Lambda the Ultimate

I'm not exactly an a domain expert on the human mind, and don't mean to start too much of an argument (or make unsupported assertions), but it doesn't much matter how people think when they're achieving a goal.

Programmers aren't doing the work; they're giving instructions. If you ask pretty much anyone how to do something, you'll get a sequential set of instructions. 'Do A, then B, if X then Y...'. Maybe that's because instructions are always sent/received between people serially (even if we do think more parallel-like), and people need to adapt to giving instructions to a computer. I don't know.

I've played the Peanut Butter Sandwich and Teach Me to Smoke games. I don't believe humans, even programmers, normally instruct one another in terms of sequential steps. If they do, they're really awful at it, and a lot of careful refinement is necessary to get it right.

When I'm verbally providing instructions, and I haven't done so before (such that the explanation becomes rote), I'll tend to jump around in time ("oh, and before you do Y, you need to do X") or between tasks. It will take me sitting down and really thinking about it, perhaps with pen and paper, before the ordering of goals as I express them will match the order in which they must be accomplished.

I hypothesize that our natural tendency is to instruct using subgoals, constraints, and contingencies that will effectively achieve a greater goal - i.e. we discuss 'strategies'. You say I'll get a sequential set of instructions, but I posit I will receive a loosely ordered declarative mishmash. This is something we could test, quite surreptitiously.

If that is how we communicate, then we would be served well by some variation of concurrent constraint programming (perhaps a fuzzy, heuristic one with probabilities and priorities) rather than by imperative. This way we could eschew the undesirable communication step of organizing our code in the temporal dimension.

A lot of things happen in parallel (hierarchically). You get some strange phenomena if the corpus callosum connecting your hemispheres get cut: one side may process something and cause a reaction (like laughing) and the other won't understand why.

However... this is all pretty low level. We're (typically) interested in the cognitive side of things. Story telling is an important ability and a good explanation for a lot of thought processes. If you lost your keys, you'll replay what you did before to find them. Why do you stay away from a ledge? Because you imagine yourself walking up to it and falling off.

Sequential thinking clearly isn't the only thing we do (e.g., association is pervasive). I think both are important: I've been wanting to get into PLs for BCIs, and supporting both parallel/subconscious and sequential/directed/conscious processes seems important. I haven't looked at this for awhile, but it's fascinating :)

Edit: I had meant to add this before, but, of perhaps most interest to us, telling a story is similar to a good proof -- you try not to jump around (even though you can)

Seems to me, when we envision how something happens, we naturally focus in on what's going on in one place at a time, as if we were an observer who could only be looking at one place at a time — that being how we ourselves experience reality.

I get the point about the peanut butter sandwich game, but to take the steps literally/pedantically is closer to programming without the benefit of existing libraries. People assume/imply quite a bit while giving instructions because they expect a common basis for that refinement. People are really awful at spelling out the elemental steps for doing things. I don't particularly see that awfulness as a failing of imperative instruction giving as much as an example how humans will abstract away steps that are seen as common knowledge.

Still, you are probably right as I think about it; the declarative mishmash is likely what you'll get for most non-trivial tasks.

Agreed that constraint programming is more natural than imperative. That is what I loved so much in Lustre at my engineering school. But I note this flavour of constraint programming has a temporal element (pre), which is what prevents Lustre programs from degrading in a impenetrable mess. In my opinion any generally useful and usable programming language needs to express sequentiality.

I agree. We need the ability to express sequencing and other ad-hoc workflows (e.g. do I before E except after C). But we don't need sequential semantics to be implicitly inflicted upon us by our syntax (at least, without our choosing to make it so).

I call a language 'declarative' to the extent it achieves commutativity, associativity, and idempotence in its syntax. I would say I want a declarative language. Constraint programming is a powerful model, but not very compositional. I would not want it for general purpose use. But there are many declarative languages that aren't about expressing and solving a system of constraints.