diff --git a/src/Analyser/NodeScopeResolver.php b/src/Analyser/NodeScopeResolver.php
index 8ff656bb57..82697affa6 100644
--- a/src/Analyser/NodeScopeResolver.php
+++ b/src/Analyser/NodeScopeResolver.php
@@ -181,6 +181,7 @@
 use PHPStan\Type\Generic\TemplateTypeVarianceMap;
 use PHPStan\Type\IntegerType;
 use PHPStan\Type\IntersectionType;
+use PHPStan\Type\IterableType;
 use PHPStan\Type\MixedType;
 use PHPStan\Type\NeverType;
 use PHPStan\Type\NullType;
@@ -1250,6 +1251,19 @@ private function processStmtNode(
 			$exprType = $scope->getType($stmt->expr);
 			$isIterableAtLeastOnce = $exprType->isIterableAtLeastOnce();
 			if ($exprType->isIterable()->no() || $isIterableAtLeastOnce->maybe()) {
+				$foreachType = $this->getForeachIterateeType();
+				if (
+					!$foreachType->isSuperTypeOf($exprType)->yes()
+					&& $finalScope->getType($stmt->expr)->equals($foreachType)
+				) {
+					// restore iteratee type, in case the type was narrowed while entering the foreach
+					$finalScope = $finalScope->assignExpression(
+						$stmt->expr,
+						$exprType,
+						$scope->getNativeType($stmt->expr),
+					);
+				}
+
 				$finalScope = $finalScope->mergeWith($scope->filterByTruthyValue(new BooleanOr(
 					new BinaryOp\Identical(
 						$stmt->expr,
@@ -6307,11 +6321,32 @@ private function processVarAnnotation(MutatingScope $scope, array $variableNames
 		return $scope;
 	}
 
+	private function getForeachIterateeType(): Type
+	{
+		return new IterableType(new MixedType(), new MixedType());
+	}
+
 	private function enterForeach(MutatingScope $scope, MutatingScope $originalScope, Foreach_ $stmt): MutatingScope
 	{
 		if ($stmt->expr instanceof Variable && is_string($stmt->expr->name)) {
 			$scope = $this->processVarAnnotation($scope, [$stmt->expr->name], $stmt);
 		}
+
+		// narrow the iteratee type to those supported by foreach
+		$foreachType = $this->getForeachIterateeType();
+		$scope = $scope->specifyExpressionType(
+			$stmt->expr,
+			TypeCombinator::intersect(
+				$scope->getType($stmt->expr),
+				$foreachType,
+			),
+			TypeCombinator::intersect(
+				$scope->getNativeType($stmt->expr),
+				$foreachType,
+			),
+			TrinaryLogic::createYes(),
+		);
+
 		$iterateeType = $originalScope->getType($stmt->expr);
 		if (
 			($stmt->valueVar instanceof Variable && is_string($stmt->valueVar->name))
diff --git a/src/Analyser/ResultCache/ResultCacheManager.php b/src/Analyser/ResultCache/ResultCacheManager.php
index 86609521db..87e6b07785 100644
--- a/src/Analyser/ResultCache/ResultCacheManager.php
+++ b/src/Analyser/ResultCache/ResultCacheManager.php
@@ -1131,7 +1131,7 @@ private function getComposerLocks(): array
 	}
 
 	/**
-	 * @return array<string, string>
+	 * @return array<string, array<mixed>>
 	 */
 	private function getComposerInstalled(): array
 	{
@@ -1149,6 +1149,10 @@ private function getComposerInstalled(): array
 			}
 
 			$installed = require $filePath;
+			if (!is_array($installed)) {
+				throw new ShouldNotHappenException();
+			}
+
 			$rootName = $installed['root']['name'];
 			unset($installed['root']);
 			unset($installed['versions'][$rootName]);
diff --git a/src/Type/MixedType.php b/src/Type/MixedType.php
index 1245743947..ce485141a6 100644
--- a/src/Type/MixedType.php
+++ b/src/Type/MixedType.php
@@ -169,7 +169,14 @@ public function setOffsetValueType(?Type $offsetType, Type $valueType, bool $uni
 
 	public function setExistingOffsetValueType(Type $offsetType, Type $valueType): Type
 	{
-		return new self($this->isExplicitMixed);
+		$types = [
+			new ArrayType(new MixedType(), new MixedType()),
+			new ObjectType(ArrayAccess::class),
+		];
+		if (!$offsetType->isInteger()->no()) {
+			$types[] = new StringType();
+		}
+		return TypeCombinator::union(...$types);
 	}
 
 	public function unsetOffset(Type $offsetType): Type
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13270a.php b/tests/PHPStan/Analyser/nsrt/bug-13270a.php
new file mode 100644
index 0000000000..3057ba009b
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13270a.php
@@ -0,0 +1,54 @@
+<?php // lint >= 8.0
+
+declare(strict_types = 1);
+
+namespace Bug13270a;
+
+use function PHPStan\Testing\assertType;
+
+final class HelloWorld
+{
+	/**
+	 * @param array<mixed> $data
+	 */
+	public function test(array $data): void
+	{
+		foreach($data as $k => $v) {
+			assertType('non-empty-array<mixed>', $data);
+			$data[$k]['a'] = true;
+			assertType("non-empty-array<(non-empty-array&hasOffsetValue('a', true))|(ArrayAccess&hasOffsetValue('a', true))>", $data);
+			foreach($data[$k] as $val) {
+			}
+		}
+	}
+
+	public function doFoo(
+		mixed $mixed,
+		mixed $mixed2,
+		mixed $mixed3,
+		mixed $mixed4,
+		int $i,
+		int $i2,
+		string|int $stringOrInt
+	): void
+	{
+		$mixed[$i]['a'] = true;
+		assertType('mixed', $mixed);
+
+		$mixed2[$stringOrInt]['a'] = true;
+		assertType('mixed', $mixed2);
+
+		$mixed3[$i][$stringOrInt] = true;
+		assertType('mixed', $mixed3);
+
+		$mixed4['a'][$stringOrInt] = true;
+		assertType('mixed', $mixed4);
+
+		$null = null;
+		$null[$i]['a'] = true;
+		assertType('non-empty-array<int, array{a: true}>', $null);
+
+		$i2['a'] = true;
+		assertType('*ERROR*', $i2);
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13270b.php b/tests/PHPStan/Analyser/nsrt/bug-13270b.php
new file mode 100644
index 0000000000..aeae142564
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13270b.php
@@ -0,0 +1,27 @@
+<?php declare(strict_types=1);
+
+namespace Bug13270b;
+
+use function PHPStan\Testing\assertType;
+
+class Test
+{
+	/**
+	 * @param mixed[] $data
+	 * @return mixed[]
+	 */
+	public function parseData(array $data): array
+	{
+		if (isset($data['price'])) {
+			assertType('mixed~null', $data['price']);
+			if (!array_key_exists('priceWithVat', $data['price'])) {
+				$data['price']['priceWithVat'] = null;
+			}
+			assertType("(non-empty-array&hasOffsetValue('priceWithVat', mixed))|(ArrayAccess&hasOffsetValue('priceWithVat', null))", $data['price']);
+			if (!array_key_exists('priceWithoutVat', $data['price'])) {
+				$data['price']['priceWithoutVat'] = null;
+			}
+		}
+		return $data;
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13312.php b/tests/PHPStan/Analyser/nsrt/bug-13312.php
new file mode 100644
index 0000000000..6a743fb6f3
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13312.php
@@ -0,0 +1,45 @@
+<?php // lint >= 8.0
+
+namespace Bug13312;
+
+use function PHPStan\Testing\assertType;
+
+function fooArr(array $arr): void {
+	assertType('array', $arr);
+	foreach ($arr as $v) {
+		assertType('non-empty-array', $arr);
+	}
+	assertType('array', $arr);
+
+	for ($i = 0; $i < count($arr); ++$i) {
+		assertType('non-empty-array', $arr);
+	}
+	assertType('array', $arr);
+}
+
+/** @param list<mixed> $arr */
+function foo(array $arr): void {
+	assertType('list<mixed>', $arr);
+	foreach ($arr as $v) {
+		assertType('non-empty-list<mixed>', $arr);
+	}
+	assertType('list<mixed>', $arr);
+
+	for ($i = 0; $i < count($arr); ++$i) {
+		assertType('non-empty-list<mixed>', $arr);
+	}
+	assertType('list<mixed>', $arr);
+}
+
+
+function fooBar(mixed $mixed): void {
+	assertType('mixed', $mixed);
+	foreach ($mixed as $v) {
+		assertType('iterable', $mixed); // could be non-empty-array|Traversable
+	}
+	assertType('mixed', $mixed);
+
+	foreach ($mixed as $v) {}
+
+	assertType('mixed', $mixed);
+}
diff --git a/tests/PHPStan/Analyser/nsrt/composer-array-bug.php b/tests/PHPStan/Analyser/nsrt/composer-array-bug.php
index 354577f098..534afc600d 100644
--- a/tests/PHPStan/Analyser/nsrt/composer-array-bug.php
+++ b/tests/PHPStan/Analyser/nsrt/composer-array-bug.php
@@ -16,15 +16,18 @@ class Foo
 	public function doFoo(): void
 	{
 		if (!empty($this->config['authors'])) {
+			assertType("mixed~(0|0.0|''|'0'|array{}|false|null)", $this->config['authors']);
 			foreach ($this->config['authors'] as $key => $author) {
+				assertType("iterable", $this->config['authors']);
+
 				if (!is_array($author)) {
 					$this->errors[] = 'authors.'.$key.' : should be an array, '.gettype($author).' given';
-					assertType("mixed", $this->config['authors']);
+					assertType("iterable", $this->config['authors']);
 					unset($this->config['authors'][$key]);
-					assertType("mixed", $this->config['authors']);
+					assertType("iterable", $this->config['authors']);
 					continue;
 				}
-				assertType("mixed", $this->config['authors']);
+				assertType("iterable", $this->config['authors']);
 				foreach (['homepage', 'email', 'name', 'role'] as $authorData) {
 					if (isset($author[$authorData]) && !is_string($author[$authorData])) {
 						$this->errors[] = 'authors.'.$key.'.'.$authorData.' : invalid value, must be a string';
@@ -32,9 +35,9 @@ public function doFoo(): void
 					}
 				}
 				if (isset($author['homepage'])) {
-					assertType("mixed", $this->config['authors']);
+					assertType("iterable", $this->config['authors']);
 					unset($this->config['authors'][$key]['homepage']);
-					assertType("mixed", $this->config['authors']);
+					assertType("iterable", $this->config['authors']);
 				}
 				if (isset($author['email']) && !filter_var($author['email'], FILTER_VALIDATE_EMAIL)) {
 					unset($this->config['authors'][$key]['email']);
@@ -44,8 +47,8 @@ public function doFoo(): void
 				}
 			}
 
-			assertType("non-empty-array&hasOffsetValue('authors', mixed)", $this->config);
-			assertType("mixed", $this->config['authors']);
+			assertType("non-empty-array&hasOffsetValue('authors', mixed~(0|0.0|''|'0'|array{}|false|null))", $this->config);
+			assertType("mixed~(0|0.0|''|'0'|array{}|false|null)", $this->config['authors']);
 
 			if (empty($this->config['authors'])) {
 				unset($this->config['authors']);
@@ -54,7 +57,7 @@ public function doFoo(): void
 				assertType("non-empty-array&hasOffsetValue('authors', mixed~(0|0.0|''|'0'|array{}|false|null))", $this->config);
 			}
 
-			assertType('array', $this->config);
+			assertType("non-empty-array&hasOffsetValue('authors', mixed~(0|0.0|''|'0'|array{}|false|null))", $this->config);
 		}
 	}
 
diff --git a/tests/PHPStan/Analyser/nsrt/composer-non-empty-array-after-unset.php b/tests/PHPStan/Analyser/nsrt/composer-non-empty-array-after-unset.php
index 0cec47c79a..1d4c09dca7 100644
--- a/tests/PHPStan/Analyser/nsrt/composer-non-empty-array-after-unset.php
+++ b/tests/PHPStan/Analyser/nsrt/composer-non-empty-array-after-unset.php
@@ -15,10 +15,10 @@ public function doFoo()
 		if (!empty($this->config['authors'])) {
 			assertType("mixed~(0|0.0|''|'0'|array{}|false|null)", $this->config['authors']);
 			foreach ($this->config['authors'] as $key => $author) {
-				assertType("mixed", $this->config['authors']);
+				assertType("iterable", $this->config['authors']);
 				if (!is_array($author)) {
 					unset($this->config['authors'][$key]);
-					assertType("mixed", $this->config['authors']);
+					assertType("iterable", $this->config['authors']);
 					continue;
 				}
 				foreach (['homepage', 'email', 'name', 'role'] as $authorData) {
@@ -33,13 +33,13 @@ public function doFoo()
 					unset($this->config['authors'][$key]['email']);
 				}
 				if (empty($this->config['authors'][$key])) {
-					assertType("mixed", $this->config['authors']);
+					assertType("iterable", $this->config['authors']);
 					unset($this->config['authors'][$key]);
-					assertType("mixed", $this->config['authors']);
+					assertType("iterable", $this->config['authors']);
 				}
-				assertType("mixed", $this->config['authors']);
+				assertType("iterable", $this->config['authors']);
 			}
-			assertType("mixed", $this->config['authors']);
+			assertType("mixed~(0|0.0|''|'0'|array{}|false|null)", $this->config['authors']);
 		}
 	}
 
diff --git a/tests/PHPStan/Rules/Arrays/IterableInForeachRuleTest.php b/tests/PHPStan/Rules/Arrays/IterableInForeachRuleTest.php
index f392ac3202..e00b70e84e 100644
--- a/tests/PHPStan/Rules/Arrays/IterableInForeachRuleTest.php
+++ b/tests/PHPStan/Rules/Arrays/IterableInForeachRuleTest.php
@@ -139,4 +139,10 @@ public function testMixed(bool $checkExplicitMixed, bool $checkImplicitMixed, ar
 		$this->analyse([__DIR__ . '/data/foreach-mixed.php'], $errors);
 	}
 
+	#[RequiresPhp('>= 8.0')]
+	public function testBug13312(): void
+	{
+		$this->analyse([__DIR__ . '/../../Analyser/nsrt/bug-13312.php'], []);
+	}
+
 }