--- title: Lazy BDDs with eager literal differences | daily.dev description: José Valim details new optimizations to Elixir's set-theoretic type system targeting difference operations in lazy BDDs (Binary Decision Diagrams). With Elixir... canonical: https://daily.dev/posts/lazy-bdds-with-eager-literal-differences-utpsbskcr twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Lazy BDDs with eager literal differences | daily.dev og:description: José Valim details new optimizations to Elixir's set-theoretic type system targeting difference operations in lazy BDDs (Binary Decision Diagrams). With Elixir... og:url: https://daily.dev/posts/lazy-bdds-with-eager-literal-differences-utpsbskcr og:image: https://api.daily.dev/og/posts/utpSBSKCr.png og:image:alt: Lazy BDDs with eager literal differences og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Lazy BDDs with eager literal differences **[Elixir](https://daily.dev/sources/elixir)** · 11 min read · 18 upvotes · 0 comments ## Summary José Valim details new optimizations to Elixir's set-theoretic type system targeting difference operations in lazy BDDs (Binary Decision Diagrams). With Elixir v1.20.0-rc.2 introducing clause-type propagation and redundant clause detection, the number of type difference computations increased significantly, causing compilation slowdowns in modules with 1000+ clauses. The post derives new mathematical formulas for eager literal differences — both when a literal appears on the left or right side of a difference — and introduces a 'one field difference' optimization for structs where only a single field type differs. These optimizations, shipping in v1.20.0-rc4, reduced compilation from dozens of seconds to milliseconds for affected projects. Claude Opus 4.6 is credited with suggesting a key algebraic simplification. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Similar posts on daily.dev - [Lazy BDDs with eager literal intersections](https://daily.dev/posts/lazy-bdds-with-eager-literal-intersections-jrqly4sxw) · Elixir · 24 upvotes · 0 comments - [Lazier Binary Decision Diagrams \(BDDs\) for set-theoretic types](https://daily.dev/posts/lazier-binary-decision-diagrams-bdds-for-set-theoretic-types-wycdb5gsa) · Elixir · 4 upvotes · 1 comments - [Elixir v1.20 released: now a gradually typed language](https://daily.dev/posts/elixir-v1-20-released-now-a-gradually-typed-language-081x31cuq) · Elixir · 4 upvotes · 0 comments --- Tags: [#compiler-optimization](https://daily.dev/tags/compiler-optimization), [#elixir](https://daily.dev/tags/elixir) [View this post on daily.dev](https://daily.dev/posts/lazy-bdds-with-eager-literal-differences-utpsbskcr) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Lazy BDDs with eager literal differences","url":"https://daily.dev/posts/lazy-bdds-with-eager-literal-differences-utpsbskcr","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/lazy-bdds-with-eager-literal-differences-utpsbskcr"},"datePublished":"2026-03-19T09:52:30.608Z","dateModified":"2026-03-30T02:17:45.740Z","description":"José Valim details new optimizations to Elixir's set-theoretic type system targeting difference operations in lazy BDDs (Binary Decision Diagrams). 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