From 32e0e105f663ace08896f22ab4079521070b0cac Mon Sep 17 00:00:00 2001 From: Amir Saeid Date: Wed, 18 Feb 2026 21:25:00 +0000 Subject: Change the theme and add a new post --- .gitmodules | 3 + content/post/fairstream.md | 86 +++++ hugo.toml | 9 +- hugo.yaml | 4 - layouts/partials/extended_head.html | 14 + package-lock.json | 18 ++ package.json | 5 + public/404.html | 220 ++++++++----- public/apple-touch-icon.png | Bin 0 -> 190 bytes public/bundle.min.js | 3 + public/categories/index.html | 228 ++++++++----- ...5203d36b442c1f66f718ff4e8164fa86cf6c61ad641.css | 1 + ...31afc5466d5f7bc2f0bc9abdd98b69385335d7baee4.css | 1 + ...84af26737007eb5051b157b86fc24487c94f3dc8bbe.css | 1 + ...a92d63e69e849e2200e0002a228d137f236b09ecd75.css | 1 + ...d52a38b19d8950fe78ca29454ea8c2595cf26aad5c0.css | 1 + ...9c6647d0223a38db52e2561dd87966eb5fc7c6bdac6.css | 1 + ...9d0897c5833d9d5bf1ff31f5e60ea3ee42ce2b1268c.css | 1 + ...68f71f519901124fa5cbb4519b2fb0667a21e9aca39.css | 1 + 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0000000..d4bba6c --- /dev/null +++ b/content/post/fairstream.md @@ -0,0 +1,86 @@ +--- +title: "Fairstream" +date: 2026-02-17T20:59:41Z +--- + +[Backtracking](https://en.wikipedia.org/wiki/Backtracking) is a versatile approach for solving search problems by building solutions incrementally. If a partial solution cannot be extended, it is discarded and the process returns to a previous step to explore an alternative path. This method is generally more efficient than brute-force searching due to pruning: stopping exploration of a branch as soon as it violates a constraint, which eliminates entire sections of the search space. + +Strictly speaking, fair backtracking is not required for all search problems. A fair strategy guarantees all branches make progress, preventing any single branch from starving the others. The List monad handles non-deterministic computation well, and within a finite search space it produces the same results as a fair stream. When the search space is infinite, or when one branch may produce unbounded results, fairness becomes essential to ensure completeness. + +[`fairstream`](https://github.com/codiff/fairstream) is a Scala implementation of fair backtracking based on the [work](https://okmij.org/ftp/Computation/monads.html#fair-bt-stream) of Oleg Kiselyov. + +## The problem with depth-first search + +Consider Pythagorean triples: tuples $(i, j, k)$ such that $i^2+j^2=k^2$, with $(3, 4, 5)$ as the canonical first example. If we try to generate all such triples using nested infinite generators, a conventional stream composition based on sequential `flatMap` gets stuck exploring an infinite branch that contains no solution and never comes back up to try a larger value, so it may fail to produce any triples at all despite solutions existing. + +The following example demonstrates how [fs2](https://fs2.io/).Stream's depth-first approach can fail to find Pythagorean triples, even though the result set is non-empty: + +```scala +val number: fs2.Stream[IO, Int] = fs2.Stream.iterate(1)(_ + 1) + +val triples = for { + i <- number + j <- number + k <- number + if i * i + j * j == k * k +} yield (i, j, k) + +triples.take(7).compile.toList +``` + +The `for` comprehension desugars into nested `flatMap` calls. Since `number` is infinite, the innermost generator tries $k = 1, 2, 3, \ldots$ forever for $i = 1, j = 1$ before it ever consider $j = 2$. No Pythagorean triple exists for $i = 1, j = 1$, so the stream never produces a result. + +This is not a quirk of ofs2. Any depth-first `flatMap` over infinite collections has this problem, including Scala's standard library `LazyList`. + +## Fair interleaving with `fairstream` + +`fairstream` solves this by replacing sequential concatenation with fair disjuction (`mplus`), which interleaves branches so that every candidate is eventually reached. + +At the time of writing, the library is published as snapshots: + +```scala +resolvers += Resolver.sonatypeCentralSnapshots + +libraryDependencies += "com.codiff" %% "fairstream" % "0.0-9f9db42-SNAPSHOT" +``` + +```scala +import com.codiff.fairstream.Fair +import com.codiff.fairstream.Fair._ + +lazy val number: Fair[Int] = mplus(unit(0), number.map(_ + 1)) + +val triples = for { + i <- number + _ <- guard(i > 0) + j <- number + _ <- guard(j > 0) + k <- number + _ <- guard(k > 0) + _ <- guard(i * i + j * j == k * k) +} yield (i, j, k) + +Fair.runM(None, Some(7), triples) +``` + +## `FairT`: effectful fair backtracking + +`Fair[A]` is a pure computation. But what if your search branches need to perform effects, like reading from a database, calling an API, or logging? That's where `FairT[F[_], A]` comes in. + +`FairT` is a monad transformer that layers fair backtracking on top of any effect `F`. This means you can interleave non-deterministic search with `IO`, `Task`, or any other cats-effect compatible monad. + +## fs2 integration + +If you want to stay in the fs2 ecosystem, `fairstream-fs2` provides a conversion from `Fair` and `FairT` to `fs2.Stream`: + +```scala +libraryDependencies += "com.codiff" %% "fairstream-fs2" % "0.0-9f9db42-SNAPSHOT" +``` + +```scala +import com.codiff.fairstream.fs2.syntax._ + +triples.toFs2.take(7).compile.toList +``` + +This should let you compose fair backtracking with all the stream processing, concurrency, and resource management that fs2 provides. You define your search logic using `Fair` or `FairT`, then convert to `fs2.Stream` at the boundary where you need to integrate with the rest of your application. diff --git a/hugo.toml b/hugo.toml index 1d5d4b5..3343f07 100644 --- a/hugo.toml +++ b/hugo.toml @@ -1,2 +1,9 @@ baseURL = 'https://blog.gluegadget.com/' -theme = 'ananke' +theme = 'terminal' + +[markup.highlight] + noClasses = false + +[params] + centerTheme = true + contentTypeName = "post" diff --git a/hugo.yaml b/hugo.yaml deleted file mode 100644 index eddefe1..0000000 --- a/hugo.yaml +++ /dev/null @@ -1,4 +0,0 @@ -baseURL: http://example.org/ -disablePathToLower: true -languageCode: en-us -title: My New Hugo Site diff --git a/layouts/partials/extended_head.html b/layouts/partials/extended_head.html new file mode 100644 index 0000000..60a4547 --- /dev/null +++ b/layouts/partials/extended_head.html @@ -0,0 +1,14 @@ + + diff --git a/package-lock.json b/package-lock.json new file mode 100644 index 0000000..3243829 --- /dev/null +++ b/package-lock.json @@ -0,0 +1,18 @@ +{ + "name": "blog.gluegadget.com", + "lockfileVersion": 3, + "requires": true, + "packages": { + "": { + "dependencies": { + "mathjax": "^3.2.2" + } + }, + "node_modules/mathjax": { + "version": "3.2.2", + "resolved": "https://registry.npmjs.org/mathjax/-/mathjax-3.2.2.tgz", + "integrity": "sha512-Bt+SSVU8eBG27zChVewOicYs7Xsdt40qm4+UpHyX7k0/O9NliPc+x77k1/FEsPsjKPZGJvtRZM1vO+geW0OhGw==", + "license": "Apache-2.0" + } + } +} diff --git a/package.json b/package.json new file mode 100644 index 0000000..c74898c --- /dev/null +++ b/package.json @@ -0,0 +1,5 @@ +{ + "dependencies": { + "mathjax": "^3.2.2" + } +} diff --git a/public/404.html b/public/404.html index 5d232cc..a97d96a 100644 --- a/public/404.html +++ b/public/404.html @@ -1,99 +1,173 @@ - - - - - - - - - - - - - - + + + 404 Page not found :: + + + + + - - + + - - - + + - + + - + + - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - + + + + + + + + + + + + + + + +
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