Finite | Finite is a simple , pure Swift finite state machine

I think you might be slightly overcomplicating things. Ideally, you'd just want a single key drawing method for the whole layer. However, because you're using a Stat to do the majority of calculations, this becomes hairy to implement. In my answer, I'm avoiding this.

Let's say I'd want to use a geom-only implementation of such a layer. I can make the following (simplified) class/constructor pair. Below, I haven't bothered width_scale or height_scale parameters, just for simplicity.

Your env is python3 and pip on mac is python2. I think. Try and use pip3 for the install or run your env in python2. Might be using different python verions.

Laziness to the rescue. We can recursively define a list of all the sub-automata, such that their transitions index into that same list:

Here are a few possible alternative approaches:

• Define your function recursively, without ever trying to inspect the full list but only the needed prefix.

• Start by filtering the list so to keep only the elements you want to count. Then, use drop (n-1) xs to drop n-1 elements (if any), and check if the resulting list is not empty (use null). Note that dropping more elements than those in the list is not an error, and it will result in an empty list.

What you're asking about ("get[ing] the last element of a lazy but finite Seq … while keeping the original Seq lazy") isn't possible. I don't mean that it's not possible with Raku – I mean that, in principle, it's not possible for any language that defines "laziness" the way Raku does with, for example, the is-lazy method.

If particular, when a Seq is lazy in Raku, that "means that [the Seq's] values are computed on demand and stored for later use." Additionally, one of the defining features of a lazy iterable is that it cannot know its own length while remaining lazy – that's why calling .elems on a lazy iterable throws an error:

The answer to both questions 1 and 2 is to use np.nanmean to ignore the nans in the data. The regression you link to was a bug that I inadvertently introduced and then fixed after it was raised. I'm not sure why you have SciPy 1.5.2 in your environment, it looks like 1.5.4 is the latest 1.5.X version so you probably want to update the environment you're using. However, that backport was applied to version 1.5.0 release versions so there should not be an issue on those versions if you have the latest.

Also, I set this up with scipy version 1.7.3 and that also works as intended for me. Here are snippets.

Version 1.5.4

(2) terminal algebras define codatatypes.

This is not right, codatatypes are terminal coalgebras. For your T functor, a coalgebra is a type x together with f :: x -> T x. A T-coalgebra morphism between (x1, f1) and (x2, f2) is a g :: x1 -> x2 such that fmap g . f1 = f2 . g. Using this definition, the terminal T-algebra defines the possibly infinite lists (so-called "colists"), and the terminality is witnessed by the unfold function:

Yes, it can be. Here's an example:

The problem seems a bit overwhelming: infinitely many infinite mazes, such that we can restrict ourselves to a multitude of different bounds (say, if we wanted a roughly 1 million x 1 million square) and still have unique paths between any two spaces (and your other conditions). Let's break this down into smaller pieces.

Suppose we could construct a 7 by 7 square maze-block, and were able to make a border of walls around it, with one or two gates on this border where we wanted. Then all we'd have to do is connect these square blocks in a spiral: a central square with one gate at the top, and a counterclockwise spiral of blocks with two gates each, in the direction of the spiral:

(Each numbered box is a 7x7 maze)

There's two general cases:

• 'Straight' pieces, where the two gates are on opposite sides, and
• 'Corner' pieces, where the spiral turns and gates are on adjacent sides.

We want to make these pieces generic, so we can mix and match mazes and have them fit together. To do this, we'll use this template:

1. Border Rule: The bottom and left sides of each square are all walls, except in the center of each side.
2. Free space Rule: Unless required by rules 1 or 3, no walls are allowed in the top and right sides of a maze square.
3. Gate Rule: Where two mazes meet, if the meeting is part of the spiral, both center sides will be open (in other words, crossings happen in the center of the borders). Otherwise, the maze which is below or to the left of the other shall have a wall in the center of this border.

That's a lot, so let's see an example. Here we have a template for a 'straight' horizontal connector, highlighted in blue (all mazes are 7 by 7). X means wall, O means required to be open (a crossing point/open gate between two mazes). Red X's are the border from rule 1, purple X's are blocked gates from rule 3.

The center 5 by 5 of each maze is customizable. We must ensure that there are no inaccessible squares or equal 2x2 within our maze only, since the rules above guarantee this is true where mazes meet.

One possible maze to fit the above template (there are many):

For an example of a corner piece:

I've similarly drawn examples of each possible connection to make sure it's always possible: there are many possible ways to do this for each piece type (including the special center piece).

Now, for how to generate infinitely many infinite mazes based on a seed. Suppose you created at least 2 examples of each connection piece (there are 2 straight connectors and 4 corners), although you can just make one of each and reflect it. (Really you only need 2 different examples of one connection type.)

Given any seed binary string, e.g. 10110, let this denote our choices of which example piece to use while we make the maze spiral, counting up as in the first picture. A '0' means means use our 1st example for this connector; a '1' means we use the second. You can then repeat this/extend the binary string infinitely (10110 10110 ...). Since this is periodic, we can, using some math, figure out the piece type at any point in the sequence.

I've left out the math for the pattern of connection types: this is easy to work out for a counterclockwise spiral. Given this pattern, and a convention that the point x,y = (0,0) is the bottom left corner of the spiral-start-maze-block, you can work out 'wall or space' for arbitrary x and y. This maze is infinite: you can also restrict the borders to any full odd square of mazes in the spiral, i.e. (7*(2n+1))^2 cells for positive n.

This framework pattern for a maze is customizable, but not very difficult to solve, as the regularity means you only need to solve it locally. There's nothing special about 7; any odd number at least 7 should work equally well with the same rules, if you want to make local maze blocks larger and more complex.