The Al Jazari 2 bots currently have six basic actions – move forward/backwards, turn 90 degrees left or right, pick up the block underneath them or drop the block to the space they are currently sitting on. Given these instructions, how do we procedurally build pyramids (of any given size) like this in their minecraft-esque world?

1. A pyramid can be built as a series of plateaus layered on top of each other, the plateaus can be built from material mined from nearby:

2. A single plateau can be built as a series of single block wide ridges next to each other, mined from a series of trenches. This is an example ridge/trench of size 3:

3. We need a gap between the ridge and the trench in order to place the plateau in the correct place in the pyramid (also the bots can only climb a single block at a time, otherwise they get stuck).

So in order to build a complete pyramid, we write the code to build a ridge/trench of any size and figure out the steps in-between to get the robot into the right position for the next one. The simplest ridge/trench is a single block long, so lets try writing some code to do that:

The lambda, and bot-sequence etc are scheme code required to get the bot language working, we’re just interested in the contents of the “seq”. After running these instructions we’re in the right place for the next block. Note that the majority of the actions are involved with positioning the bot after doing it’s work. To place the next cube we copy the code and add some more ‘forward’s (as we have to travel a bit further going back and forth):

This is already getting pretty long – we could do with a way to do repetition, so I’ve added a ‘repeat’ form to the language which takes a count, a name bound to the current iteration number (like a ‘for’ loop) and a list of instructions. This is the complete ridge/trench definition for any size, including gaps of any size:

The majority of the code is the maths to get the bot picking up and placing blocks further and further apart including the gap parameter. When collapsed into a function and run we get this:

With the bot ending up in the same place as it started. In order to create a square plateau we call this function, move sideways and repeat, and then move back to where we started again when we’re done:

Going from a plateau function to a pyramid is even shorter, and involves moving inwards diagonally and building smaller plateaus each time. Of course it also mines out a negative pyramid at the same time:

Here is a time lapse of a massive 8×8 pyramid being built, the code ‘compiles’ to 3224 low level instructions:

So this is a kind of programming that encourages solving problems through composition of abstractions – from the low level instructions, simple loops, primitive building constructs, up to complete structures. I’m not sure why in educational languages such as Scratch this is somehow sidelined (interestingly it’s not in Logo, it’s predecessor). Whether this is due to the ubiquity of imperative programming that leads to a focus on manipulation of state, or this kind of programming being considered as too advanced – but for me it’s fundamental, and I’m pretty sure it wouldn’t be that challenging for the kids in the CodeClub I’m running either.