410 lines
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410 lines
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<section id="the-template-instantiation-machine">
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<h1>The <em>Template Instantiation Machine</em><a class="headerlink" href="#the-template-instantiation-machine" title="Link to this heading">¶</a></h1>
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<p>WIP. This will hopefully be expanded into a thorough walkthrough of the state
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machine.</p>
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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/cddff17c817c1acda8498e28276cbace394ea817.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/538b0fab8c90c1abe8c6abaa3c807886040452db.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/d13a272a60d62c8a6b0ae4f178970b34b3cbc34b.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/9074d5122d0889ba7171982a92c523d35a2c447b.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/e34c3c7dbb292f28e888bfb49920d7c293055d2b.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/8282bc1515ee7f12235b6cf5ec58b653adacf9ab.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/4004b3a0b74a3d25993573e61733383293f43681.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/22bd53275636be43362c037f2ad50f5f63231e10.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/5cf94fab747054130daaf436fc83ab590969c35f.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/2a63b1f89224cb96d4e2b5a0f9494eac68234a42.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/3939cf0a8e341efac8ba1aeb5ae6271cd00c37c7.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/6d7f995d88e257359a4ce4f854c967791c1ec71d.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/96b775e1d32106f30d74a6fc743db615ea6e51ea.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/fea71c9f02d3639232648b940b80e5b9c1a03db3.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/00420770ada7197f2dc04dc2cb7be7957619046e.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/eb7dc8445c84c126f6834aa63965b5866af4862f.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/276f330b47308dae1686a2c0030783ed20a8866d.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/11cdffb9aaad97f1748e14369a93f303987914df.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/3eb2a0684a9c3d7c7a02334d788b2bd85cc83b55.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 class="current">
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<li class="toctree-l1"><a class="reference internal" href="gm.html">The <em>G-Machine</em></a></li>
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<li class="toctree-l1"><a class="reference internal" href="layout-lexing.html">Lexing, Parsing, and Layouts</a></li>
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<li class="toctree-l1 current"><a class="current reference internal" href="#">The <em>Template Instantiation Machine</em></a></li>
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</ul>
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<h3>Related Topics</h3>
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<li><a href="../index.html">Documentation overview</a><ul>
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<li>Previous: <a href="layout-lexing.html" title="previous chapter">Lexing, Parsing, and Layouts</a></li>
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