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< ol class = "chapter" > < li class = "chapter-item expanded affix " > < a href = "index.html" > halo2< / a > < / li > < li class = "chapter-item expanded " > < a href = "concepts.html" > < strong aria-hidden = "true" > 1.< / strong > Concepts< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "concepts/proofs.html" > < strong aria-hidden = "true" > 1.1.< / strong > Proof systems< / a > < / li > < li class = "chapter-item expanded " > < a href = "concepts/arithmetization.html" > < strong aria-hidden = "true" > 1.2.< / strong > PLONKish Arithmetization< / a > < / li > < li class = "chapter-item expanded " > < a href = "concepts/chips.html" > < strong aria-hidden = "true" > 1.3.< / strong > Chips< / a > < / li > < li class = "chapter-item expanded " > < a href = "concepts/gadgets.html" > < strong aria-hidden = "true" > 1.4.< / strong > Gadgets< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "user.html" > < strong aria-hidden = "true" > 2.< / strong > User Documentation< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "user/dev-tools.html" > < strong aria-hidden = "true" > 2.1.< / strong > Developer tools< / a > < / li > < li class = "chapter-item expanded " > < a href = "user/simple-example.html" > < strong aria-hidden = "true" > 2.2.< / strong > A simple example< / a > < / li > < li class = "chapter-item expanded " > < a href = "user/lookup-tables.html" > < strong aria-hidden = "true" > 2.3.< / strong > Lookup tables< / a > < / li > < li class = "chapter-item expanded " > < a href = "user/gadgets.html" > < strong aria-hidden = "true" > 2.4.< / strong > Gadgets< / a > < / li > < li class = "chapter-item expanded " > < a href = "user/tips-and-tricks.html" > < strong aria-hidden = "true" > 2.5.< / strong > Tips and tricks< / a > < / li > < li class = "chapter-item expanded " > < a href = "user/wasm-port.html" > < strong aria-hidden = "true" > 2.6.< / strong > WASM Guide< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "dev.html" > < strong aria-hidden = "true" > 3.< / strong > Developer Documentation< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "dev/features.html" > < strong aria-hidden = "true" > 3.1.< / strong > Feature development< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "design.html" class = "active" > < strong aria-hidden = "true" > 4.< / strong > Design< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "design/proving-system.html" > < strong aria-hidden = "true" > 4.1.< / strong > Proving system< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "design/proving-system/lookup.html" > < strong aria-hidden = "true" > 4.1.1.< / strong > Lookup argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/proving-system/permutation.html" > < strong aria-hidden = "true" > 4.1.2.< / strong > Permutation argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/proving-system/circuit-commitments.html" > < strong aria-hidden = "true" > 4.1.3.< / strong > Circuit commitments< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/proving-system/vanishing.html" > < strong aria-hidden = "true" > 4.1.4.< / strong > Vanishing argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/proving-system/multipoint-opening.html" > < strong aria-hidden = "true" > 4.1.5.< / strong > Multipoint opening argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/proving-system/inner-product.html" > < strong aria-hidden = "true" > 4.1.6.< / strong > Inner product argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/proving-system/comparison.html" > < strong aria-hidden = "true" > 4.1.7.< / strong > Comparison to other work< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "design/protocol.html" > < strong aria-hidden = "true" > 4.2.< / strong > Protocol Description< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/implementation.html" > < strong aria-hidden = "true" > 4.3.< / strong > Implementation< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "design/implementation/proofs.html" > < strong aria-hidden = "true" > 4.3.1.< / strong > Proofs< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/implementation/fields.html" > < strong aria-hidden = "true" > 4.3.2.< / strong > Fields< / a > < / li > < li class = "chapter-item expanded " > < a href = "design/implementation/selector-combining.html" >
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< h1 id = "design" > < a class = "header" href = "#design" > Design< / a > < / h1 >
< h2 id = "note-on-language" > < a class = "header" href = "#note-on-language" > Note on Language< / a > < / h2 >
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< p > We use slightly different language than others to describe PLONK concepts. Here's the
overview:< / p >
< ol >
< li > We like to think of PLONK-like arguments as tables, where each column corresponds to a
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"wire". We refer to entries in this table as "cells".< / li >
< li > We like to call "selector polynomials" and so on "fixed columns" instead. We then refer
specifically to a "selector constraint" when a cell in a fixed column is being used to
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control whether a particular constraint is enabled in that row.< / li >
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< li > We call the other polynomials "advice columns" usually, when they're populated by the
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prover.< / li >
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< li > We use the term "rule" to refer to a "gate" like
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< span class = "katex-display" > < span class = "katex" > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord mathnormal" > A< / span > < span class = "mopen" > (< / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "mclose" > )< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > ⋅< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > q< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mopen" > (< / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "mclose" > )< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.05017em;" > B< / span > < span class = "mopen" > (< / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "mclose" > )< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > ⋅< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > q< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.05017em;" > B< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mopen" > (< / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "mclose" > )< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord mathnormal" > A< / span > < span class = "mopen" > (< / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "mclose" > )< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > ⋅< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.05017em;" > B< / span > < span class = "mopen" > (< / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "mclose" > )< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > ⋅< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > q< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0359em;margin-rig
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< ul >
< li > TODO: Check how consistent we are with this, and update the code and docs to match.< / li >
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< script >
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window.playground_copyable = true;
< / script >
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< script src = "elasticlunr.min.js" > < / script >
< script src = "mark.min.js" > < / script >
< script src = "searcher.js" > < / script >
< script src = "clipboard.min.js" > < / script >
< script src = "highlight.js" > < / script >
< script src = "book.js" > < / script >
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<!-- Custom JS scripts -->
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< / div >
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< / body >
< / html >