I realize that for all I've talked about Logic for Programmers in this newsletter, I never once explained basic logical quantifiers. They're both simple and incredibly useful, so let's do that this week! Sets and quantifiers A set is a collection of unordered, unique elements. {1, 2, 3, …} is a set, as are "every programming language", "every programming language's Wikipedia page", and "every function ever defined in any programming language's standard library". You can put whatever you want in a set, with some very specific limitations to avoid certain paradoxes.2 Once we have a set, we can ask "is something true for all elements of the set" and "is something true for at least one element of the set?" IE, is it true that every programming language has a set collection type in the core language? We would write it like this: # all of them all l in ProgrammingLanguages: HasSetType(l) # at least one some l in ProgrammingLanguages: HasSetType(l) This is the notation I use in the book because it's easy to read, type, and search for. Mathematicians historically had a few different formats; the one I grew up with was ∀x ∈ set: P(x) to mean all x in set, and ∃ to mean some. I use these when writing for just myself, but find them confusing to programmers when communicating. "All" and "some" are respectively referred to as "universal" and "existential" quantifiers. Some cool properties We can simplify expressions with quantifiers, in the same way that we can simplify !(x && y) to !x || !y. First of all, quantifiers are commutative with themselves. some x: some y: P(x,y) is the same as some y: some x: P(x, y). For this reason we can write some x, y: P(x,y) as shorthand. We can even do this when quantifying over different sets, writing some x, x' in X, y in Y instead of some x, x' in X: some y in Y. We can not do this with "alternating quantifiers": all p in Person: some m in Person: Mother(m, p) says that every person has a mother. some m in Person: all p in Person: Mother(m, p) says that someone is every person's mother. Second, existentials distribute over || while universals distribute over &&. "There is some url which returns a 403 or 404" is the same as "there is some url which returns a 403 or some url that returns a 404", and "all PRs pass the linter and the test suites" is the same as "all PRs pass the linter and all PRs pass the test suites". Finally, some and all are duals: some x: P(x) == !(all x: !P(x)), and vice-versa. Intuitively: if some file is malicious, it's not true that all files are benign. All these rules together mean we can manipulate quantifiers almost as easily as we can manipulate regular booleans, putting them in whatever form is easiest to use in programming. Speaking of which, how do we use this in in programming? How we use this in programming First of all, people clearly have a need for directly using quantifiers in code. If we have something of the form: for x in list: if P(x): return true return false That's just some x in list: P(x). And this is a prevalent pattern, as you can see by using GitHub code search. It finds over 500k examples of this pattern in Python alone! That can be simplified via using the language's built-in quantifiers: the Python would be any(P(x) for x in list). (Note this is not quantifying over sets but iterables. But the idea translates cleanly enough.) More generally, quantifiers are a key way we express higher-level properties of software. What does it mean for a list to be sorted in ascending order? That all i, j in 0..<len(l): if i < j then l[i] <= l[j]. When should a ratchet test fail? When some f in functions - exceptions: Uses(f, bad_function). Should the image classifier work upside down? all i in images: classify(i) == classify(rotate(i, 180)). These are the properties we verify with tests and types and MISU and whatnot;1 it helps to be able to make them explicit! One cool use case that'll be in the book's next version: database invariants are universal statements over the set of all records, like all a in accounts: a.balance > 0. That's enforceable with a CHECK constraint. But what about something like all i, i' in intervals: NoOverlap(i, i')? That isn't covered by CHECK, since it spans two rows. Quantifier duality to the rescue! The invariant is equivalent to !(some i, i' in intervals: Overlap(i, i')), so is preserved if the query SELECT COUNT(*) FROM intervals CROSS JOIN intervals … returns 0 rows. This means we can test it via a database trigger.3 There are a lot more use cases for quantifiers, but this is enough to introduce the ideas! Next week's the one year anniversary of the book entering early access, so I'll be writing a bit about that experience and how the book changed. It's crazy how crude v0.1 was compared to the current version. MISU ("make illegal states unrepresentable") means using data representations that rule out invalid values. For example, if you have a location -> Optional(item) lookup and want to make sure that each item is in exactly one location, consider instead changing the map to item -> location. This is a means of implementing the property all i in item, l, l' in location: if ItemIn(i, l) && l != l' then !ItemIn(i, l'). ↩ Specifically, a set can't be an element of itself, which rules out constructing things like "the set of all sets" or "the set of sets that don't contain themselves". ↩ Though note that when you're inserting or updating an interval, you already have that row's fields in the trigger's NEW keyword. So you can just query !(some i in intervals: Overlap(new, i')), which is more efficient. ↩

After shipping my work transforming HTML with Netlify’s edge functions I realized I have a little bug: the order of the icons specified in the URL doesn’t match the order in which they are displayed on screen. Why’s this happening? I have a bunch of links in my HTML document, like this: <icon-list> <a href="/1/">…</a> <a href="/2/">…</a> <a href="/3/">…</a> <!-- 2000+ more --> </icon-list> I use html-rewriter in my edge function to strip out the HTML for icons not specified in the URL. So for a request to: /lookup?id=1&id=2 My HTML will be transformed like so: <icon-list> <!-- Parser keeps these two --> <a href="/1/">…</a> <a href="/2/">…</a> <!-- But removes this one --> <a href="/3/">…</a> </icon-list> Resulting in less HTML over the wire to the client. But what about the order of the IDs in the URL? What if the request is to: /lookup?id=2&id=1 Instead of: /lookup?id=1&id=2 In the source HTML document containing all the icons, they’re marked up in reverse chronological order. But the request for this page may specify a different order for icons in the URL. So how do I rewrite the HTML to match the URL’s ordering? The problem is that html-rewriter doesn’t give me a fully-parsed DOM to work with. I can’t do things like “move this node to the top” or “move this node to position x”. With html-rewriter, you only “see” each element as it streams past. Once it passes by, your chance at modifying it is gone. (It seems that’s just the way these edge function tools are designed to work, keeps them lean and performant and I can’t shoot myself in the foot). So how do I change the icon’s display order to match what’s in the URL if I can’t modify the order of the elements in the HTML? CSS to the rescue! Because my markup is just a bunch of <a> tags inside a custom element and I’m using CSS grid for layout, I can use the order property in CSS! All the IDs are in the URL, and their position as parameters has meaning, so I assign their ordering to each element as it passes by html-rewriter. Here’s some pseudo code: // Get all the IDs in the URL const ids = url.searchParams.getAll("id"); // Select all the icons in the HTML rewriter.on("icon-list a", { element: (element) => { // Get the ID const id = element.getAttribute('id'); // If it's in our list, set it's order // position from the URL if (ids.includes(id)) { const order = ids.indexOf(id); element.setAttribute( "style", `order: ${order}` ); // Otherwise, remove it } else { element.remove(); } }, }); Boom! I didn’t have to change the order in the source HTML document, but I can still get the displaying ordering to match what’s in the URL. I love shifty little workarounds like this! Email · Mastodon · Bluesky

In the previous article, we peeked at the reset circuit of ESP-Prog with an oscilloscope, and reproduced it with basic components. We observed that it did not behave quite as expected. In this article, we’ll look into the missing pieces. An incomplete circuit For a hint, we’ll first look a bit more closely at the … Continue reading The missing part of Espressif’s reset circuit → The post The missing part of Espressif’s reset circuit appeared first on Quentin Santos.

Snippets are a useful addition to Svelte 5. I use them in my Svelte 5 projects like Edna. Snippet basics A snippet is a function that renders html based on its arguments. Here’s how to define and use a snippet: {#snippet hello(name)} <div>Hello {name}!</div> {/snippet} {@render hello("Andrew")} {@render hello("Amy")} You can re-use snippets by exporting them: <script module> export { hello }; </script> {@snippet hello(name)}<div>Hello {name}!</div>{/snippet} Snippets use cases Snippets for less nesting Deeply nested html is hard to read. You can use snippets to extract some parts to make the structure clearer. For example, you can transform: <div> <div class="flex justify-end mt-2"> <button onclick={onclose} class="mr-4 px-4 py-1 border border-black hover:bg-gray-100" >Cancel</button > <button onclick={() => emitRename()} disabled={!canRename} class="px-4 py-1 border border-black hover:bg-gray-50 disabled:text-gray-400 disabled:border-gray-400 disabled:bg-white default:bg-slate-700" >Rename</button > </div> into: {#snippet buttonCancel()} <button onclick={onclose} class="mr-4 px-4 py-1 border border-black hover:bg-gray-100" >Cancel</button > {/snippet} {#snippet buttonRename()}...{/snippet} To make this easier to read: <div> <div class="flex justify-end mt-2"> {@render buttonCancel()} {@render buttonRename()} </div> </div> snippets replace default <slot/> In Svelte 4, if you wanted place some HTML inside the component, you used <slot />. Let’s say you have Overlay.svelte component used like this: <Overlay> <MyDialog></MyDialog> </Overlay> In Svelte 4, you would use <slot /> to render children: <div class="overlay-wrapper"> <slot /> </div> <slot /> would be replaced with <MyDialog></MyDialog>. In Svelte 5 <MyDialog></MyDialog> is passed to Overlay.svelte as children property so you would change Overlay.svelte to: <script> let { children } = $props(); </script> <div class="overlay-wrapper"> {@render children()} </div> children property is created by Svelte compiler so you should avoid naming your own props children. snippets replace named slots A component can have a default slot for rendering children and additional named slots. In Svelte 5 instead of named slots you pass snippets as props. An example of Dialog.svelte: <script> let { title, children } = $props(); </script> <div class="dialog"> <div class="title"> {@render title()} </div> {@render children()} </div> And use: {#snippet title()} <div class="fancy-title">My fancy title</div> {/snippet} <Dialog title={title}> <div>Body of the dialog</div> </Dialog> passing snippets as implicit props You can pass title snippet prop implicitly: <Dialog> {#snippet title()} <div class="fancy-title">My fancy title</div> {/snippet} <div>Body of the dialog</div> </Dialog> Because {snippet title()} is a child or <Dialog>, we don’t have to pass it as explicit title={title} prop. The compiler does it for us. snippets to reduce repetition Here’s part of how I render https://tools.arslexis.io/ {#snippet row(name, url, desc)} <tr> <td class="text-left align-top" ><a class="font-semibold whitespace-nowrap" href={url}>{name}</a> </td> <td class="pl-4 align-top">{@html desc}</td> </tr> {/snippet} {@render row("unzip", "/unzip/", "unzip a file in the browser")} {@render row("wc", "/wc/", "like <tt>wc</tt>, but in the browser")} It saves me copy & paste of the same HTML and makes the structure more readable. snippets for recursive rendering Sometimes you need to render a recursive structure, like nested menus or file tree. In Svelte 4 you could use <svelte:self> but the downside of that is that you create multiple instances of the component. That means that the state is also split among multiple instances. That makes it harder to implement functionality that requires a global view of the structure, like keyboard navigation. With snippets you can render things recursively in a single instance of the component. I used it to implement nested context menus. snippets to customize rendering Let’s say you’re building a Menu component. Each menu item is a <div> with some non-trivial children. To allow the client of Menu customize how items are rendered, you could provide props for things like colors, padding etc. or you could allow ultimate flexibility by accepting an optional menuitem prop that is a snippet that renders the item. You can think of it as a headless UI i.e. you provide the necessary structure and difficult logic like keyboard navigation etc. and allow the client lots of control over how things are rendered. snippets for library of icons Before snippets every SVG Icon I used was a Svelte component. Many icons means many files. Now I have a single Icons.svelte file, like: <script module> export { IconMenu, IconSettings }; </script> {#snippet IconMenu(arg1, arg2, ...)} <svg>... icon svg</svg> {/snippet}} {#snippet IconSettings()} <svg>... icon svg</svg> {/snippet}}

Here are a few tangentially-related ideas vaguely near the theme of comparison operators. comparison style clamp style clamp is median clamp in range range style style clash? comparison style Some languages such as BCPL, Icon, Python have chained comparison operators, like if min <= x <= max: ... In languages without chained comparison, I like to write comparisons as if they were chained, like, if min <= x && x <= max { // ... } A rule of thumb is to prefer less than (or equal) operators and avoid greater than. In a sequence of comparisons, order values from (expected) least to greatest. clamp style The clamp() function ensures a value is between some min and max, def clamp(min, x, max): if x < min: return min if max < x: return max return x I like to order its arguments matching the expected order of the values, following my rule of thumb for comparisons. (I used that flavour of clamp() in my article about GCRA.) But I seem to be unusual in this preference, based on a few examples I have seen recently. clamp is median Last month, Fabian Giesen pointed out a way to resolve this difference of opinion: A function that returns the median of three values is equivalent to a clamp() function that doesn’t care about the order of its arguments. This version is written so that it returns NaN if any of its arguments is NaN. (When an argument is NaN, both of its comparisons will be false.) fn med3(a: f64, b: f64, c: f64) -> f64 { match (a <= b, b <= c, c <= a) { (false, false, false) => f64::NAN, (false, false, true) => b, // a > b > c (false, true, false) => a, // c > a > b (false, true, true) => c, // b <= c <= a (true, false, false) => c, // b > c > a (true, false, true) => a, // c <= a <= b (true, true, false) => b, // a <= b <= c (true, true, true) => b, // a == b == c } } When two of its arguments are constant, med3() should compile to the same code as a simple clamp(); but med3()’s misuse-resistance comes at a small cost when the arguments are not known at compile time. clamp in range If your language has proper range types, there is a nicer way to make clamp() resistant to misuse: fn clamp(x: f64, r: RangeInclusive<f64>) -> f64 { let (&min,&max) = (r.start(), r.end()); if x < min { return min } if max < x { return max } return x; } let x = clamp(x, MIN..=MAX); range style For a long time I have been fond of the idea of a simple counting for loop that matches the syntax of chained comparisons, like for min <= x <= max: ... By itself this is silly: too cute and too ad-hoc. I’m also dissatisfied with the range or slice syntax in basically every programming language I’ve seen. I thought it might be nice if the cute comparison and iteration syntaxes were aspects of a more generally useful range syntax, but I couldn’t make it work. Until recently when I realised I could make use of prefix or mixfix syntax, instead of confining myself to infix. So now my fantasy pet range syntax looks like >= min < max // half-open >= min <= max // inclusive And you might use it in a pattern match if x is >= min < max { // ... } Or as an iterator for x in >= min < max { // ... } Or to take a slice xs[>= min < max] style clash? It’s kind of ironic that these range examples don’t follow the left-to-right, lesser-to-greater rule of thumb that this post started off with. (x is not lexically between min and max!) But that rule of thumb is really intended for languages such as C that don’t have ranges. Careful stylistic conventions can help to avoid mistakes in nontrivial conditional expressions. It’s much better if language and library features reduce the need for nontrivial conditions and catch mistakes automatically.