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<section id="the-g-machine">
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<h1>The <em>G-Machine</em><a class="headerlink" href="#the-g-machine" title="Link to this heading">¶</a></h1>
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<section id="motivation">
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<h2>Motivation<a class="headerlink" href="#motivation" title="Link to this heading">¶</a></h2>
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<p>Our initial model, the <em>Template Instantiator</em> (TI) was a very
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straightforward solution to compilation, but its core design has a major
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Achilles’ heel, being that Compilation is interleaved with evaluation – The
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heap nodes for supercombinators hold uninstantiated expressions, i.e. raw ASTs
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straight from the parser. When a supercombinator is found on the stack during
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evaluation, the template expression is instantiated (compiled) on the spot.</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>The process of instantiating a supercombinator goes something like this</p>
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<ol class="arabic simple">
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<li><p>Augment the environment with bindings to the arguments.</p></li>
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<li><p>Using the local augmented environment, instantiate the supercombinator body
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on the heap.</p></li>
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<li><p>Remove the nodes applying the supercombinator to its arguments from the
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stack.</p></li>
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<li><p>Push the address to the newly instantiated body onto the stack.</p></li>
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</ol>
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<div class="literal-block-wrapper docutils container" id="id1">
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<div class="code-block-caption"><span class="caption-text">src/TI.hs</span><a class="headerlink" href="#id1" title="Link to this code">¶</a></div>
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<div class="highlight-haskell notranslate"><div class="highlight"><pre><span></span><span class="nf">scStep</span><span class="w"> </span><span class="ow">::</span><span class="w"> </span><span class="kt">Name</span><span class="w"> </span><span class="ow">-></span><span class="w"> </span><span class="p">[</span><span class="kt">Name</span><span class="p">]</span><span class="w"> </span><span class="ow">-></span><span class="w"> </span><span class="kt">Expr</span><span class="w"> </span><span class="ow">-></span><span class="w"> </span><span class="kt">TiState</span><span class="w"> </span><span class="ow">-></span><span class="w"> </span><span class="kt">TiState</span>
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<span class="nf">scStep</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="n">as</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="p">(</span><span class="kt">TiState</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="n">h</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="n">sts</span><span class="p">)</span><span class="w"> </span><span class="ow">=</span>
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<span class="w"> </span><span class="kt">TiState</span><span class="w"> </span><span class="n">s'</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="n">h'</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="n">sts</span>
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<span class="w"> </span><span class="kr">where</span>
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<span class="w"> </span><span class="n">s'</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">rootAddr</span><span class="w"> </span><span class="kt">:</span><span class="w"> </span><span class="n">drop</span><span class="w"> </span><span class="p">(</span><span class="n">length</span><span class="w"> </span><span class="n">as</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="c1">-- 3., 4.</span>
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<span class="w"> </span><span class="n">h'</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">instantiateU</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="n">rootAddr</span><span class="w"> </span><span class="n">h</span><span class="w"> </span><span class="n">env</span><span class="w"> </span><span class="c1">-- 2.</span>
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<span class="w"> </span><span class="n">rootAddr</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">!!</span><span class="w"> </span><span class="n">length</span><span class="w"> </span><span class="n">as</span>
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<span class="w"> </span><span class="n">env</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">argBinds</span><span class="w"> </span><span class="o">++</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="c1">-- 1.</span>
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<span class="w"> </span><span class="n">argBinds</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">as</span><span class="w"> </span><span class="p">`</span><span class="n">zip</span><span class="p">`</span><span class="w"> </span><span class="n">argAddrs</span>
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<span class="w"> </span><span class="n">argAddrs</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">getArgs</span><span class="w"> </span><span class="n">h</span><span class="w"> </span><span class="n">s</span>
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</pre></div>
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</div>
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</div>
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<p>Instantiating the supercombinator’s body in this way is the root of our
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Achilles’ heel. Traversing a tree structure is a very non-linear task unfit for
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an assembly target. The goal of our new G-Machine is to compile a <em>linear
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sequence of instructions</em> which instantiate the expression at execution.</p>
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</section>
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<section id="trees-and-vines-in-theory">
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<h2>Trees and Vines, in Theory<a class="headerlink" href="#trees-and-vines-in-theory" title="Link to this heading">¶</a></h2>
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<p>WIP.</p>
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</section>
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<section id="evaluation-slurping-vines">
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<h2>Evaluation: Slurping Vines<a class="headerlink" href="#evaluation-slurping-vines" title="Link to this heading">¶</a></h2>
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<p>WIP.</p>
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<section id="laziness">
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<h3>Laziness<a class="headerlink" href="#laziness" title="Link to this heading">¶</a></h3>
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<p>WIP.</p>
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<ul class="simple">
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<li><p>Instead of <code class="code docutils literal notranslate"><span class="pre">Slide</span> <span class="pre">(n+1);</span> <span class="pre">Unwind</span></code>, do <code class="code docutils literal notranslate"><span class="pre">Update</span> <span class="pre">n;</span> <span class="pre">Pop</span> <span class="pre">n;</span> <span class="pre">Unwind</span></code></p></li>
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</ul>
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</section>
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</section>
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<section id="compilation-squashing-trees">
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<h2>Compilation: Squashing Trees<a class="headerlink" href="#compilation-squashing-trees" title="Link to this heading">¶</a></h2>
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<p>WIP.</p>
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<p>Notice that we do not keep a (local) environment at run-time. The environment
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only exists at compile-time to map local names to stack indices. When compiling
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a supercombinator, the arguments are enumerated from zero (the top of the
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stack), and passed to <code class="code docutils literal notranslate"><span class="pre">compileR</span></code> as an environment.</p>
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<div class="literal-block-wrapper docutils container" id="id2">
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<div class="code-block-caption"><span class="caption-text">src/GM.hs</span><a class="headerlink" href="#id2" title="Link to this code">¶</a></div>
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<div class="highlight-haskell notranslate"><div class="highlight"><pre><span></span><span class="c1">-- type CompiledSC = (Name, Int, Code)</span>
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<span class="nf">compileSc</span><span class="w"> </span><span class="ow">::</span><span class="w"> </span><span class="kt">ScDef</span><span class="w"> </span><span class="ow">-></span><span class="w"> </span><span class="kt">CompiledSC</span>
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<span class="nf">compileSc</span><span class="w"> </span><span class="p">(</span><span class="kt">ScDef</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="n">as</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="p">,</span><span class="w"> </span><span class="n">compileR</span><span class="w"> </span><span class="n">env</span><span class="w"> </span><span class="n">b</span><span class="p">)</span>
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<span class="w"> </span><span class="kr">where</span>
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<span class="w"> </span><span class="n">env</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">as</span><span class="w"> </span><span class="p">`</span><span class="n">zip</span><span class="p">`</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="o">..</span><span class="p">]</span>
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<span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">length</span><span class="w"> </span><span class="n">as</span>
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</pre></div>
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</div>
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</div>
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<p>Of course, variables being indexed relative to the top of the stack means that
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they will become inaccurate the moment we push or pop the stack a single time.
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The way around this is quite simple: simply offset the stack when w</p>
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<div class="literal-block-wrapper docutils container" id="id3">
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<div class="code-block-caption"><span class="caption-text">src/GM.hs</span><a class="headerlink" href="#id3" title="Link to this code">¶</a></div>
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<div class="highlight-haskell notranslate"><div class="highlight"><pre><span></span><span class="nf">compileC</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="p">(</span><span class="kt">App</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="n">compileC</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="n">x</span>
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<span class="w"> </span><span class="o"><></span><span class="w"> </span><span class="n">compileC</span><span class="w"> </span><span class="p">(</span><span class="n">argOffset</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="n">g</span><span class="p">)</span><span class="w"> </span><span class="n">f</span>
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<span class="w"> </span><span class="o"><></span><span class="w"> </span><span class="p">[</span><span class="kt">MkAp</span><span class="p">]</span>
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</pre></div>
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</div>
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<p class="caption" role="heading"><span class="caption-text">Commentary</span></p>
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<li class="toctree-l1 current"><a class="current reference internal" href="#">The <em>G-Machine</em></a></li>
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<p class="caption" role="heading"><span class="caption-text">References</span></p>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../references/gm-state-transitions.html">G-Machine State Transition Rules</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../references/ti-state-transitions.html">Template Instantiator State Transition Rules</a></li>
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