459 lines
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459 lines
12 KiB
HTML
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<section id="g-machine-state-transition-rules">
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<h1>G-Machine State Transition Rules<a class="headerlink" href="#g-machine-state-transition-rules" title="Link to this heading">¶</a></h1>
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<section id="core-transition-rules">
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<h2>Core Transition Rules<a class="headerlink" href="#core-transition-rules" title="Link to this heading">¶</a></h2>
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<ol class="arabic simple">
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<li><p>Lookup a global by name and push its value onto the stack</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/18d81e1fc22e6feb876a993fe30fd9e8336f5bf6.svg" alt="\gmrule
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{ \mathtt{PushGlobal} \; f : i
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& s
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& d
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& h
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& m
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\begin{bmatrix}
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f : a
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\end{bmatrix}
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}
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{ i
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& a : s
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}"/></p>
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</div><ol class="arabic simple" start="2">
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<li><p>Allocate an int node on the heap, and push the address of the newly created
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node onto the stack</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/ed6af2733291dcf5001173a8dbaf8f59c817212a.svg" alt="\gmrule
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{ \mathtt{PushInt} \; n : i
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& s
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& d
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& h
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& m
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}
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{ i
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& a : s
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\begin{bmatrix}
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a : \mathtt{NNum} \; n
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\end{bmatrix}
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& m
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}"/></p>
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</div><ol class="arabic simple" start="3">
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<li><p>Allocate an application node on the heap, applying the top of the stack to
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the address directly below it. The address of the application node is pushed
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onto the stack.</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/607985174357bbbea2e2b47ab0694b2d21a71b35.svg" alt="\gmrule
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{ \mathtt{MkAp} : i
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& f : x : s
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& d
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& h
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& m
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}
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{ i
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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{NAp} \; f \; x
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\end{bmatrix}
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& m
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}"/></p>
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</div><ol class="arabic simple" start="4">
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<li><p>Push a function’s argument onto the stack</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/643dd082a2b49d9ebdb87533aac62fdd342f4fd5.svg" alt="\gmrule
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{ \mathtt{Push} \; n : i
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& a_0 : \ldots : a_n : s
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& d
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}
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{ i
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& a_n : a_0 : \ldots : a_n : s
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& d
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& m
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}"/></p>
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</div><ol class="arabic simple" start="5">
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<li><p>Tidy up the stack after instantiating a supercombinator</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/f02d55fb6c249a7da5a9df6b7e5c96ab6be7672b.svg" alt="\gmrule
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{ \mathtt{Slide} \; n : i
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& a_0 : \ldots : a_n : s
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& d
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& h
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& m
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}
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{ i
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& a_0 : s
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& d
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}"/></p>
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</div><ol class="arabic simple" start="6">
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<li><p>If a number is on top of the stack, <code class="code docutils literal notranslate"><span class="pre">Unwind</span></code> leaves the machine in a
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halt state</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/f9a521977b1461b53094f1bae24aa6d1bb757b07.svg" alt="\gmrule
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{ \mathtt{Unwind} : \nillist
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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} \; n
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\end{bmatrix}
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& m
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}
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{ \nillist
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& a : s
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& d
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& h
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& m
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}"/></p>
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</div><ol class="arabic simple" start="7">
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<li><p>If an application is on top of the stack, <code class="code docutils literal notranslate"><span class="pre">Unwind</span></code> continues unwinding</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/b04167eaade600ab592e2a4441ffc27f5268cccf.svg" alt="\gmrule
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{ \mathtt{Unwind} : \nillist
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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{NAp} \; f \; x
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\end{bmatrix}
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& m
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}
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{ \mathtt{Unwind} : \nillist
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& f : a : s
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& d
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& h
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& m
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}"/></p>
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</div><ol class="arabic simple" start="8">
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<li><p>When a supercombinator is on top of the stack (and the correct number of
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arguments have been provided), <code class="code docutils literal notranslate"><span class="pre">Unwind</span></code> sets up the stack and jumps to
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the supercombinator’s code (<img class="math" src="../_images/math/90592e982322fa08f1b8ae0e6bcdaca11fc8de59.svg" alt="\beta" style="vertical-align: -4px"/>-reduction)</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/2dc5e48f0f26f08073e6e1cdd70ff876c6ec2434.svg" alt="\gmrule
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{ \mathtt{Unwind} : \nillist
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& a_0 : \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{NGlobal} \; n \; c \\
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a_1 : \mathtt{NAp} \; a_0 \; e_1 \\
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\vdots \\
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a_n : \mathtt{NAp} \; a_{n-1} \; e_n \\
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\end{bmatrix}
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& m
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}
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{ c
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& e_1 : \ldots : e_n : a_n : s
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& d
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& m
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}"/></p>
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</div><ol class="arabic simple" start="9">
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<li><p>Pop the stack, and update the nth node to point to the popped address</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/e299a147e6e958303111e813e82a3507ded25437.svg" alt="\gmrule
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{ \mathtt{Update} \; n : i
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& e : f : 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_1 : \mathtt{NAp} \; f \; e \\
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\vdots \\
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a_n : \mathtt{NAp} \; a_{n-1} \; e_n
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\end{bmatrix}
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& m
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}
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{ i
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& f : 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_n : \mathtt{NInd} \; e
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\end{bmatrix}
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& m
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}"/></p>
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</div><ol class="arabic simple" start="10">
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<li><p>Pop the stack.</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/aec9099fc8c459eb433947bd6c9cc0f96fe38f98.svg" alt="\gmrule
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{ \mathtt{Pop} \; n : i
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& a_1 : \ldots : a_n : s
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& d
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& m
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}
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{ i
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& s
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& m
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}"/></p>
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</div><ol class="arabic simple" start="11">
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<li><p>Follow indirections while unwinding</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/7648bfc0796ff33966fbc002c446b2242d296fd9.svg" alt="\gmrule
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{ \mathtt{Unwind} : \nillist
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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{NInd} \; a'
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\end{bmatrix}
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& m
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}
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{ \mathtt{Unwind} : \nillist
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& a' : s
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& d
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& h
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& m
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}"/></p>
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</div><ol class="arabic simple" start="12">
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<li><p>Allocate uninitialised heap space</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/5380d8227d0a06608b108a26b4a618972b4b7e28.svg" alt="\gmrule
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{ \mathtt{Alloc} \; n : i
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& s
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& d
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& h
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& m
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}
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{ i
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& 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_1 : \mathtt{NUninitialised} \\
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\vdots \\
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a_n : \mathtt{NUninitialised} \\
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\end{bmatrix}
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& m
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}"/></p>
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</div><ol class="arabic simple" start="13">
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<li><p>When unwinding, if the top of the stack is in WHNF, pop the dump</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/2417422cdf63ed202b16462208f8a62630f99679.svg" alt="\gmrule
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{ \mathtt{Unwind} : \nillist
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& a : s
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& \langle i', s' \rangle : 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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& m
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}
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{ i'
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& a : s'
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& d
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& h
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& m
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}"/></p>
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</div><ol class="arabic simple" start="14">
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<li><p>Evaluate the top of the stack to WHNF</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/e56dfd5625638bc4ad9867951a7818cf20c88a2f.svg" alt="\gmrule
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{ \mathtt{Eval} : i
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& a : s
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& d
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& h
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& m
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}
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{ i'
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& a : \nillist
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& \langle i, s \rangle
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& h
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& m
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}"/></p>
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</div></section>
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<section id="extension-rules">
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<h2>Extension Rules<a class="headerlink" href="#extension-rules" title="Link to this heading">¶</a></h2>
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<ol class="arabic simple">
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<li><p>A sneaky trick to enable sharing of <code class="code docutils literal notranslate"><span class="pre">NNum</span></code> nodes. We note that the
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global environment is a mapping of <code class="code docutils literal notranslate"><span class="pre">Name</span></code> objects (i.e. identifiers) to
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heap addresses. Strings of digits are not considered valid identifiers! We
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abuse this by modifying Core Rule 2 to update the global environment with the
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new node’s address. Consider how this rule might impact garbage collection
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(remember that the environment is intended for <em>globals</em>).</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/5a00c38ab6f040dfa75be56918953af44dc11637.svg" alt="\gmrule
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{ \mathtt{PushInt} \; n : i
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& s
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& h
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& m
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}
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{ i
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& a : s
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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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& m
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\begin{bmatrix}
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n' : a
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\end{bmatrix}
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\\
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\SetCell[c=5]{c}
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\text{where $n'$ is the base-10 string rep. of $n$}
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}"/></p>
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</div><ol class="arabic simple" start="2">
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<li><p>In order for Extension Rule 1. to be effective, we are also required to take
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action when a number already exists in the environment:</p></li>
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</ol>
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<div class="math">
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<p><img src="../_images/math/3fc332dc07916d83f75fcddf6da06a7734032ee9.svg" alt="\transrule
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{ \mathtt{PushInt} \; n : i
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& s
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& h
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& m
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\begin{bmatrix}
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n' : a
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\end{bmatrix}
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}
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{ i
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& a : s
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& h
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& m
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\\
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\SetCell[c=5]{c}
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\text{where $n'$ is the base-10 string rep. of $n$}
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}"/></p>
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</div></section>
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</section>
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<h1 class="logo"><a href="../index.html">rl'</a></h1>
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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">
|
||
<li class="toctree-l1 current"><a class="current reference internal" href="#">G-Machine State Transition Rules</a></li>
|
||
<li class="toctree-l1"><a class="reference internal" href="ti-state-transitions.html">Template Instantiator State Transition Rules</a></li>
|
||
</ul>
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<div class="relations">
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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="../commentary/ti.html" title="previous chapter">The <em>Template Instantiator</em></a></li>
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<li>Next: <a href="ti-state-transitions.html" title="next chapter">Template Instantiator State Transition Rules</a></li>
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</ul></li>
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