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</head><body><h1 id="elerea-breakout-example">Elerea Breakout example</h1><p>Breakout is one of the simplest test applications that brings up some problems with non-trivial solutions. In particular, there is a circular dependency between the position and the velocity of the ball. The position is the integral of the velocity, while velocity can have instantaneous changes due to collisions, which is a function of the position of the ball and the current state of the field. The field is dynamic, and it also forms a mutual dependency loop with the ball position. On top of these, part of the field (at least if we regard the paddle as part of it) depends on user input, and its effects start propagating in the game state as soon as the ball reaches the level of the paddle.</p><p>Elerea lets us express all these circular dependencies in a natural way, by simply referring to the respective signals by their names. User input is also seen as a signal from inside the reactive part, while the imperative framework is given a sink fuction to update it as needed. Type safety is ensured all the way.</p><img src="Breakout.png" alt="Elerea Breakout in action" /><p>Below follows the full source of the example.</p><pre><span class='hs-varop'>></span> <span class='hs-keyword'>module</span> <span class='hs-conid'>Main</span> <span class='hs-keyword'>where</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Concurrent</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>IORef</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Maybe</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>FRP</span><span class='hs-varop'>.</span><span class='hs-conid'>Elerea</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Graphics</span><span class='hs-varop'>.</span><span class='hs-conid'>UI</span><span class='hs-varop'>.</span><span class='hs-conid'>GLFW</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>GLFW</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Graphics</span><span class='hs-varop'>.</span><span class='hs-conid'>Rendering</span><span class='hs-varop'>.</span><span class='hs-conid'>OpenGL</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Common</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Common</span><span class='hs-varop'>.</span><span class='hs-conid'>Vector</span>
</pre><h2 id="global-constants">Global constants</h2><p>The dimensions of the ball, which behaves as a rectangle in collision detection, but is drawn as an ellipse.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>ballW</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.04</span>
<span class='hs-varop'>></span> <span class='hs-varid'>ballH</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.04</span>
</pre><p>The initial position and velocity of the ball.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>ballPos0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-num'>0</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>0.4</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>ballVel0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>0.4</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0.35</span><span class='hs-layout'>)</span>
</pre><p>The dimensions and vertical position of the player.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>playerW</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.2</span>
<span class='hs-varop'>></span> <span class='hs-varid'>playerH</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.03</span>
<span class='hs-varop'>></span> <span class='hs-varid'>playerY</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-varid'>fieldH</span><span class='hs-varop'>+</span><span class='hs-num'>0.01</span>
</pre><p>The dimensions of the field.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>fieldW</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.8</span>
<span class='hs-varop'>></span> <span class='hs-varid'>fieldH</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.5</span>
</pre><p>The dimensions of each brick.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>brickW</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.05</span>
<span class='hs-varop'>></span> <span class='hs-varid'>brickH</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.03</span>
</pre><p>The starting positions of the bricks. The third element of the triples is the state of the brick. A brick can either be alive or dying. Dying bricks also keep track of their fadeout level.</p><pre><span class='hs-varop'>></span> <span class='hs-keyword'>data</span> <span class='hs-conid'>BrickState</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Live</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>Dying</span> <span class='hs-conid'>Double</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Eq</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>brickPos0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>distributeBricks</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>0.7</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>0.1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0.7</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0.4</span><span class='hs-layout'>)</span> <span class='hs-num'>18</span> <span class='hs-num'>10</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>distributeBricks</span> <span class='hs-varid'>xmin</span> <span class='hs-varid'>ymin</span> <span class='hs-varid'>xmax</span> <span class='hs-varid'>ymax</span> <span class='hs-varid'>xn</span> <span class='hs-varid'>yn</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>xmin</span><span class='hs-varop'>+</span><span class='hs-varid'>xstep</span><span class='hs-varop'>*</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>ymin</span><span class='hs-varop'>+</span><span class='hs-varid'>ystep</span><span class='hs-varop'>*</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span><span class='hs-conid'>Live</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span>
<span class='hs-varop'>></span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>←</span> <span class='hs-keyglyph'>[</span><span class='hs-num'>0</span><span class='hs-keyglyph'>..</span><span class='hs-varid'>xn</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>←</span> <span class='hs-keyglyph'>[</span><span class='hs-num'>0</span><span class='hs-keyglyph'>..</span><span class='hs-varid'>yn</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>xstep</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>xmax</span><span class='hs-comment'>-</span><span class='hs-varid'>xmin</span><span class='hs-comment'>-</span><span class='hs-varid'>xn</span><span class='hs-varop'>*</span><span class='hs-varid'>brickW</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-layout'>(</span><span class='hs-varid'>xn</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span><span class='hs-varop'>+</span><span class='hs-varid'>brickW</span>
<span class='hs-varop'>></span> <span class='hs-varid'>ystep</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>ymax</span><span class='hs-comment'>-</span><span class='hs-varid'>ymin</span><span class='hs-comment'>-</span><span class='hs-varid'>yn</span><span class='hs-varop'>*</span><span class='hs-varid'>brickH</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-layout'>(</span><span class='hs-varid'>yn</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span><span class='hs-varop'>+</span><span class='hs-varid'>brickH</span>
</pre><p>The rate at which a brick fades out. The reciprocal of this value gives the fadeout time in seconds.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>brickFade</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.5</span>
</pre><h2 id="game-logic">Game logic</h2><p>The entry point performs some lightweight initialisation, and defines the two user-driven signals: window size and mouse position. The <code>external</code> function creates the signal and the corresponding sink at the same time.</p><p>When all is done <code>driveNetwork</code> is invoked. It is not a library function, but part of the tiny <code>Utils</code> module .</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>main</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-comment'>-- Creating a window without a depth buffer</span>
<span class='hs-varop'>></span> <span class='hs-varid'>initialize</span>
<span class='hs-varop'>></span> <span class='hs-varid'>openWindow</span> <span class='hs-layout'>(</span><span class='hs-conid'>Size</span> <span class='hs-num'>640</span> <span class='hs-num'>480</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>DisplayRGBBits</span> <span class='hs-num'>8</span> <span class='hs-num'>8</span> <span class='hs-num'>8</span><span class='hs-layout'>,</span> <span class='hs-conid'>DisplayAlphaBits</span> <span class='hs-num'>8</span><span class='hs-keyglyph'>]</span> <span class='hs-conid'>Window</span>
<span class='hs-varop'>></span> <span class='hs-varid'>windowTitle</span> <span class='hs-varop'>$=</span> <span class='hs-str'>"Elerea Breakout"</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-comment'>-- External signals available for the game logic</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varid'>windowSize</span><span class='hs-layout'>,</span><span class='hs-varid'>windowSizeSink</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>←</span> <span class='hs-varid'>external</span> <span class='hs-varid'>vnull</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varid'>mousePosition</span><span class='hs-layout'>,</span><span class='hs-varid'>mousePositionSink</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>←</span> <span class='hs-varid'>external</span> <span class='hs-varid'>vnull</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-comment'>-- Wrapping up the init phase</span>
<span class='hs-varop'>></span> <span class='hs-varid'>closed</span> <span class='hs-keyglyph'>←</span> <span class='hs-varid'>newIORef</span> <span class='hs-conid'>False</span>
<span class='hs-varop'>></span> <span class='hs-varid'>windowSizeCallback</span> <span class='hs-varop'>$=</span> <span class='hs-varid'>resizeGLScene</span> <span class='hs-varid'>windowSizeSink</span>
<span class='hs-varop'>></span> <span class='hs-varid'>windowCloseCallback</span> <span class='hs-varop'>$=</span> <span class='hs-varid'>writeIORef</span> <span class='hs-varid'>closed</span> <span class='hs-conid'>True</span>
<span class='hs-varop'>></span> <span class='hs-varid'>initGL</span> <span class='hs-num'>640</span> <span class='hs-num'>480</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-comment'>-- All we need to get going is an IO-valued signal and an IO</span>
<span class='hs-varop'>></span> <span class='hs-comment'>-- function to update the external signals</span>
<span class='hs-varop'>></span> <span class='hs-varid'>driveNetwork</span> <span class='hs-layout'>(</span><span class='hs-varid'>breakout</span> <span class='hs-varid'>mousePosition</span> <span class='hs-varid'>windowSize</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varid'>readInput</span> <span class='hs-varid'>mousePositionSink</span> <span class='hs-varid'>closed</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-comment'>-- The inevitable sad ending</span>
<span class='hs-varop'>></span> <span class='hs-varid'>closeWindow</span>
</pre><p>The <code>breakout</code> function creates a reactive signal that carries the rendering actions to be performed at each instant. The principal signals forming the game logic are the following:</p><ul><li><code>playerX</code>: the position of the player, a direct function of the mouse position;</li><li><code>ballPos</code>: the position of the ball given as an integral of its velocity, <code>ballVel</code>;</li><li><code>bricks</code>: the collection of live and dying bricks along with collision information.</li></ul><p>The position and velocity of the ball form a circular dependency, as velocity is changed whenever a collision is detected, which is a function of the position.</p><p>The signal carrying the collection of the bricks is obtained by applying a stateful transformation (a transfer function) on the ball position. The state contains the bricks still relevant to the game as well as collision information. Although the latter is technically redundant, it is still worth including here, since it has to be calculated while advancing the state of the bricks, and it is needed elsewhere too.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>breakout</span> <span class='hs-varid'>mousePos</span> <span class='hs-varid'>windowSize</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>renderLevel</span> <span class='hs-varop'><$></span> <span class='hs-varid'>playerX</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ballPos</span> <span class='hs-varop'><*></span> <span class='hs-layout'>(</span><span class='hs-varid'>getBricks</span> <span class='hs-varop'><$></span> <span class='hs-varid'>bricks</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span>
</pre><p>User-driven player position:</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>playerX</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>adjustPlayerPos</span> <span class='hs-varop'><$></span> <span class='hs-varid'>mousePos</span> <span class='hs-varop'><*></span> <span class='hs-varid'>windowSize</span>
<span class='hs-varop'>></span> <span class='hs-varid'>adjustPlayerPos</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>x</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>w</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>min</span> <span class='hs-layout'>(</span><span class='hs-varid'>fieldW</span><span class='hs-comment'>-</span><span class='hs-varid'>playerW</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>max</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>fieldW</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-num'>2</span><span class='hs-varop'>*</span><span class='hs-varid'>x</span><span class='hs-varop'>/</span><span class='hs-varid'>w</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-comment'>-</span><span class='hs-varid'>playerW</span><span class='hs-varop'>/</span><span class='hs-num'>2</span>
</pre><p>Ball state: position and velocity. Note the use of the latcher: we wrap a signal created by <code>adjustVel</code> in a <code>pure</code>, hence adding another signal layer around it.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>ballPos</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>integralVec</span> <span class='hs-layout'>(</span><span class='hs-varid'>ballPos0</span><span class='hs-layout'>)</span> <span class='hs-varid'>ballVel</span>
<span class='hs-varop'>></span> <span class='hs-varid'>ballVel</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>latcher</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-varid'>ballVel0</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varid'>ballCollHorz</span> <span class='hs-varop'>||@</span> <span class='hs-varid'>ballCollVert</span> <span class='hs-varop'>||@</span> <span class='hs-varid'>ballCollPlayer</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-varop'><$></span> <span class='hs-layout'>(</span><span class='hs-varid'>adjustVel</span> <span class='hs-varop'><$></span> <span class='hs-varid'>ballCollHorz</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ballCollVert</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ballCollPlayer</span> <span class='hs-varop'><*></span>
<span class='hs-varop'>></span> <span class='hs-varid'>ballVel</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ballNewVelX</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
</pre><p>The <code>adjustVel</code> function calculates a candidate velocity for the next frame given collision information and the current velocity. Even though it would return the current speed if there are no collisions, we rather not evaluate it at all thanks to the latcher. In the end, velocity is not recalculated in each frame.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>adjustVel</span> <span class='hs-varid'>ch</span> <span class='hs-varid'>cv</span> <span class='hs-varid'>cp</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>bvx</span> <span class='hs-varid'>bvy</span><span class='hs-layout'>)</span> <span class='hs-varid'>bvx'</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-keyword'>if</span> <span class='hs-varid'>ch</span> <span class='hs-keyword'>then</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <span class='hs-keyword'>else</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-layout'>(</span><span class='hs-keyword'>if</span> <span class='hs-varid'>cp</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>bvx'</span><span class='hs-varop'>*</span><span class='hs-num'>4</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>bvx</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>cv</span> <span class='hs-varop'>||</span> <span class='hs-varid'>cp</span> <span class='hs-keyword'>then</span> <span class='hs-comment'>-</span><span class='hs-varid'>bvy</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>bvy</span>
<span class='hs-varop'>></span> <span class='hs-varid'>ballNewVelX</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>getX</span> <span class='hs-varop'><$></span> <span class='hs-varid'>ballPos</span><span class='hs-layout'>)</span><span class='hs-comment'>-</span><span class='hs-varid'>playerX</span><span class='hs-comment'>-</span><span class='hs-varid'>pure</span> <span class='hs-layout'>(</span><span class='hs-varid'>playerW</span><span class='hs-varop'>/</span><span class='hs-num'>2</span><span class='hs-layout'>)</span>
</pre><p>Collision events are modelled with bool signals that turn true while the ball overlaps the offending surface and approaches it at the same time. Collision response will make sure that the second condition does not hold in the next instant, so there is no need to push these through an <code>edge</code> transfer function.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>ballCollHorz</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>getHColl</span> <span class='hs-varop'><$></span> <span class='hs-varid'>bricks</span><span class='hs-layout'>)</span> <span class='hs-varop'>||@</span> <span class='hs-layout'>(</span><span class='hs-varid'>check</span> <span class='hs-varop'><$></span> <span class='hs-varid'>ballPos</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ballVel</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>check</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>bx</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>bvx</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>bx</span> <span class='hs-varop'><</span> <span class='hs-comment'>-</span><span class='hs-varid'>fieldW</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>bvx</span> <span class='hs-varop'><</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>||</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varid'>bx</span> <span class='hs-varop'>></span> <span class='hs-varid'>fieldW</span><span class='hs-comment'>-</span><span class='hs-varid'>ballW</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>bvx</span> <span class='hs-varop'>></span> <span class='hs-num'>0</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>ballCollVert</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>getVColl</span> <span class='hs-varop'><$></span> <span class='hs-varid'>bricks</span><span class='hs-layout'>)</span> <span class='hs-varop'>||@</span> <span class='hs-layout'>(</span><span class='hs-varid'>check</span> <span class='hs-varop'><$></span> <span class='hs-varid'>ballPos</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ballVel</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>check</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>bx</span> <span class='hs-varid'>by</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>bvy</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>by</span> <span class='hs-varop'>></span> <span class='hs-varid'>fieldH</span><span class='hs-comment'>-</span><span class='hs-varid'>ballH</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>bvy</span> <span class='hs-varop'>></span> <span class='hs-num'>0</span>
<span class='hs-varop'>></span> <span class='hs-varid'>ballCollPlayer</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>check</span> <span class='hs-varop'><$></span> <span class='hs-varid'>ballPos</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ballVel</span> <span class='hs-varop'><*></span> <span class='hs-varid'>playerX</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>check</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>bx</span> <span class='hs-varid'>by</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>bvy</span><span class='hs-layout'>)</span> <span class='hs-varid'>px</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bvy</span> <span class='hs-varop'><</span> <span class='hs-num'>0</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>doRectsIntersect</span> <span class='hs-varid'>bx</span> <span class='hs-varid'>by</span> <span class='hs-varid'>ballW</span> <span class='hs-varid'>ballH</span>
<span class='hs-varop'>></span> <span class='hs-varid'>px</span> <span class='hs-varid'>playerY</span> <span class='hs-varid'>playerW</span> <span class='hs-varid'>playerH</span>
<span class='hs-varop'>></span>
</pre><p>The dynamic list of bricks along with ball-brick collision information, all of which are updated in each frame.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>bricks</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transfer</span> <span class='hs-layout'>(</span><span class='hs-conid'>False</span><span class='hs-layout'>,</span><span class='hs-conid'>False</span><span class='hs-layout'>,</span><span class='hs-varid'>brickPos0</span><span class='hs-layout'>)</span> <span class='hs-varid'>updateBricks</span> <span class='hs-varid'>ballPos</span>
<span class='hs-varop'>></span> <span class='hs-varid'>getBricks</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bs</span>
<span class='hs-varop'>></span> <span class='hs-varid'>getHColl</span> <span class='hs-layout'>(</span><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>c</span>
<span class='hs-varop'>></span> <span class='hs-varid'>getVColl</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>c</span>
</pre><p>Brick updater function: fading and checking collision. We need to do this the traditional way, because Elerea does not provide constructs to deal with collections of signals in the reactive layer, unlike Yampa.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>updateBricks</span> <span class='hs-varid'>dt</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>bx</span> <span class='hs-varid'>by</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>bricksPrev</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>collHorz</span><span class='hs-layout'>,</span><span class='hs-varid'>collVert</span><span class='hs-layout'>,</span><span class='hs-varid'>bricksNext</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>bricksNext</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>catMaybes</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>evolveBrick</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>killBrick</span> <span class='hs-varid'>bricksDel</span><span class='hs-varop'>++</span><span class='hs-varid'>bricksRem</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varid'>bricksDel</span><span class='hs-layout'>,</span><span class='hs-varid'>bricksNotHit</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>partition</span> <span class='hs-varid'>classifyBrick</span> <span class='hs-varid'>bricksPrev</span>
<span class='hs-varop'>></span> <span class='hs-varid'>bricksRem</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>by</span> <span class='hs-varop'>></span> <span class='hs-comment'>-</span><span class='hs-varid'>fieldH</span><span class='hs-comment'>-</span><span class='hs-varid'>ballH</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>bricksNotHit</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>map</span> <span class='hs-varid'>killBrick</span> <span class='hs-varid'>bricksNotHit</span>
<span class='hs-varop'>></span> <span class='hs-varid'>classifyBrick</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>s</span> <span class='hs-varop'>==</span> <span class='hs-conid'>Live</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>killed</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>killed</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>doRectsIntersect</span> <span class='hs-varid'>bx</span> <span class='hs-varid'>by</span> <span class='hs-varid'>ballW</span> <span class='hs-varid'>ballH</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>brickW</span> <span class='hs-varid'>brickH</span>
<span class='hs-varop'>></span> <span class='hs-varid'>evolveBrick</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span><span class='hs-conid'>Dying</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>a</span> <span class='hs-varop'><</span> <span class='hs-varid'>fade</span> <span class='hs-keyword'>then</span> <span class='hs-conid'>Nothing</span> <span class='hs-keyword'>else</span> <span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span><span class='hs-conid'>Dying</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-comment'>-</span><span class='hs-varid'>fade</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>fade</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>realToFrac</span> <span class='hs-varid'>dt</span><span class='hs-varop'>*</span><span class='hs-varid'>brickFade</span>
<span class='hs-varop'>></span> <span class='hs-varid'>evolveBrick</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>b</span>
<span class='hs-varop'>></span> <span class='hs-varid'>killBrick</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span><span class='hs-conid'>Live</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span><span class='hs-conid'>Dying</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>killBrick</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<span class='hs-varop'>></span> <span class='hs-varid'>collHorz</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>or</span> <span class='hs-varid'>collHBricks</span>
<span class='hs-varop'>></span> <span class='hs-varid'>collVert</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>or</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>not</span> <span class='hs-varid'>collHBricks</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>collHBricks</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-varid'>isHorz</span> <span class='hs-varid'>bricksDel</span>
<span class='hs-varop'>></span> <span class='hs-varid'>isHorz</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xDist</span><span class='hs-varop'>/</span><span class='hs-varid'>brickW</span> <span class='hs-varop'>></span> <span class='hs-varid'>yDist</span><span class='hs-varop'>/</span><span class='hs-varid'>brickH</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>xDist</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>abs</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>+</span><span class='hs-varid'>brickW</span><span class='hs-varop'>/</span><span class='hs-num'>2</span><span class='hs-layout'>)</span><span class='hs-comment'>-</span><span class='hs-layout'>(</span><span class='hs-varid'>bx</span><span class='hs-varop'>+</span><span class='hs-varid'>ballW</span><span class='hs-varop'>/</span><span class='hs-num'>2</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>yDist</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>abs</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-varop'>+</span><span class='hs-varid'>brickH</span><span class='hs-varop'>/</span><span class='hs-num'>2</span><span class='hs-layout'>)</span><span class='hs-comment'>-</span><span class='hs-layout'>(</span><span class='hs-varid'>by</span><span class='hs-varop'>+</span><span class='hs-varid'>ballH</span><span class='hs-varop'>/</span><span class='hs-num'>2</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
</pre><p>The <code>doRectsIntersect</code> function decides whether two rectangles defined by their top left corners and dimensions overlap.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>doRectsIntersect</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span> <span class='hs-varid'>sx1</span> <span class='hs-varid'>sy1</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span> <span class='hs-varid'>sx2</span> <span class='hs-varid'>sy2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>collIV</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>sx1</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>sx2</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>collIV</span> <span class='hs-varid'>y1</span> <span class='hs-varid'>sy1</span> <span class='hs-varid'>y2</span> <span class='hs-varid'>sy2</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>where</span> <span class='hs-varid'>collIV</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>s1</span> <span class='hs-varid'>p2</span> <span class='hs-varid'>s2</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>p1</span> <span class='hs-varop'><=</span> <span class='hs-varid'>p2</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>p2</span> <span class='hs-varop'><=</span> <span class='hs-varid'>p1</span><span class='hs-varop'>+</span><span class='hs-varid'>s1</span><span class='hs-layout'>)</span> <span class='hs-varop'>||</span> <span class='hs-layout'>(</span><span class='hs-varid'>p2</span> <span class='hs-varop'><=</span> <span class='hs-varid'>p1</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>p1</span> <span class='hs-varop'><=</span> <span class='hs-varid'>p2</span><span class='hs-varop'>+</span><span class='hs-varid'>s2</span><span class='hs-layout'>)</span>
</pre><p>The <code>renderLevel</code> function takes a snapshot of the game and turns it into an IO action that displays this snapshot on the screen. The <code>breakout</code> signal is the time-varying version of this IO action.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>renderLevel</span> <span class='hs-varid'>playerX</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-varid'>ballX</span> <span class='hs-varid'>ballY</span><span class='hs-layout'>)</span> <span class='hs-varid'>bricks</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>let</span> <span class='hs-varid'>drawRect</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-varid'>loadIdentity</span>
<span class='hs-varop'>></span> <span class='hs-varid'>renderPrimitive</span> <span class='hs-conid'>Quads</span> <span class='hs-varop'>$</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vertex</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Vertex3</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vertex</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Vertex3</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>+</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vertex</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Vertex3</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>+</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-varop'>+</span><span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vertex</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Vertex3</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-varop'>+</span><span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>drawEllipse</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>let</span> <span class='hs-varid'>xc</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span><span class='hs-varop'>+</span><span class='hs-varid'>xs</span><span class='hs-varop'>/</span><span class='hs-num'>2</span>
<span class='hs-varop'>></span> <span class='hs-varid'>yc</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>y</span><span class='hs-varop'>+</span><span class='hs-varid'>ys</span><span class='hs-varop'>/</span><span class='hs-num'>2</span>
<span class='hs-varop'>></span> <span class='hs-varid'>loadIdentity</span>
<span class='hs-varop'>></span> <span class='hs-varid'>renderPrimitive</span> <span class='hs-conid'>TriangleStrip</span> <span class='hs-varop'>$</span> <span class='hs-varid'>forM_</span> <span class='hs-keyglyph'>[</span><span class='hs-num'>0</span><span class='hs-keyglyph'>..</span><span class='hs-varid'>n</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>i</span> <span class='hs-keyglyph'>→</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>let</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>2</span><span class='hs-varop'>*</span><span class='hs-varid'>pi</span><span class='hs-varop'>*</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>i</span><span class='hs-varop'>/</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>n</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vertex</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Vertex3</span> <span class='hs-layout'>(</span><span class='hs-varid'>xc</span><span class='hs-varop'>+</span><span class='hs-varid'>xs</span><span class='hs-varop'>/</span><span class='hs-num'>2</span><span class='hs-varop'>*</span><span class='hs-varid'>sin</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>yc</span><span class='hs-varop'>+</span><span class='hs-varid'>ys</span><span class='hs-varop'>/</span><span class='hs-num'>2</span><span class='hs-varop'>*</span><span class='hs-varid'>cos</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>0</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vertex</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Vertex3</span> <span class='hs-varid'>xc</span> <span class='hs-varid'>yc</span> <span class='hs-layout'>(</span><span class='hs-num'>0</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>clear</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>ColorBuffer</span><span class='hs-keyglyph'>]</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>color</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Color4</span> <span class='hs-num'>0.2</span> <span class='hs-num'>0.2</span> <span class='hs-num'>0.2</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>drawRect</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>fieldW</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>fieldH</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fieldW</span><span class='hs-varop'>*</span><span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fieldH</span><span class='hs-varop'>*</span><span class='hs-num'>2</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>forM_</span> <span class='hs-varid'>bricks</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>→</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>s</span> <span class='hs-keyword'>of</span>
<span class='hs-varop'>></span> <span class='hs-conid'>Live</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>color</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Color4</span> <span class='hs-num'>0.8</span> <span class='hs-num'>0.5</span> <span class='hs-num'>0.5</span> <span class='hs-layout'>(</span><span class='hs-num'>0.6</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-conid'>Dying</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>color</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Color4</span> <span class='hs-num'>0.9</span> <span class='hs-num'>0.9</span> <span class='hs-num'>0.2</span> <span class='hs-varid'>a</span>
<span class='hs-varop'>></span> <span class='hs-varid'>drawRect</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>brickW</span> <span class='hs-varid'>brickH</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>color</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Color4</span> <span class='hs-num'>1</span> <span class='hs-num'>1</span> <span class='hs-num'>1</span> <span class='hs-layout'>(</span><span class='hs-num'>0.6</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>drawEllipse</span> <span class='hs-varid'>ballX</span> <span class='hs-varid'>ballY</span> <span class='hs-varid'>ballW</span> <span class='hs-varid'>ballH</span> <span class='hs-num'>20</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>color</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Color4</span> <span class='hs-num'>0.3</span> <span class='hs-num'>0.4</span> <span class='hs-num'>0.8</span> <span class='hs-layout'>(</span><span class='hs-num'>0.5</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>drawRect</span> <span class='hs-varid'>playerX</span> <span class='hs-varid'>playerY</span> <span class='hs-varid'>playerW</span> <span class='hs-varid'>playerH</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>flush</span>
<span class='hs-varop'>></span> <span class='hs-varid'>swapBuffers</span>
</pre><h2 id="backend">Backend</h2><p>The <code>readInput</code> function has two responsibilities: it provides input for the <code>mousePosition</code> peripheral signal through its associated sink, and also feeds the time difference between two states into the system, deciding when to exit altogether (by returning <code>Nothing</code> instead of the current <code>dt</code> value wrapped in <code>Just</code>).</p><p>The <code>threadDelay</code> call at the beginning is just a trick to give the scheduler a breath. It will cause a wait equal to a scheduler tick, which is 20ms by default. The program can run perfectly without it, but it eats up all the free CPU to produce an unnecessarily high frame rate.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>readInput</span> <span class='hs-varid'>mousePos</span> <span class='hs-varid'>closed</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-varid'>threadDelay</span> <span class='hs-num'>0</span>
<span class='hs-varop'>></span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>←</span> <span class='hs-varid'>get</span> <span class='hs-conid'>GLFW</span><span class='hs-varop'>.</span><span class='hs-varid'>time</span>
<span class='hs-varop'>></span> <span class='hs-conid'>GLFW</span><span class='hs-varop'>.</span><span class='hs-varid'>time</span> <span class='hs-varop'>$=</span> <span class='hs-num'>0</span>
<span class='hs-varop'>></span> <span class='hs-conid'>Position</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>←</span> <span class='hs-varid'>get</span> <span class='hs-conid'>GLFW</span><span class='hs-varop'>.</span><span class='hs-varid'>mousePos</span>
<span class='hs-varop'>></span> <span class='hs-varid'>mousePos</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>←</span> <span class='hs-varid'>getKey</span> <span class='hs-conid'>ESC</span>
<span class='hs-varop'>></span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>←</span> <span class='hs-varid'>readIORef</span> <span class='hs-varid'>closed</span>
<span class='hs-varop'>></span> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-keyword'>if</span> <span class='hs-varid'>c</span> <span class='hs-varop'>||</span> <span class='hs-varid'>k</span> <span class='hs-varop'>==</span> <span class='hs-conid'>Press</span> <span class='hs-keyword'>then</span> <span class='hs-conid'>Nothing</span> <span class='hs-keyword'>else</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
</pre><p>The <code>initGL</code> function sets up almost nothing, which means that most functionality is turned off. Only alpha blending is enabled to provide some minimalistic eye candy.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>initGL</span> <span class='hs-varid'>width</span> <span class='hs-varid'>height</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-varid'>clearColor</span> <span class='hs-varop'>$=</span> <span class='hs-conid'>Color4</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span> <span class='hs-num'>1</span>
<span class='hs-varop'>></span> <span class='hs-varid'>blend</span> <span class='hs-varop'>$=</span> <span class='hs-conid'>Enabled</span>
<span class='hs-varop'>></span> <span class='hs-varid'>blendFunc</span> <span class='hs-varop'>$=</span> <span class='hs-layout'>(</span><span class='hs-conid'>SrcAlpha</span><span class='hs-layout'>,</span><span class='hs-conid'>OneMinusSrcAlpha</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>cullFace</span> <span class='hs-varop'>$=</span> <span class='hs-conid'>Just</span> <span class='hs-conid'>Back</span>
</pre><p>The resize callback feeds the <code>windowSize</code> signal through its sink besides adjusting the projection matrix.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>resizeGLScene</span> <span class='hs-varid'>winSize</span> <span class='hs-varid'>size</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Size</span> <span class='hs-varid'>w</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-varid'>winSize</span> <span class='hs-layout'>(</span><span class='hs-conid'>V</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>viewport</span> <span class='hs-varop'>$=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Position</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span><span class='hs-layout'>,</span><span class='hs-varid'>size</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>matrixMode</span> <span class='hs-varop'>$=</span> <span class='hs-conid'>Projection</span>
<span class='hs-varop'>></span> <span class='hs-varid'>loadIdentity</span>
<span class='hs-varop'>></span> <span class='hs-varid'>scale</span> <span class='hs-num'>1</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>w</span><span class='hs-varop'>/</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>GLfloat</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-varid'>matrixMode</span> <span class='hs-varop'>$=</span> <span class='hs-conid'>Modelview</span> <span class='hs-num'>0</span>
</pre><h1 id="utils-module">Utils module</h1><p>This module contains some functions that might make it into the core library eventually.</p><pre><span class='hs-varop'>></span> <span class='hs-keyword'>module</span> <span class='hs-conid'>Common</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span> <span class='hs-keyword'>where</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>FRP</span><span class='hs-varop'>.</span><span class='hs-conid'>Elerea</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Common</span><span class='hs-varop'>.</span><span class='hs-conid'>Vector</span>
</pre><p>The <code>driveNetwork</code> function simply executes the supersteps while the <code>driver</code> function keeps returning valid delta time values.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>driveNetwork</span> <span class='hs-varid'>network</span> <span class='hs-varid'>driver</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<span class='hs-varop'>></span> <span class='hs-varid'>dt</span> <span class='hs-keyglyph'>←</span> <span class='hs-varid'>driver</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>dt</span> <span class='hs-keyword'>of</span>
<span class='hs-varop'>></span> <span class='hs-conid'>Just</span> <span class='hs-varid'>dt</span> <span class='hs-keyglyph'>→</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>join</span> <span class='hs-varop'>$</span> <span class='hs-varid'>superstep</span> <span class='hs-varid'>network</span> <span class='hs-varid'>dt</span>
<span class='hs-varop'>></span> <span class='hs-varid'>driveNetwork</span> <span class='hs-varid'>network</span> <span class='hs-varid'>driver</span>
<span class='hs-varop'>></span> <span class='hs-conid'>Nothing</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>return</span> <span class='hs-conid'>()</span>
</pre><p>The <code>edge</code> transfer function takes a bool signal and emits another bool signal that turns true only at the moment when there is a rising edge on the input. We are relying on the delay introduced by the <code>transfer</code> primitive for this to work.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>edge</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>transfer</span> <span class='hs-conid'>False</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>dt</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>not</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varop'>&&@</span> <span class='hs-varid'>b</span>
</pre><p>A scalar integral function. Since it is based on <code>transfer</code>, it is delayed by one superstep, i.e. the value of the input signal in the n<sup>th</sup> step affects its output only in the (n+1)<sup>th</sup> step.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>integral</span> <span class='hs-varid'>v0</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transfer</span> <span class='hs-varid'>v0</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>dt</span> <span class='hs-varid'>v</span> <span class='hs-varid'>v0</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v0</span><span class='hs-varop'>+</span><span class='hs-varid'>v</span><span class='hs-varop'>*</span><span class='hs-varid'>realToFrac</span> <span class='hs-varid'>dt</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
</pre><p>An integral function for two-dimensional vectors defined in the <code>Vector</code> module with the same caveat.</p><pre><span class='hs-varop'>></span> <span class='hs-varid'>integralVec</span> <span class='hs-varid'>v0</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transfer</span> <span class='hs-varid'>v0</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>dt</span> <span class='hs-varid'>v</span> <span class='hs-varid'>v0</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v0</span><span class='hs-varop'>^+^</span><span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-varop'>^*.</span><span class='hs-varid'>realToFrac</span> <span class='hs-varid'>dt</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
</pre><p>Logic relations lifted into signals. Useful to combine event-like signals.</p><pre><span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>||@</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Signal</span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>→</span> <span class='hs-conid'>Signal</span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>→</span> <span class='hs-conid'>Signal</span> <span class='hs-conid'>Bool</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>||@</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>||</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>&&@</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Signal</span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>→</span> <span class='hs-conid'>Signal</span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>→</span> <span class='hs-conid'>Signal</span> <span class='hs-conid'>Bool</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>&&@</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>&&</span><span class='hs-layout'>)</span>
</pre><h1 id="vector-module">Vector module</h1><p>This module contains a class for two-dimensional vectors, a strict datatype to instantiate it, and another instance for signals of the same type.</p><pre><span class='hs-varop'>></span> <span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-}</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>module</span> <span class='hs-conid'>Common</span><span class='hs-varop'>.</span><span class='hs-conid'>Vector</span> <span class='hs-keyword'>where</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>FRP</span><span class='hs-varop'>.</span><span class='hs-conid'>Elerea</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>import</span> <span class='hs-conid'>Graphics</span><span class='hs-varop'>.</span><span class='hs-conid'>Rendering</span><span class='hs-varop'>.</span><span class='hs-conid'>OpenGL</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>data</span> <span class='hs-conid'>Vec</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getX</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-conid'>Float</span><span class='hs-layout'>,</span> <span class='hs-varid'>getY</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-conid'>Float</span> <span class='hs-layout'>}</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>infixl</span> <span class='hs-num'>7</span> <span class='hs-varop'>^*.</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>infixl</span> <span class='hs-num'>7</span> <span class='hs-varop'>.*^</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>infixl</span> <span class='hs-num'>7</span> <span class='hs-varop'>`dot`</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>infixl</span> <span class='hs-num'>7</span> <span class='hs-varop'>`cross`</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>infixl</span> <span class='hs-num'>6</span> <span class='hs-varop'>^+^</span>
<span class='hs-varop'>></span> <span class='hs-keyword'>infixl</span> <span class='hs-num'>6</span> <span class='hs-varop'>^-^</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>class</span> <span class='hs-conid'>Vector2D</span> <span class='hs-varid'>v</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>c</span> <span class='hs-keyword'>where</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>^+^</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>^-^</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>^*.</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>.*^</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vnull</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>v</span>
<span class='hs-varop'>></span> <span class='hs-varid'>dot</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>c</span>
<span class='hs-varop'>></span> <span class='hs-varid'>cross</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>→</span> <span class='hs-varid'>c</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Vector2D</span> <span class='hs-conid'>Vec</span> <span class='hs-conid'>Float</span> <span class='hs-keyword'>where</span>
<span class='hs-varop'>></span> <span class='hs-conid'>V</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span> <span class='hs-varop'>^+^</span> <span class='hs-conid'>V</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-varop'>+</span><span class='hs-varid'>x2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span><span class='hs-varop'>+</span><span class='hs-varid'>y2</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-conid'>V</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span> <span class='hs-varop'>^-^</span> <span class='hs-conid'>V</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-comment'>-</span><span class='hs-varid'>x2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span><span class='hs-comment'>-</span><span class='hs-varid'>y2</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-conid'>V</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varop'>^*.</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>*</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-varop'>*</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>t</span> <span class='hs-varop'>.*^</span> <span class='hs-conid'>V</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>*</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-varop'>*</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vnull</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span>
<span class='hs-varop'>></span> <span class='hs-conid'>V</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span> <span class='hs-varop'>`dot`</span> <span class='hs-conid'>V</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x1</span><span class='hs-varop'>*</span><span class='hs-varid'>y1</span><span class='hs-varop'>+</span><span class='hs-varid'>x2</span><span class='hs-varop'>*</span><span class='hs-varid'>y2</span>
<span class='hs-varop'>></span> <span class='hs-conid'>V</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span> <span class='hs-varop'>`cross`</span> <span class='hs-conid'>V</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x1</span><span class='hs-varop'>*</span><span class='hs-varid'>y2</span><span class='hs-comment'>-</span><span class='hs-varid'>x2</span><span class='hs-varop'>*</span><span class='hs-varid'>y1</span>
<span class='hs-varop'>></span>
<span class='hs-varop'>></span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Vector2D</span> <span class='hs-layout'>(</span><span class='hs-conid'>Signal</span> <span class='hs-conid'>Vec</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Signal</span> <span class='hs-conid'>Float</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>^+^</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>^+^</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>^-^</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>^-^</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>^*.</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>^*.</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-layout'>(</span><span class='hs-varop'>.*^</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>.*^</span><span class='hs-layout'>)</span>
<span class='hs-varop'>></span> <span class='hs-varid'>vnull</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>vnull</span>
<span class='hs-varop'>></span> <span class='hs-varid'>dot</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-varid'>dot</span>
<span class='hs-varop'>></span> <span class='hs-varid'>cross</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-varid'>cross</span>
</pre>
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