Specify predicates

2 files changed, 6 insertions, 5 deletions

diff --git a/docs/spec/evaluate.html b/docs/spec/evaluate.html
index b80c60ab..9b57dd5f 100644
--- a/docs/spec/evaluate.html
+++ b/docs/spec/evaluate.html
@@ -11,10 +11,11 @@
 <p>As specified, BQN programs can involve an arbitrary amount of information, but when run there will be memory and possibly other limitations. To accommodate this, any part of evaluation can cause an error, if a resource such as memory, stack memory, or limited execution time is exhausted.</p>
 <h3 id="programs-and-blocks"><a class="header" href="#programs-and-blocks">Programs and blocks</a></h3>
 <p>The result of parsing a valid BQN program is a <code><span class='Function'>PROGRAM</span></code>, and the program is run by evaluating this term.</p>
-<p>A <code><span class='Function'>PROGRAM</span></code> or <code><span class='Function'>BODY</span></code> is a list of <code><span class='Function'>STMT</span></code>s, which are evaluated in program order. A result is always required for <code><span class='Function'>BODY</span></code> nodes, and sometimes for <code><span class='Function'>PROGRAM</span></code> nodes (for example, when loaded with <code><span class='Function'>•Import</span></code>). If any identifiers in the node's scope are exported, or any of its statements is an <code><span class='Function'>EXPORT</span></code>, then the result is the namespace created in order to evaluate the node. If a result is required but the namespace case doesn't apply, then the last <code><span class='Function'>STMT</span></code> node must be an <code><span class='Function'>EXPR</span></code> and its result is used. The statement <code><span class='Function'>EXPR</span></code> evaluates some BQN code and possibly assigns the results, while <code><span class='Value'>nothing</span></code> evaluates any <code><span class='Value'>subject</span></code> or <code><span class='Function'>Derv</span></code> terms it contains but discards the results. An <code><span class='Function'>EXPORT</span></code> statement performs no action.</p>
-<p>A block consists of several <code><span class='Function'>BODY</span></code> terms, some of which may have an accompanying header describing accepted inputs and how they are processed. An immediate block <code><span class='Value'>brImm</span></code> can only have one <code><span class='Function'>BODY</span></code>, and is evaluated by evaluating the code in it. Other types of blocks do not evaluate any <code><span class='Function'>BODY</span></code> immediately, but instead return a function or modifier that obtains its result by evaluating a particular <code><span class='Function'>BODY</span></code>. The <code><span class='Function'>BODY</span></code> is identified and evaluated once the block has received enough inputs (operands or arguments), which for modifiers can take one or two calls: if two calls are required, then on the first call the operands are simply stored and no code is evaluated yet. The stored values can be accessed by equality checking, or <code><span class='Function'>•Decompose</span></code> if defined. Two calls are required if there is more than one <code><span class='Function'>BODY</span></code> term, if the <code><span class='Function'>BODY</span></code> contains the special names <code><span class='Value'>𝕨𝕩𝕤</span><span class='Function'>𝕎𝕏𝕊</span></code>, or if its header specifies arguments (the header-body combination is a <code><span class='Modifier'>_mCase</span></code> or <code><span class='Modifier2'>_cCase_</span></code>). Otherwise only one is required.</p>
+<p>A <code><span class='Function'>PROGRAM</span></code> or <code><span class='Function'>BODY</span></code> is a list of <code><span class='Function'>STMT</span></code>s, which are evaluated in program order. A <code><span class='Function'>BODY</span></code> also allows an <code><span class='Function'>EXPR</span></code> followed by <code><span class='String'>&quot;?&quot;</span></code> in place of an <code><span class='Function'>STMT</span></code>: then the expression is evaluated as usual but its result is checked as discussed below. A result is always required for <code><span class='Function'>BODY</span></code> nodes, and sometimes for <code><span class='Function'>PROGRAM</span></code> nodes (for example, when loaded with <code><span class='Function'>•Import</span></code>). If any identifiers in the node's scope are exported, or any of its statements is an <code><span class='Function'>EXPORT</span></code>, then the result is the namespace created in order to evaluate the node. If a result is required but the namespace case doesn't apply, then the last <code><span class='Function'>STMT</span></code> node must be an <code><span class='Function'>EXPR</span></code> and its result is used. The statement <code><span class='Function'>EXPR</span></code> evaluates some BQN code and possibly assigns the results, while <code><span class='Value'>nothing</span></code> evaluates any <code><span class='Value'>subject</span></code> or <code><span class='Function'>Derv</span></code> terms it contains but discards the results. An <code><span class='Function'>EXPORT</span></code> statement performs no action.</p>
+<p>A block consists of several <code><span class='Function'>BODY</span></code> terms, some of which may have an accompanying header describing accepted inputs and how they are processed. An immediate block <code><span class='Value'>brImm</span></code> can only have one <code><span class='Function'>BODY</span></code>, and is evaluated by evaluating it. Other types of blocks don't evaluate any <code><span class='Function'>BODY</span></code> immediately, but instead return a function or modifier that obtains its result by evaluating a particular <code><span class='Function'>BODY</span></code>. The <code><span class='Function'>BODY</span></code> is identified and evaluated once the block has received enough inputs (operands or arguments), which for modifiers can take one or two calls: if two calls are required, then on the first call the operands are simply stored and no code is evaluated yet. The stored values can be accessed by equality checking, or <code><span class='Function'>•Decompose</span></code> if defined. Two calls are required if there is more than one <code><span class='Function'>BODY</span></code> term, if the <code><span class='Function'>BODY</span></code> contains the special names <code><span class='Value'>𝕨𝕩𝕤</span><span class='Function'>𝕎𝕏𝕊</span></code>, or if its header specifies arguments (the header-body combination is a <code><span class='Modifier'>_mCase</span></code> or <code><span class='Modifier2'>_cCase_</span></code>). Otherwise only one is required.</p>
 <p>To evaluate a block when enough inputs have been received, first the correct case must be identified. To do this, first each special case (<code><span class='Function'>FCase</span></code>, <code><span class='Modifier'>_mCase</span></code>, or <code><span class='Modifier2'>_cCase_</span></code>), excluding <code><span class='Function'>FCase</span></code> nodes containing <code><span class='Function'>UndoHead</span></code>, is checked in order to see if its arguments are strucurally compatible with the given arguments. That is, is <code><span class='Value'>headW</span></code> is a <code><span class='Value'>subject</span></code>, there must be a left argument matching that structure, and if <code><span class='Value'>headX</span></code> is a <code><span class='Value'>subject</span></code>, the right argument must match that structure. This means that <code><span class='Value'>𝕨</span></code> not only matches any left argument but also no argument. The test for compatibility is the same as for multiple assignment described below, except that the header may contain constants, which must match the corresponding part of the given argument. If no special case matches, then an appropriate general case (<code><span class='Function'>FMain</span></code>, <code><span class='Modifier'>_mMain</span></code>, or <code><span class='Modifier2'>_cMain_</span></code>) is used: if there are two, the first is used with no left argument and the second with a left argument; if there are one, it is always used, and if there are none, an error results.</p>
-<p>The only remaining step before evaluating the <code><span class='Function'>BODY</span></code> is to bind the inputs and other names. Special names are always bound when applicable: <code><span class='Value'>𝕨𝕩𝕤</span></code> if arguments are used, <code><span class='Value'>𝕨</span></code> if there is a left argument, <code><span class='Value'>𝕗𝕘</span></code> if operands are used, and <code><span class='Modifier'>_𝕣</span></code> and <code><span class='Modifier2'>_𝕣_</span></code> for modifiers and combinators, respectively. Any names in the header are also bound, allowing multiple assignment for arguments.</p>
+<p>When a predicate <code><span class='String'>&quot;?&quot;</span></code> is evaluated, it may change the choice of case. The associated <code><span class='Function'>EXPR</span></code> is evaluated and its result is checked. If it's not one of the numbers <code><span class='Number'>0</span></code> or <code><span class='Number'>1</span></code>, an error results. If it's <code><span class='Number'>1</span></code>, evaluation of the <code><span class='Function'>BODY</span></code> continues as usual. If it's <code><span class='Number'>0</span></code>, evaluation is stopped and the next compatible <code><span class='Function'>BODY</span></code> term is evaluated using the block's original inputs.</p>
+<p>Inputs and other names are bound when evaluation of a <code><span class='Function'>BODY</span></code> is begun. Special names are always bound when applicable: <code><span class='Value'>𝕨𝕩𝕤</span></code> if arguments are used, <code><span class='Value'>𝕨</span></code> if there is a left argument, <code><span class='Value'>𝕗𝕘</span></code> if operands are used, and <code><span class='Modifier'>_𝕣</span></code> and <code><span class='Modifier2'>_𝕣_</span></code> for modifiers and combinators, respectively. Any names in the header are also bound, allowing multiple assignment for arguments.</p>
 <p>If there is no left argument, but the <code><span class='Function'>BODY</span></code> contains <code><span class='Value'>𝕨</span></code> or <code><span class='Function'>𝕎</span></code> at the top level, then it is conceptually re-parsed with <code><span class='Value'>𝕨</span></code> replaced by <code><span class='Nothing'>·</span></code> to give a monadic version before application; this modifies the syntax tree by replacing some instances of <code><span class='Value'>subject</span></code>, <code><span class='Value'>arg</span></code>, or <code><span class='Function'>Operand</span></code> with <code><span class='Value'>nothing</span></code>. The token <code><span class='Function'>𝕎</span></code> is not allowed in this case and causes an error. Re-parsing <code><span class='Value'>𝕨</span></code> can also cause an error if it's used as an operand or list element, where <code><span class='Value'>nothing</span></code> is not allowed by the grammar. Note that these errors must not appear if the block is always called with two arguments. True re-parsing is not required, as the same effect can also be achieved dynamically by treating <code><span class='Nothing'>·</span></code> as a value and checking for it during execution. If it's used as a left argument, then the function should instead be called with no left argument (and similarly in trains); if it's used as a right argument, then the function and its left argument are evaluated but rather than calling the function <code><span class='Nothing'>·</span></code> is &quot;returned&quot; immediately; and if it's used in another context then it causes an error.</p>
 <h3 id="assignment"><a class="header" href="#assignment">Assignment</a></h3>
 <p>An <em>assignment</em> is one of the four rules containing <code><span class='Function'>ASGN</span></code>. It is evaluated by first evaluating the right-hand-side <code><span class='Value'>subExpr</span></code>, <code><span class='Function'>FuncExpr</span></code>, <code><span class='Modifier'>_m1Expr</span></code>, or <code><span class='Modifier2'>_m2Exp_</span></code> expression, and then storing the result in the left-hand-side identifier or identifiers. The result of the assignment expression is the result of its right-hand side. Except for subjects, only a lone identifier is allowed on the left-hand side and storage sets it equal to the result. For subjects, <em>destructuring assignment</em> is performed when an <code><span class='Value'>lhs</span></code> is <code><span class='Value'>lhsList</span></code> or <code><span class='Value'>lhsStr</span></code>. Destructuring assignment is performed recursively by assigning right-hand-side values to the left-hand-side targets, with single-identifier assignment as the base case.</p>
diff --git a/docs/spec/grammar.html b/docs/spec/grammar.html
index 457fd039..99058319 100644
--- a/docs/spec/grammar.html
+++ b/docs/spec/grammar.html
@@ -84,8 +84,8 @@
          <span class='Function'>|</span> <span class='Value'>headW</span>  <span class='Paren'>(</span> <span class='Function'>F</span> <span class='Function'>|</span> <span class='String'>&quot;𝕊&quot;</span> <span class='Paren'>)</span> <span class='String'>&quot;˜&quot;</span>  <span class='String'>&quot;⁼&quot;</span> <span class='Value'>headX</span>
          <span class='Function'>|</span>        <span class='Paren'>(</span> <span class='Function'>F</span> <span class='Function'>|</span> <span class='String'>&quot;𝕊&quot;</span> <span class='Paren'>)</span> <span class='String'>&quot;˜&quot;</span><span class='Value'>?</span> <span class='String'>&quot;⁼&quot;</span>
 </pre>
-<p>A braced block contains bodies, which are lists of statements, separated by semicolons and possibly preceded by headers, which are separated from the body with a colon. Multiple bodies allow different handling for various cases, which are pattern-matched by headers. For an immediate block there are no inputs, so there can only be one possible case and one body. Functions and modifiers allow any number of &quot;matched&quot; bodies, with headers that have arguments, followed by at most two &quot;main&quot; bodies with either no headers or headers without arguments. If there is one main body, it is ambivalent, but two main bodies refer to the monadic and dyadic cases.</p>
-<pre><span class='Function'>BODY</span>     <span class='Function'>=</span> <span class='Function'>PROGRAM</span>
+<p>A braced block contains bodies, which are lists of statements, separated by semicolons and possibly preceded by headers, which are separated from the body with a colon. A non-final expression can be made into a predicate by following it with the separator-like <code><span class='Value'>?</span></code>. Multiple bodies allow different handling for various cases, which are pattern-matched by headers. For an immediate block there are no inputs, so there can only be one possible case and one body. Functions and modifiers allow any number of &quot;matched&quot; bodies, with headers that have arguments, followed by at most two &quot;main&quot; bodies with either no headers or headers without arguments. If there is one main body, it is ambivalent, but two main bodies refer to the monadic and dyadic cases.</p>
+<pre><span class='Function'>BODY</span>     <span class='Function'>=</span> <span class='Separator'>⋄</span><span class='Value'>?</span> <span class='Paren'>(</span> <span class='Function'>STMT</span> <span class='Separator'>⋄</span> <span class='Function'>|</span> <span class='Function'>EXPR</span> <span class='Separator'>⋄</span><span class='Value'>?</span> <span class='String'>&quot;?&quot;</span> <span class='Separator'>⋄</span><span class='Value'>?</span> <span class='Paren'>)</span><span class='Value'>*</span> <span class='Function'>STMT</span> <span class='Separator'>⋄</span><span class='Value'>?</span>
 <span class='Function'>FCase</span>    <span class='Function'>=</span> <span class='Separator'>⋄</span><span class='Value'>?</span> <span class='Function'>FuncHead</span> <span class='String'>&quot;:&quot;</span> <span class='Function'>BODY</span>
 <span class='Modifier'>_mCase</span>   <span class='Function'>=</span> <span class='Separator'>⋄</span><span class='Value'>?</span> <span class='Modifier'>_m1Head</span>  <span class='String'>&quot;:&quot;</span> <span class='Function'>BODY</span>
 <span class='Modifier2'>_cCase_</span>  <span class='Function'>=</span> <span class='Separator'>⋄</span><span class='Value'>?</span> <span class='Modifier2'>_m2Head_</span> <span class='String'>&quot;:&quot;</span> <span class='Function'>BODY</span>