diff --git a/src/__phutil_library_map__.php b/src/__phutil_library_map__.php
--- a/src/__phutil_library_map__.php
+++ b/src/__phutil_library_map__.php
@@ -2107,6 +2107,7 @@
     'PhabricatorAccessLog' => 'infrastructure/log/PhabricatorAccessLog.php',
     'PhabricatorAccessLogConfigOptions' => 'applications/config/option/PhabricatorAccessLogConfigOptions.php',
     'PhabricatorAccessibilitySetting' => 'applications/settings/setting/PhabricatorAccessibilitySetting.php',
+    'PhabricatorAccumulateChartFunction' => 'applications/fact/chart/PhabricatorAccumulateChartFunction.php',
     'PhabricatorActionListView' => 'view/layout/PhabricatorActionListView.php',
     'PhabricatorActionView' => 'view/layout/PhabricatorActionView.php',
     'PhabricatorActivitySettingsPanel' => 'applications/settings/panel/PhabricatorActivitySettingsPanel.php',
@@ -2695,6 +2696,7 @@
     'PhabricatorCommitSearchEngine' => 'applications/audit/query/PhabricatorCommitSearchEngine.php',
     'PhabricatorCommitTagsField' => 'applications/repository/customfield/PhabricatorCommitTagsField.php',
     'PhabricatorCommonPasswords' => 'applications/auth/constants/PhabricatorCommonPasswords.php',
+    'PhabricatorComposeChartFunction' => 'applications/fact/chart/PhabricatorComposeChartFunction.php',
     'PhabricatorConduitAPIController' => 'applications/conduit/controller/PhabricatorConduitAPIController.php',
     'PhabricatorConduitApplication' => 'applications/conduit/application/PhabricatorConduitApplication.php',
     'PhabricatorConduitCallManagementWorkflow' => 'applications/conduit/management/PhabricatorConduitCallManagementWorkflow.php',
@@ -3425,6 +3427,7 @@
     'PhabricatorHeraldContentSource' => 'applications/herald/contentsource/PhabricatorHeraldContentSource.php',
     'PhabricatorHexdumpDocumentEngine' => 'applications/files/document/PhabricatorHexdumpDocumentEngine.php',
     'PhabricatorHighSecurityRequestExceptionHandler' => 'aphront/handler/PhabricatorHighSecurityRequestExceptionHandler.php',
+    'PhabricatorHigherOrderChartFunction' => 'applications/fact/chart/PhabricatorHigherOrderChartFunction.php',
     'PhabricatorHomeApplication' => 'applications/home/application/PhabricatorHomeApplication.php',
     'PhabricatorHomeConstants' => 'applications/home/constants/PhabricatorHomeConstants.php',
     'PhabricatorHomeController' => 'applications/home/controller/PhabricatorHomeController.php',
@@ -4725,6 +4728,7 @@
     'PhabricatorSubscriptionsUIEventListener' => 'applications/subscriptions/events/PhabricatorSubscriptionsUIEventListener.php',
     'PhabricatorSubscriptionsUnsubscribeEmailCommand' => 'applications/subscriptions/command/PhabricatorSubscriptionsUnsubscribeEmailCommand.php',
     'PhabricatorSubtypeEditEngineExtension' => 'applications/transactions/engineextension/PhabricatorSubtypeEditEngineExtension.php',
+    'PhabricatorSumChartFunction' => 'applications/fact/chart/PhabricatorSumChartFunction.php',
     'PhabricatorSupportApplication' => 'applications/support/application/PhabricatorSupportApplication.php',
     'PhabricatorSyntaxHighlighter' => 'infrastructure/markup/PhabricatorSyntaxHighlighter.php',
     'PhabricatorSyntaxHighlightingConfigOptions' => 'applications/config/option/PhabricatorSyntaxHighlightingConfigOptions.php',
@@ -4952,7 +4956,6 @@
     'PhabricatorWorkingCopyDiscoveryTestCase' => 'applications/repository/engine/__tests__/PhabricatorWorkingCopyDiscoveryTestCase.php',
     'PhabricatorWorkingCopyPullTestCase' => 'applications/repository/engine/__tests__/PhabricatorWorkingCopyPullTestCase.php',
     'PhabricatorWorkingCopyTestCase' => 'applications/repository/engine/__tests__/PhabricatorWorkingCopyTestCase.php',
-    'PhabricatorXChartFunction' => 'applications/fact/chart/PhabricatorXChartFunction.php',
     'PhabricatorXHPASTDAO' => 'applications/phpast/storage/PhabricatorXHPASTDAO.php',
     'PhabricatorXHPASTParseTree' => 'applications/phpast/storage/PhabricatorXHPASTParseTree.php',
     'PhabricatorXHPASTViewController' => 'applications/phpast/controller/PhabricatorXHPASTViewController.php',
@@ -7987,6 +7990,7 @@
     'PhabricatorAccessLog' => 'Phobject',
     'PhabricatorAccessLogConfigOptions' => 'PhabricatorApplicationConfigOptions',
     'PhabricatorAccessibilitySetting' => 'PhabricatorSelectSetting',
+    'PhabricatorAccumulateChartFunction' => 'PhabricatorChartFunction',
     'PhabricatorActionListView' => 'AphrontTagView',
     'PhabricatorActionView' => 'AphrontView',
     'PhabricatorActivitySettingsPanel' => 'PhabricatorSettingsPanel',
@@ -8691,6 +8695,7 @@
     'PhabricatorCommitSearchEngine' => 'PhabricatorApplicationSearchEngine',
     'PhabricatorCommitTagsField' => 'PhabricatorCommitCustomField',
     'PhabricatorCommonPasswords' => 'Phobject',
+    'PhabricatorComposeChartFunction' => 'PhabricatorHigherOrderChartFunction',
     'PhabricatorConduitAPIController' => 'PhabricatorConduitController',
     'PhabricatorConduitApplication' => 'PhabricatorApplication',
     'PhabricatorConduitCallManagementWorkflow' => 'PhabricatorConduitManagementWorkflow',
@@ -9520,6 +9525,7 @@
     'PhabricatorHeraldContentSource' => 'PhabricatorContentSource',
     'PhabricatorHexdumpDocumentEngine' => 'PhabricatorDocumentEngine',
     'PhabricatorHighSecurityRequestExceptionHandler' => 'PhabricatorRequestExceptionHandler',
+    'PhabricatorHigherOrderChartFunction' => 'PhabricatorChartFunction',
     'PhabricatorHomeApplication' => 'PhabricatorApplication',
     'PhabricatorHomeConstants' => 'PhabricatorHomeController',
     'PhabricatorHomeController' => 'PhabricatorController',
@@ -11053,6 +11059,7 @@
     'PhabricatorSubscriptionsUIEventListener' => 'PhabricatorEventListener',
     'PhabricatorSubscriptionsUnsubscribeEmailCommand' => 'MetaMTAEmailTransactionCommand',
     'PhabricatorSubtypeEditEngineExtension' => 'PhabricatorEditEngineExtension',
+    'PhabricatorSumChartFunction' => 'PhabricatorHigherOrderChartFunction',
     'PhabricatorSupportApplication' => 'PhabricatorApplication',
     'PhabricatorSyntaxHighlighter' => 'Phobject',
     'PhabricatorSyntaxHighlightingConfigOptions' => 'PhabricatorApplicationConfigOptions',
@@ -11323,7 +11330,6 @@
     'PhabricatorWorkingCopyDiscoveryTestCase' => 'PhabricatorWorkingCopyTestCase',
     'PhabricatorWorkingCopyPullTestCase' => 'PhabricatorWorkingCopyTestCase',
     'PhabricatorWorkingCopyTestCase' => 'PhabricatorTestCase',
-    'PhabricatorXChartFunction' => 'PhabricatorChartFunction',
     'PhabricatorXHPASTDAO' => 'PhabricatorLiskDAO',
     'PhabricatorXHPASTParseTree' => 'PhabricatorXHPASTDAO',
     'PhabricatorXHPASTViewController' => 'PhabricatorController',
diff --git a/src/applications/fact/chart/PhabricatorAccumulateChartFunction.php b/src/applications/fact/chart/PhabricatorAccumulateChartFunction.php
new file mode 100644
--- /dev/null
+++ b/src/applications/fact/chart/PhabricatorAccumulateChartFunction.php
@@ -0,0 +1,81 @@
+<?php
+
+final class PhabricatorAccumulateChartFunction
+  extends PhabricatorChartFunction {
+
+  const FUNCTIONKEY = 'accumulate';
+
+  protected function newArguments() {
+    return array(
+      $this->newArgument()
+        ->setName('x')
+        ->setType('function'),
+    );
+  }
+
+  public function getDomain() {
+    return $this->getArgument('x')->getDomain();
+  }
+
+  public function newInputValues(PhabricatorChartDataQuery $query) {
+    return $this->getArgument('x')->newInputValues($query);
+  }
+
+  public function evaluateFunction(array $xv) {
+    // First, we're going to accumulate the underlying function. Then
+    // we'll map the inputs through the accumulation.
+
+    $datasource = $this->getArgument('x');
+
+    // Use an unconstrained query to pull all the data from the underlying
+    // source. We need to accumulate data since the beginning of time to
+    // figure out the right Y-intercept -- otherwise, we'll always start at
+    // "0" wherever our domain begins.
+    $empty_query = new PhabricatorChartDataQuery();
+
+    $datasource_xv = $datasource->newInputValues($empty_query);
+    if (!$datasource_xv) {
+      // TODO: Maybe this should just be an error?
+      $datasource_xv = $xv;
+    }
+
+    $yv = $datasource->evaluateFunction($datasource_xv);
+
+    $map = array_combine($datasource_xv, $yv);
+
+    $accumulator = 0;
+    foreach ($map as $x => $y) {
+      $accumulator += $y;
+      $map[$x] = $accumulator;
+    }
+
+    // The value of "accumulate(x)" is the largest datapoint in the map which
+    // is no larger than "x".
+
+    $map_x = array_keys($map);
+    $idx = -1;
+    $max = count($map_x) - 1;
+
+    $yv = array();
+
+    $value = 0;
+    foreach ($xv as $x) {
+      // While the next "x" we need to evaluate the function at lies to the
+      // right of the next datapoint, move the current datapoint forward until
+      // we're at the rightmost datapoint which is not larger than "x".
+      while ($idx < $max) {
+        if ($map_x[$idx + 1] > $x) {
+          break;
+        }
+
+        $idx++;
+        $value = $map[$map_x[$idx]];
+      }
+
+      $yv[] = $value;
+    }
+
+    return $yv;
+  }
+
+}
diff --git a/src/applications/fact/chart/PhabricatorChartDataQuery.php b/src/applications/fact/chart/PhabricatorChartDataQuery.php
--- a/src/applications/fact/chart/PhabricatorChartDataQuery.php
+++ b/src/applications/fact/chart/PhabricatorChartDataQuery.php
@@ -34,4 +34,48 @@
     return $this->limit;
   }
 
+  public function selectInputValues(array $xv) {
+    $result = array();
+
+    $x_min = $this->getMinimumValue();
+    $x_max = $this->getMaximumValue();
+    $limit = $this->getLimit();
+
+    if ($x_min !== null) {
+      foreach ($xv as $key => $x) {
+        if ($x < $x_min) {
+          unset($xv[$key]);
+        }
+      }
+    }
+
+    if ($x_max !== null) {
+      foreach ($xv as $key => $x) {
+        if ($x > $x_max) {
+          unset($xv[$key]);
+        }
+      }
+    }
+
+    // If we have too many data points, throw away some of the data.
+
+    // TODO: This doesn't work especially well right now.
+
+    if ($limit !== null) {
+      $count = count($xv);
+      if ($count > $limit) {
+        $ii = 0;
+        $every = ceil($count / $limit);
+        foreach ($xv as $key => $x) {
+          $ii++;
+          if (($ii % $every) && ($ii != $count)) {
+            unset($xv[$key]);
+          }
+        }
+      }
+    }
+
+    return array_values($xv);
+  }
+
 }
diff --git a/src/applications/fact/chart/PhabricatorChartFunction.php b/src/applications/fact/chart/PhabricatorChartFunction.php
--- a/src/applications/fact/chart/PhabricatorChartFunction.php
+++ b/src/applications/fact/chart/PhabricatorChartFunction.php
@@ -3,11 +3,7 @@
 abstract class PhabricatorChartFunction
   extends Phobject {
 
-  private $xAxis;
-  private $yAxis;
-
   private $argumentParser;
-  private $sourceFunction;
 
   final public function getFunctionKey() {
     return $this->getPhobjectClassConstant('FUNCTIONKEY', 32);
@@ -44,125 +40,115 @@
     $parser->setHaveAllArguments(true);
     $parser->parseArguments();
 
-    $source_argument = $parser->getSourceFunctionArgument();
-    if ($source_argument) {
-      $source_function = $this->getArgument($source_argument->getName());
-      $this->setSourceFunction($source_function);
-    }
-
     return $this;
   }
 
-  abstract protected function newArguments();
+  public function getSubfunctions() {
+    $result = array();
+    $result[] = $this;
 
-  final protected function newArgument() {
-    return new PhabricatorChartFunctionArgument();
-  }
+    foreach ($this->getFunctionArguments() as $argument) {
+      foreach ($argument->getSubfunctions() as $subfunction) {
+        $result[] = $subfunction;
+      }
+    }
 
-  final protected function getArgument($key) {
-    return $this->getArgumentParser()->getArgumentValue($key);
+    return $result;
   }
 
-  final protected function getArgumentParser() {
-    if (!$this->argumentParser) {
-      $parser = id(new PhabricatorChartFunctionArgumentParser())
-        ->setFunction($this);
+  public function getFunctionArguments() {
+    $results = array();
 
-      $this->argumentParser = $parser;
+    $parser = $this->getArgumentParser();
+    foreach ($parser->getAllArguments() as $argument) {
+      if ($argument->getType() !== 'function') {
+        continue;
+      }
+
+      $name = $argument->getName();
+      $value = $this->getArgument($name);
+
+      if (!is_array($value)) {
+        $results[] = $value;
+      } else {
+        foreach ($value as $arg_value) {
+          $results[] = $arg_value;
+        }
+      }
     }
-    return $this->argumentParser;
-  }
 
-  public function loadData() {
-    return;
+    return $results;
   }
 
-  protected function setSourceFunction(PhabricatorChartFunction $source) {
-    $this->sourceFunction = $source;
-    return $this;
-  }
+  public function newDatapoints(PhabricatorChartDataQuery $query) {
+    $xv = $this->newInputValues($query);
 
-  protected function getSourceFunction() {
-    return $this->sourceFunction;
-  }
+    if ($xv === null) {
+      $xv = $this->newDefaultInputValues($query);
+    }
 
-  final public function setXAxis(PhabricatorChartAxis $x_axis) {
-    $this->xAxis = $x_axis;
-    return $this;
-  }
+    $xv = $query->selectInputValues($xv);
 
-  final public function getXAxis() {
-    return $this->xAxis;
-  }
+    $n = count($xv);
+    $yv = $this->evaluateFunction($xv);
 
-  final public function setYAxis(PhabricatorChartAxis $y_axis) {
-    $this->yAxis = $y_axis;
-    return $this;
-  }
+    $points = array();
+    for ($ii = 0; $ii < $n; $ii++) {
+      $y = $yv[$ii];
 
-  final public function getYAxis() {
-    return $this->yAxis;
-  }
+      if ($y === null) {
+        continue;
+      }
 
-  protected function canEvaluateFunction() {
-    return false;
-  }
+      $points[] = array(
+        'x' => $xv[$ii],
+        'y' => $y,
+      );
+    }
 
-  protected function evaluateFunction($x) {
-    throw new PhutilMethodNotImplementedException();
+    return $points;
   }
 
-  public function hasDomain() {
-    if ($this->canEvaluateFunction()) {
-      return false;
-    }
+  abstract protected function newArguments();
 
-    throw new PhutilMethodNotImplementedException();
+  final protected function newArgument() {
+    return new PhabricatorChartFunctionArgument();
   }
 
-  public function getDatapoints(PhabricatorChartDataQuery $query) {
-    if ($this->canEvaluateFunction()) {
-      $points = $this->newSourceDatapoints($query);
-      foreach ($points as $key => $point) {
-        $y = $point['y'];
-        $y = $this->evaluateFunction($y);
-        $points[$key]['y'] = $y;
-      }
+  final protected function getArgument($key) {
+    return $this->getArgumentParser()->getArgumentValue($key);
+  }
 
-      return $points;
-    }
+  final protected function getArgumentParser() {
+    if (!$this->argumentParser) {
+      $parser = id(new PhabricatorChartFunctionArgumentParser())
+        ->setFunction($this);
 
-    return $this->newDatapoints($query);
+      $this->argumentParser = $parser;
+    }
+    return $this->argumentParser;
   }
 
-  protected function newDatapoints(PhabricatorChartDataQuery $query) {
-    throw new PhutilMethodNotImplementedException();
+  abstract public function evaluateFunction(array $xv);
+
+  public function getDomain() {
+    return null;
   }
 
-  protected function newSourceDatapoints(PhabricatorChartDataQuery $query) {
-    $source = $this->getSourceFunction();
-    if ($source) {
-      return $source->getDatapoints($query);
-    }
+  public function newInputValues(PhabricatorChartDataQuery $query) {
+    return null;
+  }
 
-    return $this->newDefaultDatapoints($query);
+  public function loadData() {
+    return;
   }
 
-  protected function newDefaultDatapoints(PhabricatorChartDataQuery $query) {
+  protected function newDefaultInputValues(PhabricatorChartDataQuery $query) {
     $x_min = $query->getMinimumValue();
     $x_max = $query->getMaximumValue();
     $limit = $query->getLimit();
 
-    $points = array();
-    $steps = $this->newLinearSteps($x_min, $x_max, $limit);
-    foreach ($steps as $step) {
-      $points[] = array(
-        'x' => $step,
-        'y' => $step,
-      );
-    }
-
-    return $points;
+    return $this->newLinearSteps($x_min, $x_max, $limit);
   }
 
   protected function newLinearSteps($src, $dst, $count) {
@@ -213,5 +199,4 @@
 
     return $steps;
   }
-
 }
diff --git a/src/applications/fact/chart/PhabricatorChartFunctionArgument.php b/src/applications/fact/chart/PhabricatorChartFunctionArgument.php
--- a/src/applications/fact/chart/PhabricatorChartFunctionArgument.php
+++ b/src/applications/fact/chart/PhabricatorChartFunctionArgument.php
@@ -5,7 +5,7 @@
 
   private $name;
   private $type;
-  private $isSourceFunction;
+  private $repeatable;
 
   public function setName($name) {
     $this->name = $name;
@@ -16,6 +16,15 @@
     return $this->name;
   }
 
+  public function setRepeatable($repeatable) {
+    $this->repeatable = $repeatable;
+    return $this;
+  }
+
+  public function getRepeatable() {
+    return $this->repeatable;
+  }
+
   public function setType($type) {
     $types = array(
       'fact-key' => true,
@@ -40,15 +49,6 @@
     return $this->type;
   }
 
-  public function setIsSourceFunction($is_source_function) {
-    $this->isSourceFunction = $is_source_function;
-    return $this;
-  }
-
-  public function getIsSourceFunction() {
-    return $this->isSourceFunction;
-  }
-
   public function newValue($value) {
     switch ($this->getType()) {
       case 'fact-key':
diff --git a/src/applications/fact/chart/PhabricatorChartFunctionArgumentParser.php b/src/applications/fact/chart/PhabricatorChartFunctionArgumentParser.php
--- a/src/applications/fact/chart/PhabricatorChartFunctionArgumentParser.php
+++ b/src/applications/fact/chart/PhabricatorChartFunctionArgumentParser.php
@@ -11,6 +11,7 @@
   private $argumentMap = array();
   private $argumentPosition = 0;
   private $argumentValues = array();
+  private $repeatableArgument = null;
 
   public function setFunction(PhabricatorChartFunction $function) {
     $this->function = $function;
@@ -55,6 +56,32 @@
           $name));
     }
 
+    if ($this->repeatableArgument) {
+      if ($spec->getRepeatable()) {
+        throw new Exception(
+          pht(
+            'Chart function "%s" emitted multiple repeatable argument '.
+            'specifications ("%s" and "%s"). Only one argument may be '.
+            'repeatable and it must be the last argument.',
+            $this->getFunctionArgumentSignature(),
+            $name,
+            $this->repeatableArgument->getName()));
+      } else {
+        throw new Exception(
+          pht(
+            'Chart function "%s" emitted a repeatable argument ("%s"), then '.
+            'another argument ("%s"). No arguments are permitted after a '.
+            'repeatable argument.',
+            $this->getFunctionArgumentSignature(),
+            $this->repeatableArgument->getName(),
+            $name));
+      }
+    }
+
+    if ($spec->getRepeatable()) {
+      $this->repeatableArgument = $spec;
+    }
+
     $this->argumentMap[$name] = $spec;
     $this->unparsedArguments[] = $spec;
 
@@ -72,12 +99,26 @@
     return $this;
   }
 
+  public function getAllArguments() {
+    return array_values($this->argumentMap);
+  }
+
   public function parseArguments() {
     $have_count = count($this->rawArguments);
     $want_count = count($this->argumentMap);
 
     if ($this->haveAllArguments) {
-      if ($want_count !== $have_count) {
+      if ($this->repeatableArgument) {
+        if ($want_count > $have_count) {
+          throw new Exception(
+            pht(
+              'Function "%s" expects %s or more argument(s), but only %s '.
+              'argument(s) were provided.',
+              $this->getFunctionArgumentSignature(),
+              $want_count,
+              $have_count));
+        }
+      } else if ($want_count !== $have_count) {
         throw new Exception(
           pht(
             'Function "%s" expects %s argument(s), but %s argument(s) were '.
@@ -105,6 +146,14 @@
       $raw_argument = array_shift($this->unconsumedArguments);
       $this->argumentPosition++;
 
+      $is_repeatable = $argument->getRepeatable();
+
+      // If this argument is repeatable and we have more arguments, add it
+      // back to the end of the list so we can continue parsing.
+      if ($is_repeatable && $this->unconsumedArguments) {
+        $this->unparsedArguments[] = $argument;
+      }
+
       try {
         $value = $argument->newValue($raw_argument);
       } catch (Exception $ex) {
@@ -118,7 +167,14 @@
             $ex->getMessage()));
       }
 
-      $this->argumentValues[$name] = $value;
+      if ($is_repeatable) {
+        if (!isset($this->argumentValues[$name])) {
+          $this->argumentValues[$name] = array();
+        }
+        $this->argumentValues[$name][] = $value;
+      } else {
+        $this->argumentValues[$name] = $value;
+      }
     }
   }
 
@@ -141,7 +197,7 @@
       $argument_list[] = $key;
     }
 
-    if (!$this->haveAllArguments) {
+    if (!$this->haveAllArguments || $this->repeatableArgument) {
       $argument_list[] = '...';
     }
 
@@ -151,43 +207,4 @@
       implode(', ', $argument_list));
   }
 
-  public function getSourceFunctionArgument() {
-    $required_type = 'function';
-
-    $sources = array();
-    foreach ($this->argumentMap as $key => $argument) {
-      if (!$argument->getIsSourceFunction()) {
-        continue;
-      }
-
-      if ($argument->getType() !== $required_type) {
-        throw new Exception(
-          pht(
-            'Function "%s" defines an argument "%s" which is marked as a '.
-            'source function, but the type of this argument is not "%s".',
-            $this->getFunctionArgumentSignature(),
-            $argument->getName(),
-            $required_type));
-      }
-
-      $sources[$key] = $argument;
-    }
-
-    if (!$sources) {
-      return null;
-    }
-
-    if (count($sources) > 1) {
-      throw new Exception(
-        pht(
-          'Function "%s" defines more than one argument as a source '.
-          'function (arguments: %s). Functions must have zero or one '.
-          'source function.',
-          $this->getFunctionArgumentSignature(),
-          implode(', ', array_keys($sources))));
-    }
-
-    return head($sources);
-  }
-
 }
diff --git a/src/applications/fact/chart/PhabricatorComposeChartFunction.php b/src/applications/fact/chart/PhabricatorComposeChartFunction.php
new file mode 100644
--- /dev/null
+++ b/src/applications/fact/chart/PhabricatorComposeChartFunction.php
@@ -0,0 +1,73 @@
+<?php
+
+final class PhabricatorComposeChartFunction
+  extends PhabricatorHigherOrderChartFunction {
+
+  const FUNCTIONKEY = 'compose';
+
+  protected function newArguments() {
+    return array(
+      $this->newArgument()
+        ->setName('f')
+        ->setType('function')
+        ->setRepeatable(true),
+    );
+  }
+
+  public function evaluateFunction(array $xv) {
+    $original_positions = array_keys($xv);
+    $remaining_positions = $original_positions;
+    foreach ($this->getFunctionArguments() as $function) {
+      $xv = $function->evaluateFunction($xv);
+
+      // If a function evaluates to "null" at some positions, we want to return
+      // "null" at those positions and stop evaluating the function.
+
+      // We also want to pass "evaluateFunction()" a natural list containing
+      // only values it should evaluate: keys should not be important and we
+      // should not pass "null". This simplifies implementation of functions.
+
+      // To do this, first create a map from original input positions to
+      // function return values.
+      $xv = array_combine($remaining_positions, $xv);
+
+      // If a function evaluated to "null" at any position where we evaluated
+      // it, the result will be "null". We remove the position from the
+      // vector so we stop evaluating it.
+      foreach ($xv as $x => $y) {
+        if ($y !== null) {
+          continue;
+        }
+
+        unset($xv[$x]);
+      }
+
+      // Store the remaining original input positions for the next round, then
+      // throw away the array keys so we're passing the next function a natural
+      // list with only non-"null" values.
+      $remaining_positions = array_keys($xv);
+      $xv = array_values($xv);
+
+      // If we have no more inputs to evaluate, we can bail out early rather
+      // than passing empty vectors to functions for evaluation.
+      if (!$xv) {
+        break;
+      }
+    }
+
+
+    $yv = array();
+    $xv = array_combine($remaining_positions, $xv);
+    foreach ($original_positions as $position) {
+      if (isset($xv[$position])) {
+        $y = $xv[$position];
+      } else {
+        $y = null;
+      }
+      $yv[$position] = $y;
+    }
+
+    return $yv;
+  }
+
+}
diff --git a/src/applications/fact/chart/PhabricatorConstantChartFunction.php b/src/applications/fact/chart/PhabricatorConstantChartFunction.php
--- a/src/applications/fact/chart/PhabricatorConstantChartFunction.php
+++ b/src/applications/fact/chart/PhabricatorConstantChartFunction.php
@@ -13,12 +13,16 @@
     );
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $n = $this->getArgument('n');
+
+    $yv = array();
+
+    foreach ($xv as $x) {
+      $yv[] = $n;
+    }
 
-  protected function evaluateFunction($x) {
-    return $this->getArgument('n');
+    return $yv;
   }
 
 }
diff --git a/src/applications/fact/chart/PhabricatorCosChartFunction.php b/src/applications/fact/chart/PhabricatorCosChartFunction.php
--- a/src/applications/fact/chart/PhabricatorCosChartFunction.php
+++ b/src/applications/fact/chart/PhabricatorCosChartFunction.php
@@ -6,20 +6,17 @@
   const FUNCTIONKEY = 'cos';
 
   protected function newArguments() {
-    return array(
-      $this->newArgument()
-        ->setName('x')
-        ->setType('function')
-        ->setIsSourceFunction(true),
-    );
+    return array();
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $yv = array();
+
+    foreach ($xv as $x) {
+      $yv[] = cos(deg2rad($x));
+    }
 
-  protected function evaluateFunction($x) {
-    return cos(deg2rad($x));
+    return $yv;
   }
 
 }
diff --git a/src/applications/fact/chart/PhabricatorFactChartFunction.php b/src/applications/fact/chart/PhabricatorFactChartFunction.php
--- a/src/applications/fact/chart/PhabricatorFactChartFunction.php
+++ b/src/applications/fact/chart/PhabricatorFactChartFunction.php
@@ -6,7 +6,7 @@
   const FUNCTIONKEY = 'fact';
 
   private $fact;
-  private $datapoints;
+  private $map;
 
   protected function newArguments() {
     $key_argument = $this->newArgument()
@@ -44,73 +44,46 @@
       return;
     }
 
-    $points = array();
+    $map = array();
+    foreach ($data as $row) {
+      $value = (int)$row['value'];
+      $epoch = (int)$row['epoch'];
 
-    $sum = 0;
-    foreach ($data as $key => $row) {
-      $sum += (int)$row['value'];
-      $points[] = array(
-        'x' => (int)$row['epoch'],
-        'y' => $sum,
-      );
+      if (!isset($map[$epoch])) {
+        $map[$epoch] = 0;
+      }
+
+      $map[$epoch] += $value;
     }
 
-    $this->datapoints = $points;
+    $this->map = $map;
   }
 
-  public function getDatapoints(PhabricatorChartDataQuery $query) {
-    $points = $this->datapoints;
-    if (!$points) {
-      return array();
-    }
+  public function getDomain() {
+    return array(
+      head_key($this->map),
+      last_key($this->map),
+    );
+  }
 
-    $x_min = $query->getMinimumValue();
-    $x_max = $query->getMaximumValue();
-    $limit = $query->getLimit();
+  public function newInputValues(PhabricatorChartDataQuery $query) {
+    return array_keys($this->map);
+  }
 
-    if ($x_min !== null) {
-      foreach ($points as $key => $point) {
-        if ($point['x'] < $x_min) {
-          unset($points[$key]);
-        }
-      }
-    }
+  public function evaluateFunction(array $xv) {
+    $map = $this->map;
 
-    if ($x_max !== null) {
-      foreach ($points as $key => $point) {
-        if ($point['x'] > $x_max) {
-          unset($points[$key]);
-        }
-      }
-    }
+    $yv = array();
 
-    // If we have too many data points, throw away some of the data.
-    if ($limit !== null) {
-      $count = count($points);
-      if ($count > $limit) {
-        $ii = 0;
-        $every = ceil($count / $limit);
-        foreach ($points as $key => $point) {
-          $ii++;
-          if (($ii % $every) && ($ii != $count)) {
-            unset($points[$key]);
-          }
-        }
+    foreach ($xv as $x) {
+      if (isset($map[$x])) {
+        $yv[] = $map[$x];
+      } else {
+        $yv[] = null;
       }
     }
 
-    return $points;
-  }
-
-  public function hasDomain() {
-    return true;
-  }
-
-  public function getDomain() {
-    // TODO: We can examine the data to fit a better domain.
-
-    $now = PhabricatorTime::getNow();
-    return array($now - phutil_units('90 days in seconds'), $now);
+    return $yv;
   }
 
 }
diff --git a/src/applications/fact/chart/PhabricatorHigherOrderChartFunction.php b/src/applications/fact/chart/PhabricatorHigherOrderChartFunction.php
new file mode 100644
--- /dev/null
+++ b/src/applications/fact/chart/PhabricatorHigherOrderChartFunction.php
@@ -0,0 +1,56 @@
+<?php
+
+abstract class PhabricatorHigherOrderChartFunction
+  extends PhabricatorChartFunction {
+
+  public function getDomain() {
+    $minv = array();
+    $maxv = array();
+    foreach ($this->getFunctionArguments() as $function) {
+      $domain = $function->getDomain();
+      if ($domain !== null) {
+        list($min, $max) = $domain;
+        $minv[] = $min;
+        $maxv[] = $max;
+      }
+    }
+
+    if (!$minv && !$maxv) {
+      return null;
+    }
+
+    $min = null;
+    $max = null;
+
+    if ($minv) {
+      $min = min($minv);
+    }
+
+    if ($maxv) {
+      $max = max($maxv);
+    }
+
+    return array($min, $max);
+  }
+
+  public function newInputValues(PhabricatorChartDataQuery $query) {
+    $map = array();
+    foreach ($this->getFunctionArguments() as $function) {
+      $xv = $function->newInputValues($query);
+      if ($xv !== null) {
+        foreach ($xv as $x) {
+          $map[$x] = true;
+        }
+      }
+    }
+
+    if (!$map) {
+      return null;
+    }
+
+    ksort($map);
+
+    return array_keys($map);
+  }
+
+}
diff --git a/src/applications/fact/chart/PhabricatorScaleChartFunction.php b/src/applications/fact/chart/PhabricatorScaleChartFunction.php
--- a/src/applications/fact/chart/PhabricatorScaleChartFunction.php
+++ b/src/applications/fact/chart/PhabricatorScaleChartFunction.php
@@ -7,22 +7,22 @@
 
   protected function newArguments() {
     return array(
-      $this->newArgument()
-        ->setName('x')
-        ->setType('function')
-        ->setIsSourceFunction(true),
       $this->newArgument()
         ->setName('scale')
         ->setType('number'),
     );
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $scale = $this->getArgument('scale');
+
+    $yv = array();
+
+    foreach ($xv as $x) {
+      $yv[] = $x * $scale;
+    }
 
-  protected function evaluateFunction($x) {
-    return $x * $this->getArgument('scale');
+    return $yv;
   }
 
 }
diff --git a/src/applications/fact/chart/PhabricatorShiftChartFunction.php b/src/applications/fact/chart/PhabricatorShiftChartFunction.php
--- a/src/applications/fact/chart/PhabricatorShiftChartFunction.php
+++ b/src/applications/fact/chart/PhabricatorShiftChartFunction.php
@@ -7,22 +7,22 @@
 
   protected function newArguments() {
     return array(
-      $this->newArgument()
-        ->setName('x')
-        ->setType('function')
-        ->setIsSourceFunction(true),
       $this->newArgument()
         ->setName('shift')
         ->setType('number'),
     );
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $shift = $this->getArgument('shift');
+
+    $yv = array();
+
+    foreach ($xv as $x) {
+      $yv[] = $x + $shift;
+    }
 
-  protected function evaluateFunction($x) {
-    return $x * $this->getArgument('shift');
+    return $yv;
   }
 
 }
diff --git a/src/applications/fact/chart/PhabricatorSinChartFunction.php b/src/applications/fact/chart/PhabricatorSinChartFunction.php
--- a/src/applications/fact/chart/PhabricatorSinChartFunction.php
+++ b/src/applications/fact/chart/PhabricatorSinChartFunction.php
@@ -6,20 +6,17 @@
   const FUNCTIONKEY = 'sin';
 
   protected function newArguments() {
-    return array(
-      $this->newArgument()
-        ->setName('x')
-        ->setType('function')
-        ->setIsSourceFunction(true),
-    );
+    return array();
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $yv = array();
+
+    foreach ($xv as $x) {
+      $yv[] = sin(deg2rad($x));
+    }
 
-  protected function evaluateFunction($x) {
-    return sin(deg2rad($x));
+    return $yv;
   }
 
 }
diff --git a/src/applications/fact/chart/PhabricatorSumChartFunction.php b/src/applications/fact/chart/PhabricatorSumChartFunction.php
new file mode 100644
--- /dev/null
+++ b/src/applications/fact/chart/PhabricatorSumChartFunction.php
@@ -0,0 +1,40 @@
+<?php
+
+final class PhabricatorSumChartFunction
+  extends PhabricatorHigherOrderChartFunction {
+
+  const FUNCTIONKEY = 'sum';
+
+  protected function newArguments() {
+    return array(
+      $this->newArgument()
+        ->setName('f')
+        ->setType('function')
+        ->setRepeatable(true),
+    );
+  }
+
+  public function evaluateFunction(array $xv) {
+    $fv = array();
+    foreach ($this->getFunctionArguments() as $function) {
+      $fv[] = $function->evaluateFunction($xv);
+    }
+
+    $n = count($xv);
+    $yv = array_fill(0, $n, null);
+
+    foreach ($fv as $f) {
+      for ($ii = 0; $ii < $n; $ii++) {
+        if ($f[$ii] !== null) {
+          if (!isset($yv[$ii])) {
+            $yv[$ii] = 0;
+          }
+          $yv[$ii] += $f[$ii];
+        }
+      }
+    }
+
+    return $yv;
+  }
+
+}
diff --git a/src/applications/fact/chart/PhabricatorXChartFunction.php b/src/applications/fact/chart/PhabricatorXChartFunction.php
deleted file mode 100644
--- a/src/applications/fact/chart/PhabricatorXChartFunction.php
+++ /dev/null
@@ -1,20 +0,0 @@
-<?php
-
-final class PhabricatorXChartFunction
-  extends PhabricatorChartFunction {
-
-  const FUNCTIONKEY = 'x';
-
-  protected function newArguments() {
-    return array();
-  }
-
-  protected function canEvaluateFunction() {
-    return true;
-  }
-
-  protected function evaluateFunction($x) {
-    return $x;
-  }
-
-}
diff --git a/src/applications/fact/controller/PhabricatorFactChartController.php b/src/applications/fact/controller/PhabricatorFactChartController.php
--- a/src/applications/fact/controller/PhabricatorFactChartController.php
+++ b/src/applications/fact/controller/PhabricatorFactChartController.php
@@ -12,43 +12,50 @@
     $is_chart_mode = ($mode === 'chart');
     $is_draw_mode = ($mode === 'draw');
 
+    $argvs = array();
+
+    $argvs[] = array('fact', 'tasks.count.create');
+
+    $argvs[] = array('constant', 360);
+
+    $argvs[] = array('fact', 'tasks.open-count.create');
+
+    $argvs[] = array(
+      'sum',
+      array(
+        'accumulate',
+        array('fact', 'tasks.count.create'),
+      ),
+      array(
+        'accumulate',
+        array('fact', 'tasks.open-count.create'),
+      ),
+    );
+
+    $argvs[] = array(
+      'compose',
+      array('scale', 0.001),
+      array('cos'),
+      array('scale', 100),
+      array('shift', 800),
+    );
+
     $functions = array();
+    foreach ($argvs as $argv) {
+      $functions[] = id(new PhabricatorComposeChartFunction())
+        ->setArguments(array($argv));
+    }
 
-    $functions[] = id(new PhabricatorFactChartFunction())
-      ->setArguments(array('tasks.count.create'));
-
-    $functions[] = id(new PhabricatorFactChartFunction())
-      ->setArguments(array('tasks.open-count.create'));
-
-    $x_function = id(new PhabricatorXChartFunction())
-      ->setArguments(array());
-
-    $functions[] = id(new PhabricatorConstantChartFunction())
-      ->setArguments(array(360));
-
-    $functions[] = id(new PhabricatorSinChartFunction())
-      ->setArguments(array($x_function));
-
-    $cos_function = id(new PhabricatorCosChartFunction())
-      ->setArguments(array($x_function));
-
-    $functions[] = id(new PhabricatorShiftChartFunction())
-      ->setArguments(
-        array(
-          array(
-            'scale',
-            array(
-              'cos',
-              array(
-                'scale',
-                array('x'),
-                0.001,
-              ),
-            ),
-            10,
-          ),
-          200,
-        ));
+    $subfunctions = array();
+    foreach ($functions as $function) {
+      foreach ($function->getSubfunctions() as $subfunction) {
+        $subfunctions[] = $subfunction;
+      }
+    }
+
+    foreach ($subfunctions as $subfunction) {
+      $subfunction->loadData();
+    }
 
     list($domain_min, $domain_max) = $this->getDomain($functions);
 
@@ -63,11 +70,7 @@
 
     $datasets = array();
     foreach ($functions as $function) {
-      $function->setXAxis($axis);
-
-      $function->loadData();
-
-      $points = $function->getDatapoints($data_query);
+      $points = $function->newDatapoints($data_query);
 
       $x = array();
       $y = array();
@@ -157,19 +160,18 @@
   private function getDomain(array $functions) {
     $domain_min_list = null;
     $domain_max_list = null;
+
     foreach ($functions as $function) {
-      if ($function->hasDomain()) {
-        $domain = $function->getDomain();
+      $domain = $function->getDomain();
 
-        list($domain_min, $domain_max) = $domain;
+      list($function_min, $function_max) = $domain;
 
-        if ($domain_min !== null) {
-          $domain_min_list[] = $domain_min;
-        }
+      if ($function_min !== null) {
+        $domain_min_list[] = $function_min;
+      }
 
-        if ($domain_max !== null) {
-          $domain_max_list[] = $domain_max;
-        }
+      if ($function_max !== null) {
+        $domain_max_list[] = $function_max;
       }
     }