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diff --git a/docs/spec/inferred.html b/docs/spec/inferred.html index 08041156..b4c5d3f5 100644 --- a/docs/spec/inferred.html +++ b/docs/spec/inferred.html @@ -474,7 +474,7 @@ <li><em>Structural</em> Under: If <code><span class='Function'>πΎ</span></code> is a structural function (to be defined below) and <code><span class='Value'>v</span></code> is compatible with <code><span class='Function'>πΎ</span></code> on <code><span class='Value'>π©</span></code>, then the result is obtained by inserting <code><span class='Value'>v</span></code> back into <code><span class='Value'>π©</span></code>.</li> <li><em>Computational</em> Under: If <code><span class='Function'>πΎ</span></code> is provably not a structural function, then the result is <code><span class='Function'>πΎ</span><span class='Modifier'>βΌ</span><span class='Value'>v</span></code> if it is defined.</li> </ul> -<p>When implementing, there is no need to implement invertable Under specially: it can be handled as part of the structural and computation cases.</p> +<p>When implementing, there is no need to implement invertible Under specially: it can be handled as part of the structural and computation cases.</p> <h3 id="mathematical-definition-of-structural-under"><a class="header" href="#mathematical-definition-of-structural-under">Mathematical definition of structural Under</a></h3> <p>In general, structural Under requires information from the original right argument to be computed. Here we will define the <em>structural inverse of</em> structural function <code><span class='Function'>πΎ</span></code> <em>on</em> <code><span class='Value'>v</span></code> <em>into</em> <code><span class='Value'>π©</span></code>, where <code><span class='Value'>π©</span></code> gives this information. The value <code><span class='Value'>π¨</span><span class='Function'>π½</span><span class='Modifier2'>βΎ</span><span class='Function'>πΎ</span><span class='Value'>π©</span></code> is then the structural inverse of <code><span class='Function'>πΎ</span></code> on <code><span class='Value'>π¨</span><span class='Function'>π½</span><span class='Modifier2'>β</span><span class='Function'>πΎ</span><span class='Value'>π©</span></code> into <code><span class='Value'>π©</span></code>.</p> <p>We define a <em>structure</em> to be either the value <code><span class='Nothing'>Β·</span></code> or an array of structures (substitute <code><span class='Number'>0</span></code> or any other specific value for <code><span class='Nothing'>Β·</span></code> if you'd like structures to be a subset of BQN arrays; the value is irrelevant). A given structure <code><span class='Value'>s</span></code> <em>captures</em> a BQN value or structure <code><span class='Value'>π©</span></code> if it is <code><span class='Nothing'>Β·</span></code>, or if <code><span class='Value'>s</span></code> and <code><span class='Value'>π©</span></code> are arrays of the same shape, and each element of <code><span class='Value'>s</span></code> captures the corresponding element of <code><span class='Value'>π©</span></code>. Thus a structure shares some or all of the structural information in arrays it captures, but none of the data.</p> diff --git a/spec/inferred.md b/spec/inferred.md index 73fc4abd..ee899f5d 100644 --- a/spec/inferred.md +++ b/spec/inferred.md @@ -174,7 +174,7 @@ Let `vβπ¨π½βπΎπ©`, so that `vβ‘πΎz`. `v` is of course well-define - *Structural* Under: If `πΎ` is a structural function (to be defined below) and `v` is compatible with `πΎ` on `π©`, then the result is obtained by inserting `v` back into `π©`. - *Computational* Under: If `πΎ` is provably not a structural function, then the result is `πΎβΌv` if it is defined. -When implementing, there is no need to implement invertable Under specially: it can be handled as part of the structural and computation cases. +When implementing, there is no need to implement invertible Under specially: it can be handled as part of the structural and computation cases. ### Mathematical definition of structural Under |