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𝟘𝟠·
The separation of church and state protects our religious freedom, perhaps the most important principle America was founded upon. Extremists have been attacking that
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freedom for almost two centuries, eroding our right to think for ourselves. This administrations pursuit of Project 2025's goals have amplified those attacks.
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Whatever the reasons for war with Iran, this administration is using it as an oppurtinity to turn our military into an unconstitutional crusader army. But there are
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organizations fighting to preserve these freedoms and one of the most important is Americans United for Separation of Church and State. the-bonfire
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𝟘𝟟·
coding Ugh. Struggling to extend ideas from the AC-3 algorithm to a complete finite Constraint Satisfaction Solver without resorting to direct search. The reason is
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my interest in symbolic approaches which I hope to apply to very large problems and even infinite domains. It may not be doable, but for the time being I've been
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playing with generalizing the notion of variable in AC-3 to potentially overlapping variable vectors.
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AC-3 prunes away at an explicit representation of each variable's range by eliminating values which are not consistent with all constraints. When a the range of a
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variable is reduced, the constraints it participates are re-examined in turn, possibly reducing the range of one or more other variables. For the AC-3 algorithm to be
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helpful, the primary constraints are local, applying only to a subset of variables. The constraints can be locally but not globally satisfied when AC-3 terminates.
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Variables can be combined - a vector variable with a range of vectors; explicit storage of those compound ranges can be similarly pruned, extending the AC-3
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algorithm. The approach to chosing combinations for the lower end of time and space requirements is what I'm up against.
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𝟘𝟙·
Purpose is a profound and relevant concern... the-bonfire
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𝟚𝟜·
the-bonfire An open message to the American legislature: it is past time to step forward with Constitutional Amendments that will restore, preserve, and enhance
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honesty, civility and rationality in American governance. These qualities are the true measures of any Nation's greatness.
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𝟚𝟛·
In an interview, Hany Farid discusses taking action... the-bonfire
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𝟙𝟟·
logic I have been loking at Sudoku puzzles and results posted with a class assignment on CSPs from UC Davis, and decided to revamp my ⟪Silver⟫ solver. Input
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⟪Sapphire⟫ assertions will be evaluated, analyzed, and simplified to identify variables and their domains, but from there I'll start on incrementally reducing
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variable domains, using an AC-3 like strategy extended to assertions which relate increasingly larger groups of variables.
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𝟙𝟜·
logic It looks like my CSP solver core gets as far as the AC-3 algorithm, but really, really slowly. While still maintaining symbolic elements in the ⟪Silver⟫ solver,
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I can package the more efficient AC-3 algorithm as a "resolution" step. With better management of initial and added assertions, I should have a decent framework.
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𝟙𝟜·
coding Periodically, I tell myself I'm going to alternate exploratory coding (aka hacking) with a phase of refactoring toward a clear design (aka cleanup). The
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problem is the clear design phase may never happen - it's too easy to be satisfied with code that passes the current testing, however informal. On the other hand,
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it's easy to overcommit to a clear, elegant design, and if it doesn't meet some of the goals set for the project, it can be a major issue.
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I'm here again, thinking my solo recreational coding would be more fun if I took time to consolidate what I've learned into a good design. Process options are plenty,
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but I probably can't master the discipline of most - e.g. separate branches for exploratory phases seems heavy handed on a solo project. Alternating priorities always
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feels like the best thing to try, but I usually can't stick to it - maybe that ADHD diagnosis isn't so far off...
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Of course, AI assistance is becoming standard practice, and beyond quickly finding simple mistakes, it can refactor efficiently and even take part in a friendly chat
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about what the plan is. The increases in productivity, even if human programmers end up only in a code review role, is hard to resist in business.
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But I'm programming because I enjoy it. Algorithmic assistance is great, as long as I could have a hope of understanding the algorithms being used. Maybe I could
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figure out how LLM's work, but the current systems are massive, remote black box servers - which isn't part of the fun for me. The fun is opening the black boxes and
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figuring out what's going on inside.
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𝟙𝟘·
To better understand why I seemed to be getting so much wrong about AI... the-bonfire
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𝟘𝟡·
I've posted online in a few forums about AI, and I wish I could just retract it all... the-bonfire
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𝟘𝟞·
coding Woof! Slow progress... ⟪Sapphire⟫ has both logic and domain variables - a named value which may be left unspecified, given a value as assertions are simplified
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and resolved. Both ‘x=3’ and ‘3=x’ mean the same thing - as an assertion it is resolved in ⟪Silver⟫ if ‘x’ evaluates to 3, but if something else, a contradiction is
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flagged. If x has no value, ⟪Silver⟫ resolves the assertion by assigning 3 to x. For finite problems, functions and relations can be treated as domain or logic
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variable spaces, respectively. To dig myself out from under earlier hacks, I'm rewriting things around what I'm calling ‘free order variables’ for now, which are just
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⟨key table⟩ pairs, replacing constrained expressions with, in theory at least, nested function calls...
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𝟘𝟝·
Christian Nationalism is the new face of the KKK... the-bonfire
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𝟘𝟛·
I just learned about the beautiful discovery of Pentagonal tilings by Marjorie Rice. Doris Schattsneider encouraged Rice to present her work at the MAA - notable only
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because I met her as part of The Visual Geometry Project. Maybe I can connect ⟪Sapphire⟫ back to my early life through geometry!
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𝟘𝟙·
It might be my unfathomably old age of 57, but time flies like a peregrine falcon! Soon I'll get started on my plans for January... For now I'm still trundling along
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on first class constraints, and at this point, I'm not sure it's a good idea. It's probably time to read up on research and prior software (from the 1970's). At least
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I'm still living and learning.
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𝟚𝟡·
I left Stack Overflow because, like all social media-ish sites, it triggered PTSD from going to high school in the the 1980s. My eyes prefer ‘Dark Mode’ on emissive
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displays and the highest rated answer here shares a javascript one-liner in a bookmark that tweaks the pdf viewer object to invert the pdf image. I didn't even know
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‘bookmarklets’ were a thing!
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𝟚𝟟·
logic In trying to add expressive set comprehensions to ⟪Sapphire⟫, it's hard to avoid Russell's Paradox. Expressed in ⟪Sapphire⟫ extended with unrestricted
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quantifiers it would be expressed as ‘∃x ∀y y∈x≡y¬∈y’. The restrictions I want to place on quantifiers complicate things, and with Python-like comprehensions as
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values, it get's even more complicated. Lots to think about.
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𝟚𝟞·
puzzles Using summation for Slitherlink and Killer Sudoku is a natural choice, but Peano's Axioms are insufficient to define the integers using only first order
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logic. I want to dig into the theoretical concerns, but I'm going to defer them for now while I try to get some functionality working.
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𝟚𝟝·
puzzles I'm a focused on solving logic pencil puzzles as Constraint Satisfaction Problems in part because I'd like to try my hand at a puzzle generator. Perhaps my
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ambition to share a monthly or even weekly sheet of puzzles at my local puzzle & game store is misguided, but for now it's on my hopes and dreams list.
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𝟚𝟝·
coding Changes are settling and maybe my OCD will give me a chance to work on something else for a bit. Between making these changes too haphazardly and global
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distractions, everything else has been suffering neglect. A pause, then forward on Slitherlink puzzles and, hopefully, some graphics fun!
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𝟚𝟛·
coding The transition to treating constraints as a class of ⟪Iron⟫ Interpreter internal values has been... slow. I make a mess when I'm exploring to find a solution
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or implementation that works and meets my design goals. Breaking changes are a time to consolidate the current design before going forward... I was too focused on
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getting to the next exploration - constraints as first class values, and, well, messed up.
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𝟚𝟘·
logic By encoding logic pencil puzzles, rules and instances, in ⟪Sapphire⟫ I define a CSP (Constraint Satisfaction Problem) and ⟪Silver⟫ is my ad-hoc solver. My
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⟪Iron⟫ interpreter can, when an expression would be undefined with eager evaluation, return a meta-object, referencing the only partially evaluated expression. These
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can be interpreted as errors by the environment, but are used by Silver to find solutions: an assertion such as ‘x=5+7’ might not be evaluated past ‘x=12’ if ‘x’ is
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completely unkown, but can be fully resolved by commiting ‘x’ in the solution to be ‘12’. If ‘y’ is undefined, ‘y∈{3 12 15}’ won't be evaluated, but can be used as a
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constraint on ‘y’ in the solution. These, combined with an assertion that ‘x=y’ yields the solution ‘x=12 ∧ y=12’.
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Previously, I didn't allow constraints to be passed around as a ‘first class’ meta-value with ⟪Silver⟫ relied almost on re-evaluating the current unresolved
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assertions with various ‘resolution’ steps that reconcile constraints. Now constraints can be passed as values, and carry, along with information what the domain
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value could be, but also information about the source of the constraint. As an example, given ‘x∈{1 2 3}’ and ‘y∈{3 4 5}’ as constraints, ‘x+y’ can be evaluated to
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the constraint ‘x+y∈{4⋯8}’ which, returned as a meta-value means ‘x+y<10’ can be evaluted to true.
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This can't eliminate the need for specialized resolution steps, like my ⟪Silver⟫ pigeonholer, but the hope is that they can be kept simple and orthogonal to be used,
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along with extended evaluation, as primitive steps in a search.
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Lazy evaluation, if I want to use it for optimization or expressiveness, will hopefully be follow as a relatively straightforward extension of all this.
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𝟚𝟘·
the-bonfire The Trump Adminstration's demands for lists of Jewish Faculty... the-bonfire
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𝟙𝟡·
the-bonfire The title of Robert Wachter's recent article... the-bonfire
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𝟙𝟠·
the-bonfire I was updating my rant about how Unicode is poorly suited ... the-bonfire
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𝟙𝟠·
logic I've ‘discovered’ the field of Mathematics called Finite Model Theory! Model Theory includes, and is introduced with, a focus on infite structures, so I put it
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on the future pile - logic pencil puzzles are finite. But Finite Model Theory looks relevant - it is likely over my head, but I'll dig in a bit and see if I can
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connect any dots to my playground.
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𝟙𝟞·
puzzles To even solve the trivial Slitherlink Puzzle (a 1×1 puzzle with a single ‘4’) semi-symbolically, I'm going to have to up my constraint handling. My plan was
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to support constraint expressions - special objects which give some information about an otherwise indeterminate value.
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My choice was to wrap a logical formula (another expression) using the variable ‘_’ to represent the constraint expression. This could get unweildy, so in practice I
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have kept them simple enough to be useful for my current, puzzle-solving purposes.
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As an example, if x is ‘_∈{1 2}’ and y is ‘_∈{2 7}’ we can deduce ‘x+y’ will satisfy the constraint ‘_∈{3 4 8 9}’and we could also deduce from ‘x=y’ that ‘x=y=2’. The
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pigeonholer I implemented to solve Sudoku puzzles in ⟪Silver⟫ starts with ‘_∈{1⋯9}’ for blank squares and 27 9-way not-equal expressions using an n-ary ‘¬=’ operator.
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The handling is not Sudoku specific - I'm hoping it will work for a few more puzzles before I tidy things up.
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Which brings me back to the start - I didn't implement constraint expressions properly, and now that I'm counting the number of edges around a square that are on the
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path, I have to do at least some tidying.
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𝟙𝟞·
Some online news source or other asked if AI could create anything original... the-bonfire
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𝟙𝟝·
I don't know how to address the political situation here in the US... the-bonfire
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puzzles with formulas defining 10 different puzzle types. Nikoli, the company that popularized “Number Place” puzzles under the Japanese trademark ‘Sudoku’, publishes
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collections in Japan and describes each on their website:
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As I get my ⟪Silver⟫ Solver working on each, I'll post my ⟪Sapphire⟫ definitions.
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𝟘𝟡·
coding I often pass keyword parameters to a subroutine unchanged, and ended up with alot of ‘keyword=keyword’ code in Python function calls. Reserving ‘=’ for the
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equality predicate (I just replace ‘=’ with ‘==’ when generating Python or C) I instead use ‘→’ to pass keyword parameters - ‘keyword→7’. I added a postfix operator
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‘→←’ to pass the value of the variable as the keyword, so I can abbreviate ‘keyword→keyword’ ·as ‘keyword→←’.
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𝟘𝟠·
logic I've added ‘comprehensions’ which support set and sequence expressions such as { _^3 ⋮ 1⋯2026} and ⟨ ⦗str _⦘ ⋮ x y z ⟩, where the variable ‘_’ (displayed as ◒
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in logical contexts, to satisfy my aesthic preferences) which is evaluated for each of the elements to the right of the ‘⋮’ symbol. I use ‘⋯’ as an inclusive, integer
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range operator, so ⟨1⋯3⟩ is the tuple ⟨1 2 3⟩. It meshes well with my implementation of sets of integers expressed as intervals.
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𝟘𝟠·
coding I've been on a side trip to additional ‘rational’ code generation based on syntactic analysis rather than ad-hoc text manipulation. This next stage let me
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translate operators (‘⊗’ and ‘⊙’ for cross and dot-product) into calls to generic functions, but there's more work to make it remotely robust.
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𝟘𝟝·
puzzles I started on a formulation of Slitherlink rules in ⟪Sapphire⟫. Connectivity, as a pairwise relation could be easily satisfied by being true for any vertices
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that are connected to anything. I ended up defining a distance function with a special value (rather than a distinct relation) for ‘not connected’. In the next day or
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two, I'll see how ⟪Silver⟫ does trying to find a satisfying model (aka solution).
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𝟛𝟘·
I've been bogged down by my bootstrapping ... coding
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𝟚𝟠·
More language infrastructure progress - I've got code generating from the ⟪Violet⟫ language layer that bridges between ⟪Cobalt⟫ (aka C) and ⟪Midnight⟫ (aka Python). I
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generate code that uses Python's ‘ctypes’ module to call C from Python, making it easy to mix and match implementations.
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𝟚𝟞·
I took a small step toward sensible language handling by generating a full parse tree for a small input file. Starting life as a no-op, my evolving ‘zypp’
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preprocessor converts ⟪Midnight⟫ and ⟪Cobalt⟫ to Python and C, respectively, in an entirely ad-hoc fashion. At least I know I can create an inviting bug hotel.
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Eventually, each language layer I use will share a unified parser, but different intermediate code generators which will perform first level semantic checks. The
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intermiedate language will support high level primitives that can be lowered to target subsets which can be used to emit code. My ⟪Sapphire⟫ project has a good deal
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of infrastructure to cope with.
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𝟚𝟝·
I finished implementing SDL ‘framebuffer’ objects which display a screen sized OpenGL texture. Framebuffer support is primarily for debugging, but also can be used
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with small ‘gadget’ displays, like Pimoroni's Display Hat Mini, ePaper displays, also available from Pimoroni or from Waveshare, which I used to prototype a Raspberry
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Pi based e-Reader.
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𝟚𝟜·
the-bonfire I finally got around to watching Jordan Peele's documentary "Get Out" the other night. I have to say, the re-enactments were grisly, but well done.
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𝟚𝟛·
I've added support for the Cartesian Product, represented by ‘×’ in Unicode (U+D7). What I call “tuple constrained quantification” (∀⟨x y⟩∈Z×Z) is accepted in
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⟪Sapphire⟫ as well as set exponentiation by an integer (Z^4 ▷ Z×Z×Z×Z) ({1⋯3}^3 ▷ {1⋯3}×{1⋯3}×{1⋯3}). Finite expressions can be evaluated in calculator fashion (⟨1 2
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3⟩∈{1⋯3}^3 ▷ ✔) (∀⟨a b⟩∈{1⋯3}^2 a>3 ⇒ a+b>4 ▷ ✔) and can also be symbolically manipulated by ⟪Ag⟫, aka “The Silver Solver”. I've updated my Sudoku rules to use these
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new features
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𝟚𝟚·
I'm using ‘⊙‘ for dot product and ‘⊗’ for cross product. My preprocessor translates these from binary operators into calls to ‘dot’ and ‘cross’, which are native in
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GLSL and implemented in Python to work on number sequences of equal length (dot) or only 3-tuples of numbers (cross).
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𝟚𝟚·
While I use Unicode extensively and appreciate its near universal adoption and support, I object to any description of it as a "character set". ... coding
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𝟚𝟙·
I updated my color text routines that I use in all my Python tools to proceess faster when read into Emacs. One day, I may create an IDE for my ‘neo-retro’
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logic-puzzle computing environment, but Emacs is still the best tool for me.
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𝟘𝟞·
I now have a somewhat general "pigeonhole solver" ... logic