chanman doesn’t have any need to restart channels since they are supposed to die when they hit zero participants, and upon death the participant count winds up being zero.

But this assumes that the chanman itself will never die. This is always a faulty assumption. As a user it might be mildly inconvenient to suddenly be kicked from all channels, but it isn’t unusual for chat services to hiccup and it is easy to re-join whatever died. Resource exhaustion and an inconsistent channel registry is worse. If orphaned channels are left lying about the output of \list can never match reality, and identically named ones can be created in ways that don’t make sense. Even a trivial chat service with a tiny codebase like this can wind up with system partitions and inconsistent states (oh no!).

All channels crashing with the chanman might suck a little, but letting the server get to a corrupted state is unrecoverable without a restart. That requires taking the game and everything else down with it just because the chat service had a hiccup. This is totally unacceptable. Here we have one of the most important examples of why supervision trees matter: they create a direct chain of command, and enforce a no-orphan policy by annihilation. Notice that I have been writing “managers” not “supervisors” so far. This is to force me to (re)discover the utility of separating the concepts of process supervision and resource management (they are not the same thing, as we will see later).

Now that most of the “scaffolding” bits have been written in raw Erlang it is a good time to sit back and check out just how much repetitive code has been popping up all over the place. The repetitions aren’t resulting from some mandatory framework or environment boilerplate — I’m deliberately making an effort to write really “low level” Erlang, so low that there are no system or framework imposed patterns — they are resulting from the basic, natural fact that service workers form constellations of similarly defined processes and supervision trees provide one of the only known ways to guarantee fallback to a known state throughout the entire system without resorting to global restarts.

Another very important thing to notice is how inconsistent my off-the-cuff implementation of several of these patterns has been. Sometimes a loop has a single State variable that wraps the state of a service, sometimes bits are split out, sometimes it was one way to begin with and switched a few commits ago (especially once the argument list grew long enough to annoy me when typing). Some code_change/N functions have flipped back and forth along with this, and that required hand tweaking code that really could have been easier had every loop accepted a single wrapped State (or at least some standard structure that didn’t change every time I added something to the main loop without messing with code_change). Some places I start with a monitor and wind up with a link or vice versa, etc.

While the proper selection of OTP elements is more an art than a science in many cases, having commonly used components of a known utility already grouped together avoids the need for all this dancing about in code to figure out just what I want to do. I suppose the most damning point about all this is that none of the code I’ve been flip-flopping on has been essential to the actual problem I’m trying to solve. I didn’t set out to write a bunch of monitor or link or registry management code. The only message handler I care about is the one that sends a chat message to the right people. Very little of my code has been about solving that particular problem, and instead I consumed a few hours thinking through how I want the system to support itself, and spent very little time actually dealing with the problem I wanted to treat. Of course, writing this sort of thing without the help of any external libraries in any other language or environment I can think of would have been much more difficult, but the commit history today is a very strong case for making an effort to extract the common patterns used and isolate them from the actual problem solving bits.

The final thing to note is something I commented on a few commits ago, which is just how confusing tracing message passage can be when not using module interface functions. The send and receive locations are distant in the code, so checking for where things are sent from and where they are going to is a bit of a trick in the more complex cases (and fortunately none of this has been particularly complex, or I probably would have needed to write interface functions just to get anything done). One of the best things about using interface functions is the ability to glance at them for type information while working on other modules, use tools like Dialyzer (which we won’t get into we get into “pure Erlang” in v0.2), and easily grep or let Emacs or an IDE find calling sites for you. This is nearly impossible with pure ad hoc messaging. Ad hoc messaging is fine when writing a stub or two to test a concept, but anything beyond that starts getting very hard to keep track of, because the locations significant to the message protocol are both scattered about the code (seemingly at random) and can’t be defined by any typing tools.

I think this code proves three things:

  • Raw Erlang is amazingly quick for hacking things together that are more difficult to get right in other languages, even when writing the “robust” bits and scaffolding without the assistance of external libraries or applications. I wrote a robust chat system this afternoon that can be “hot” updated, from scratch, all by hand, with no framework code — that’s sort of amazing. But doing it sucked more than it needed to since I deliberately avoided adhering to most coding standards, but it was still possible and relatively quick. I wouldn’t want to have to maintain this two months from now, though — and that’s the real sticking point if you want to write production code.
  • Code convention recommendations from folks like Joe Armstrong (who actually does a good bit of by-hand, pure Erlang server writing — but is usually rather specific about how he does it), and standard set utilities like OTP exists for an obvious reason. Just look at the mess I’ve created!
  • Deployment clearly requires a better solution than this. We won’t touch on this issue for a while yet, but seriously, how in the hell would you automate deployment of a scattering of files like this?

A Technically Inaccurate Explanation of Monads

I’ve come across a multitude of technically inaccurate explanations of monads on the web, all intending to explain them in simple terms to FP newbies, most revolving around their use in Haskell. They all suck. This is mine. It also sucks, but I hope it sucks less.

[NOTE: I have no intent here to explain the mathematical concept of monads, the semantic gap between the way the term is used in set theory and in some flavors of functional programming, or any of that high-minded magic. My purpose is to explain what a monad is in terms of a computing utility to a functional programmer. This is a discussion about the sort of tool it is, not the theory behind that tool.]


Imagine using a purely functional language where side effects are verboten and we can’t do IO or anything else useful because of this. The host environment can clearly do IO just fine, otherwise our environment couldn’t do things like read memory locations (or our code) and our program would be useless. So it is obvious the host environment can do things externally that our program itself cannot do directly. This does not prevent us from describing what we wish it would do on behalf of our program, however.

In this way the host environment is sort of like a pantheon of gods and our programs are mere mortal blips of disembodied consciousness — capable of thought, desire and expression but powerless to touch the physical world in any way. All we can do is express our desires as regard the results of our thoughts and appeal to the gods to pity us and take action in accordance with our desires. Whether they take actions on our behalf is entirely up to them.*

With this in mind…
Imagine a function written in SomeLanguage:

int f(x): return x

It takes an integer and returns an integer. So what? The system doesn’t do anything with it so it is practically useless.

Now imagine a wrapper function:

tuple w(int x):
    tuple t = (f(x), "Please put this in STDOUT")
    return t

So w() has taken the output of f() and wrapped it in a tuple that contains the value returned by f() and a prayer to the system gods to “Please put this in STDOUT”. Pretty straight forward. Now the system gods can do whatever they want with it, but our language itself can’t — because talking to STDOUT would be a side effect and that’s strictly forbidden on Planet Functon. What we can do, however, is pray that the gods take mercy on us and act according to our wishes as regard the value that accompanies the prayer.

If this is the best model of a monad you can muster at the moment, then just stop here. This model is sufficient to make the concept of monads useful to you as you write programs that do useful work. (Which is the whole point. Unless you’re an academic, in which case your point is to write a lengthy article in a peer reviewed journal in which your explanation of monads is prefaced with a demonstration of your deep knowledge of set theory and type theory and esoteric discussion of things like monoids and thus make it appear that unfamiliarity with these subjects precludes the ability to use monads in a useful way in functional programs.)

But there are a few unresolved issues above, most of which I won’t address below, but the glaring issue of typing is relevant… (The other glaring issue of the undefined and imaginary syntax of SomeLanguage won’t be addressed at all.)

The type tuple is pretty ambiguous for this use (we could be talking about coordinates or relational values or immutable strings or whatever). How are the gods to know that we have a prayer for them? Should they inspect every tuple, or even every value we dream up, just checking for a “prayer” type? Of course not, they are busy doing immaculate things. We need a more clear signal.

One way to clear this up is to make a function that takes a function, its arguments and a request specification and returns a type prayer whose existence is itself a magical signal to get the attention of the gods. So ultimately a prayer is a type whose definition is a combined value composed of a thingy plus a prayer request regarding that thingy:

prayer p(function z, list l, request r):
    return (z(*l), r())

And then define an action of type request and rewrite w() in a way that returns a prayer:

request q = "Print to STDOUT"

prayer w(int x):
    return p(f, x, q)

Here we have defined a request for the system to perform, passed a reference/pointer/label to the function f() along with its arguments to the prayer maker function p(), which has executed f() along with its argument and returned a bundle of type prayer that contains the original integer return value along with a request to the system gods to do something regarding the bundled value.

Note that in Haskell it is common to define the underlying function (represented here by f()) and its monadic version (represented here as w()) separately. I suppose this isn’t strictly necessary — one could define monads in terms of lambdas — but this is the way things are done.

So we have specified a side effect, but we are only praying that the system takes an action based on our specification. Nothing more. Obviously I’m glossing over the details of how a request object itself is actually defined, but this is the general idea behind how monads are used to write programs in purely functional languages that have side effects.

An interesting consequence of this idea of a program specifying actions instead of actually taking them is that it is now trivial to write a host environment that deliberately ignores all prayers. In this way writing a host environment purely for the purpose of examining the behavior is also trivial. Its the ultimate sandboxing tool. It is equally easy to write a host environment that selectively observes requests, taking only some and ignoring all others, or ignoring some and taking all others.

I believe the abundance of confusing monad explanations to be a side effect of the Haskell community being disproportionately populated with mathematicians, type theorists and set theorists (“for real” or self-educated) and their explanations assume a knowledge base and vocabulary that is foreign and intimidating to most newcomers. The Clojure community doesn’t seem to have this problem, at least not as deeply.

[*It is easy to reverse this metaphor, of course, and imagine that we are uncorporeal gods, capable of thought and expression of our command to the slavish host to do whatever we specify. But I like the “program as mortals, host as gods” way better, because it extends to include the very real case of writing a test host that takes no action and merely observes (or even checks for the correctness of) the program’s behavior.]