diff --git a/src/Analyser/MutatingScope.php b/src/Analyser/MutatingScope.php
index f10fc22508..424319e7f9 100644
--- a/src/Analyser/MutatingScope.php
+++ b/src/Analyser/MutatingScope.php
@@ -150,6 +150,7 @@
 use function is_string;
 use function ltrim;
 use function md5;
+use function preg_match;
 use function sprintf;
 use function str_starts_with;
 use function strlen;
@@ -2224,25 +2225,45 @@ static function (Node $node, Scope $scope) use ($arrowScope, &$arrowFunctionImpu
 		}
 
 		if ($node instanceof FuncCall) {
-			if ($node->name instanceof Expr) {
+			$functionName = null;
+			if ($node->name instanceof Name) {
+				$functionName = $node->name;
+			} elseif ($node->name instanceof Expr) {
 				$calledOnType = $this->getType($node->name);
 				if ($calledOnType->isCallable()->no()) {
 					return new ErrorType();
 				}
 
-				return ParametersAcceptorSelector::selectFromArgs(
-					$this,
-					$node->getArgs(),
-					$calledOnType->getCallableParametersAcceptors($this),
-					null,
-				)->getReturnType();
+				if ($node->name instanceof String_) {
+					/** @var non-empty-string $name */
+					$name = $node->name->value;
+					$functionName = new Name($name);
+				} elseif ($node->name instanceof FuncCall && $node->name->isFirstClassCallable() &&
+						  $node->name->getAttribute('phpstan_cache_printer') !== null &&
+						  preg_match('/\A(?<name>\\\\?[^()]+)\(...\)\z/', $node->name->getAttribute('phpstan_cache_printer'), $m) === 1
+				) {
+					/** @var non-falsy-string $name */
+					$name = $m['name'];
+					$functionName = new Name($name);
+				} else {
+					return ParametersAcceptorSelector::selectFromArgs(
+						$this,
+						$node->getArgs(),
+						$calledOnType->getCallableParametersAcceptors($this),
+						null,
+					)->getReturnType();
+				}
+			}
+
+			if ($functionName === null) {
+				throw new ShouldNotHappenException();
 			}
 
-			if (!$this->reflectionProvider->hasFunction($node->name, $this)) {
+			if (!$this->reflectionProvider->hasFunction($functionName, $this)) {
 				return new ErrorType();
 			}
 
-			$functionReflection = $this->reflectionProvider->getFunction($node->name, $this);
+			$functionReflection = $this->reflectionProvider->getFunction($functionName, $this);
 			if ($this->nativeTypesPromoted) {
 				return ParametersAcceptorSelector::combineAcceptors($functionReflection->getVariants())->getNativeReturnType();
 			}
diff --git a/src/Type/Php/ArrayMapFunctionReturnTypeExtension.php b/src/Type/Php/ArrayMapFunctionReturnTypeExtension.php
index 24561b5598..404cf14996 100644
--- a/src/Type/Php/ArrayMapFunctionReturnTypeExtension.php
+++ b/src/Type/Php/ArrayMapFunctionReturnTypeExtension.php
@@ -2,8 +2,12 @@
 
 namespace PHPStan\Type\Php;
 
+use PhpParser\Node\Arg;
 use PhpParser\Node\Expr\FuncCall;
+use PhpParser\Node\Name;
+use PhpParser\Node\Scalar\String_;
 use PHPStan\Analyser\Scope;
+use PHPStan\Node\Expr\TypeExpr;
 use PHPStan\Reflection\FunctionReflection;
 use PHPStan\Type\Accessory\AccessoryArrayListType;
 use PHPStan\Type\Accessory\NonEmptyArrayType;
@@ -37,6 +41,7 @@ public function getTypeFromFunctionCall(FunctionReflection $functionReflection,
 		$singleArrayArgument = !isset($functionCall->getArgs()[2]);
 		$callableType = $scope->getType($functionCall->getArgs()[0]->value);
 		$callableIsNull = $callableType->isNull()->yes();
+		$callback = null;
 
 		if ($callableType->isCallable()->yes()) {
 			$valueTypes = [new NeverType()];
@@ -44,6 +49,7 @@ public function getTypeFromFunctionCall(FunctionReflection $functionReflection,
 				$valueTypes[] = $parametersAcceptor->getReturnType();
 			}
 			$valueType = TypeCombinator::union(...$valueTypes);
+			$callback = $functionCall->getArgs()[0]->value;
 		} elseif ($callableIsNull) {
 			$arrayBuilder = ConstantArrayTypeBuilder::createEmpty();
 			foreach (array_slice($functionCall->getArgs(), 1) as $index => $arg) {
@@ -73,7 +79,11 @@ public function getTypeFromFunctionCall(FunctionReflection $functionReflection,
 						foreach ($constantArray->getKeyTypes() as $i => $keyType) {
 							$returnedArrayBuilder->setOffsetValueType(
 								$keyType,
-								$valueType,
+								$callback === null
+									? $valueType
+									: $scope->getType(new FuncCall($callback, [
+										new Arg(new TypeExpr($constantArray->getValueTypes()[$i])),
+									])),
 								$constantArray->isOptionalKey($i),
 							);
 						}
diff --git a/tests/PHPStan/Analyser/nsrt/array-map-callable81.php b/tests/PHPStan/Analyser/nsrt/array-map-callable81.php
new file mode 100644
index 0000000000..ae5270ff2f
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/array-map-callable81.php
@@ -0,0 +1,43 @@
+<?php
+
+namespace ArrayMapCallable81;
+
+use function PHPStan\Testing\assertType;
+use function strval as str;
+
+class Foo
+{
+	/**
+	 * @template T of int
+	 * @param T $n
+	 * @return (T is 3 ? 'Fizz' : (T is 5 ? 'Buzz' : T))
+	 */
+	public static function fizzbuzz(int $n): int|string
+	{
+		return match ($n) {
+			3 => 'Fizz',
+			5 => 'Buzz',
+			default => $n,
+		};
+	}
+
+	public function doFoo(): void
+	{
+		$a = range(0, 1);
+
+		assertType("array{'0', '1'}", array_map('strval', $a));
+		assertType("array{'0', '1'}", array_map(strval(...), $a));
+		assertType("array{'0', '1'}", array_map(str(...), $a));
+		assertType("array{'0'|'1', '0'|'1'}", array_map(fn ($v) => strval($v), $a));
+		assertType("array{'0'|'1', '0'|'1'}", array_map(fn ($v) => (string)$v, $a));
+	}
+
+	public function doFizzBuzz(): void
+	{
+		assertType("array{1, 2, 'Fizz', 4, 'Buzz', 6}", array_map([__CLASS__, 'fizzbuzz'], range(1, 6)));
+		assertType("array{1, 2, 'Fizz', 4, 'Buzz', 6}", array_map([$this, 'fizzbuzz'], range(1, 6)));
+		assertType("array{1|'Buzz'|'Fizz', 2|'Buzz'|'Fizz', 3|'Buzz'|'Fizz', 4|'Buzz'|'Fizz', 5|'Buzz'|'Fizz', 6|'Buzz'|'Fizz'}", array_map(self::fizzbuzz(...), range(1, 6)));
+		assertType("array{1|'Buzz'|'Fizz', 2|'Buzz'|'Fizz', 3|'Buzz'|'Fizz', 4|'Buzz'|'Fizz', 5|'Buzz'|'Fizz', 6|'Buzz'|'Fizz'}", array_map($this->fizzbuzz(...), range(1, 6)));
+	}
+
+}