413 lines
13 KiB
HTML
413 lines
13 KiB
HTML
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<section id="template-instantiator-state-transition-rules">
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<h1>Template Instantiator State Transition Rules<a class="headerlink" href="#template-instantiator-state-transition-rules" title="Link to this heading">¶</a></h1>
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<p>Evaluation is complete when a single <code class="code docutils literal notranslate"><span class="pre">NNum</span></code> remains on the stack and the
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dump is empty.</p>
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<div class="math">
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<p><img src="../_images/math/90d7e53e2606d1ffdcc0d85fcc0be2db9b919797.svg" alt="\transrule
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{ a : \nillist
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& \nillist
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& h
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\begin{bmatrix}
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a : \mathtt{NNum} \; n
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\end{bmatrix}
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& g
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}
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{ \mathtt{HALT}
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}"/></p>
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</div><p>Dereference an indirection passed as an argument to a function.</p>
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<div class="math">
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<p><img src="../_images/math/2e21d478eedaa358bccb9aa3c57a5b290e671863.svg" alt="\transrule
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{a : s & d & h
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\begin{bmatrix}
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a : \mathtt{NAp} \; a_1 \; a_2 \\
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a_2 : \mathtt{NInd} \; a_3
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\end{bmatrix} & g}
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{a : s & d & h[a : \mathtt{NAp} \; a_1 \; a_3] & g}"/></p>
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</div><p>Dereference an indirection on top of the stack.</p>
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<div class="math">
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<p><img src="../_images/math/d30cef88d057bcc5920fca7d63d0682f802d9006.svg" alt="\transrule
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{p : s & d & h
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\begin{bmatrix}
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p : \mathtt{NInd} \; a
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\end{bmatrix} & g}
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{a : s & d & h & g}"/></p>
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</div><p>Perform a unary operation <img class="math" src="../_images/math/6bdb1b0b4006f5b62d10449cd280f311f4cf12f8.svg" alt="o(n)" style="vertical-align: -5px"/> with internal <code class="code docutils literal notranslate"><span class="pre">Prim</span></code> constructor
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<code class="code docutils literal notranslate"><span class="pre">O</span></code> on an argument in normal form.</p>
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<div class="math">
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<p><img src="../_images/math/e4dc66520823a07e0df31b43dda92f9b2ea9e792.svg" alt="\transrule
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{ f : a : s
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{O} \\
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a : \mathtt{NAp} \; f \; x \\
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x : \mathtt{NNum} \; n
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\end{bmatrix}
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& g
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}
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{ a : s
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& d
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& h
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\begin{bmatrix}
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a : \mathtt{NNum} \; (o(n))
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\end{bmatrix}
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& g
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}"/></p>
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</div><p>Evaluate the argument of a unary operation with internal <code class="code docutils literal notranslate"><span class="pre">Prim</span></code>
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constructor <code class="code docutils literal notranslate"><span class="pre">O</span></code>.</p>
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<div class="math">
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<p><img src="../_images/math/620e45afe56ccc0dae7d9566d244b13bb6cb0631.svg" alt="\transrule
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{ f : a : \nillist
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{O} \\
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a : \mathtt{NAp} \; f \; x
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\end{bmatrix}
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& g
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}
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{ x : \nillist
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& (f : a : \nillist) : d
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& h
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& g
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}"/></p>
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</div><p>Restore the stack when a sub-computation has completed.</p>
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<div class="math">
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<p><img src="../_images/math/4d427448f9b8b54db19e316c805033a7abfe11d2.svg" alt="\transrule
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{ a : \nillist
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& s : d
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& h
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\begin{bmatrix}
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a : \mathtt{NNum} \; n
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\end{bmatrix}
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& g
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}
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{ s
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& d
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& h
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& g
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}"/></p>
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</div><p>Reduce a supercombinator and update the root with the <img class="math" src="../_images/math/90592e982322fa08f1b8ae0e6bcdaca11fc8de59.svg" alt="\beta" style="vertical-align: -4px"/>-reduced form</p>
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<div class="math">
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<p><img src="../_images/math/20219b0570be52c3f596972c4cd5461a162cccf9.svg" alt="\transrule
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{ a_0 : a_1 : \ldots : a_n : s
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& d
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& h
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\begin{bmatrix}
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a_0 : \mathtt{NSupercomb} \; [x_1,\ldots,x_n] \; e
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\end{bmatrix}
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& g
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}
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{ a_n : s
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& d
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& h'
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& g
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\\
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& \SetCell[c=3]{c}
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\text{where } h' = \mathtt{instantiateU} \; e \; a_n \; h \; g
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}"/></p>
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</div><p>Perform a binary operation <img class="math" src="../_images/math/c9ac657e040edf18bbbf248d15d73ab640a93f2d.svg" alt="o(x,y)" style="vertical-align: -5px"/> associated with internal <code class="code docutils literal notranslate"><span class="pre">Prim</span></code>
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constructor <code class="code docutils literal notranslate"><span class="pre">O</span></code> on two <code class="code docutils literal notranslate"><span class="pre">NNum</span></code> s both in normal form.</p>
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<div class="math">
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<p><img src="../_images/math/7c31cda93cce15a6bef0ecb07b4221f15d15cc9f.svg" alt="\transrule
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{ f : a_1 : a_2 : s
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{O} \\
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a_1 : \mathtt{NAp} \; f \; (\mathtt{NNum} \; x) \\
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a_2 : \mathtt{NAp} \; a_1 \; (\mathtt{NNum} \; y)
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\end{bmatrix}
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& g
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}
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{ a_2 : s
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& d
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& h
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\begin{bmatrix}
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a_2 : \mathtt{NNum} \; (o(x,y))
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\end{bmatrix}
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& g
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}"/></p>
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</div><p>In a conditional primitive, perform the reduction if the condition has been
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evaluated as True (<code class="code docutils literal notranslate"><span class="pre">NData</span> <span class="pre">1</span> <span class="pre">[]</span></code>).</p>
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<div class="math">
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<p><img src="../_images/math/1543958253280895e6abea369c0f9abf4898649c.svg" alt="\transrule
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{ f : a_1 : a_2 : a_3 : s
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{IfP} \\
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c : \mathtt{NPrim} \; (\mathtt{NData} \; 1 \; \nillist) \\
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a_1 : \mathtt{NAp} \; f \; c \\
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a_2 : \mathtt{NAp} \; a_1 \; x \\
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a_3 : \mathtt{NAp} \; a_2 \; y
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\end{bmatrix}
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& g
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}
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{ x : s
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& d
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& h
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& g
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}"/></p>
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</div><p>In a conditional primitive, perform the reduction if the condition has been
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evaluated as False (<code class="code docutils literal notranslate"><span class="pre">NData</span> <span class="pre">0</span> <span class="pre">[]</span></code>).</p>
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<div class="math">
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<p><img src="../_images/math/6d95eec30809d2f72c4d645e69ee6ba5fd3f0767.svg" alt="\transrule
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{ f : a_1 : a_2 : a_3 : s
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{IfP} \\
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c : \mathtt{NPrim} \; (\mathtt{NData} \; 0 \; \nillist) \\
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a_1 : \mathtt{NAp} \; f \; c \\
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a_2 : \mathtt{NAp} \; a_1 \; x \\
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a_3 : \mathtt{NAp} \; a_2 \; y
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\end{bmatrix}
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& g
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}
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{ y : s
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& d
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& h
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& g
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}"/></p>
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</div><p>In a conditional primitive, evaluate the condition.</p>
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<div class="math">
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<p><img src="../_images/math/625a1ccce064b171eb9d5ec015e07d234ef26c74.svg" alt="\transrule
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{ f : a_1 : \nillist
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{IfP} \\
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a_1 : \mathtt{NAp} \; f \; x
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\end{bmatrix}
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& g
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}
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{ x : \nillist
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& (f : a_1 : \nillist) : d
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& h
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& g
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}"/></p>
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</div><p>Construct <code class="code docutils literal notranslate"><span class="pre">NData</span></code> out of a constructor and its arguments</p>
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<div class="math">
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<p><img src="../_images/math/b0285722e6eed4a0fa69945efe4dfe0fbe124582.svg" alt="\transrule
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{ c : a_1 : \ldots : a_n : \nillist
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; (\mathtt{ConP} \; t \; n) \\
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a_1 : \mathtt{NAp} \; c \; x_1 \\
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\vdots \\
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a_n : \mathtt{NAp} \; a_{n-1} \; x_n
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\end{bmatrix}
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& g
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}
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{ a_n : \nillist
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& d
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& h
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\begin{bmatrix}
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a_n : \mathtt{NData} \; t \; [x_1, \ldots, x_n]
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\end{bmatrix}
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& g
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}"/></p>
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</div><section id="pairs">
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<h2>Pairs<a class="headerlink" href="#pairs" title="Link to this heading">¶</a></h2>
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<p>Evaluate the first argument if necessary</p>
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<div class="math">
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<p><img src="../_images/math/478aeca314882e29dc3a52d64624061fb36948f0.svg" alt="\transrule
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{ c : a_1 : a_2 : \nillist
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; \mathtt{CasePairP} \\
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p : \mathtt{NAp} \; \_ \: \_ \\
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a_1 : \mathtt{NAp} \; c \; p \\
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a_2 : \mathtt{NAp} \; a_2 \; f
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\end{bmatrix}
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& g
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}
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{ p : \nillist
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& (a_1 : a_2 : \nillist) : d
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& h
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& g
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}"/></p>
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</div><p>Perform the reduction if the first argument is in normal form</p>
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<div class="math">
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<p><img src="../_images/math/c5937687478d980ab66b85de909dcb73d4bc9b13.svg" alt="\transrule
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{ c : a_1 : a_2 : s
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; \mathtt{CasePairP} \\
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p : \mathtt{NData} \; 0 \; [x,y] \\
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a_1 : \mathtt{NAp} \; c \; p \\
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a_2 : \mathtt{NAp} \; a_1 \; f
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\end{bmatrix}
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& g
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}
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{ a_1 : a_2 : s
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& d
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& h
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\begin{bmatrix}
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a_1 : \mathtt{NAp} \; f \; x \\
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a_2 : \mathtt{NAp} \; a_1 \; y
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\end{bmatrix}
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& g
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}"/></p>
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</div></section>
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<section id="lists">
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<h2>Lists<a class="headerlink" href="#lists" title="Link to this heading">¶</a></h2>
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<p>Evaluate the scrutinee</p>
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<div class="math">
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<p><img src="../_images/math/5bd3cd582dce130ac602d5d805972076e5bc0f56.svg" alt="\transrule
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{ c : a_1 : a_2 : a_3 : \nillist
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; \mathtt{CaseListP} \\
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a_1 : \mathtt{NAp} \; c \; x
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\end{bmatrix}
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& g
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}
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{ x
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& (a_1 : a_2 : a_3) : \nillist
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& h
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& g
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}"/></p>
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</div><p>If the scrutinee is <code class="code docutils literal notranslate"><span class="pre">Nil</span></code>, perform the appropriate reduction.</p>
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<div class="math">
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<p><img src="../_images/math/a6502e03af9f1e3d8a7dce9053c7125364a0cae5.svg" alt="\transrule
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{ c : a_1 : a_2 : a_3 : s
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; \mathtt{CaseListP} \\
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p : \mathtt{NData} \; 1 \; \nillist \\
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a_1 : \mathtt{NAp} \; c \; p \\
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a_2 : \mathtt{NAp} \; p \; f_\text{nil} \\
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a_3 : \mathtt{NAp} \; a_2 \; f_\text{cons}
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\end{bmatrix}
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& g
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}
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{ a_3 : s
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& d
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& h
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\begin{bmatrix}
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a_3 : \mathtt{NAp} \; f_\text{nil}
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\end{bmatrix}
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& g
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}"/></p>
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</div></section>
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</section>
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<h3>Navigation</h3>
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<p class="caption" role="heading"><span class="caption-text">Index</span></p>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../glossary.html">Glossary</a></li>
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</ul>
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<p class="caption" role="heading"><span class="caption-text">Commentary</span></p>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../commentary/gm.html">The <em>G-Machine</em></a></li>
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<li class="toctree-l1"><a class="reference internal" href="../commentary/layout-lexing.html">Lexing, Parsing, and Layouts</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../commentary/ti.html">The <em>Template Instantiator</em></a></li>
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</ul>
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<p class="caption" role="heading"><span class="caption-text">References</span></p>
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<ul class="current">
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<li class="toctree-l1"><a class="reference internal" href="gm-state-transition-rules.html">G-Machine State Transition Rules</a></li>
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<li class="toctree-l1 current"><a class="current reference internal" href="#">Template Instantiator State Transition Rules</a></li>
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</ul>
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<h3>Related Topics</h3>
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<ul>
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<li><a href="../index.html">Documentation overview</a><ul>
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<li>Previous: <a href="gm-state-transition-rules.html" title="previous chapter">G-Machine State Transition Rules</a></li>
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</ul></li>
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