Schema for intersection types are invalid

[Andy2003]

Given:

const schema1 = z.object({
    foo: z.string()
});
const schema2= z.object({
    bar: z.string()
});
const intersection = z.intersection(schema1, schema2);
const jsonSchema = parseIntersectionDef(intersection._def, getRefs());

the following schema is generated:

{
    "allOf": [
        {
            "additionalProperties": false,
            "properties": {
                "foo": {
                    "type": "string"
                }
            },
            "required": [
                "foo"
            ],
            "type": "object"
        },
        {
            "additionalProperties": false,
            "properties": {
                "bar": {
                    "type": "string"
                }
            },
            "required": [
                "bar"
            ],
            "type": "object"
        }
    ]
}

The following input:

{ foo: 'foo', bar: 'bar' }

results in an validation error:

The Problem is, that the additionalProperties in both allOf-schemas resullts in failing each separate sub-schema validation. This seems to be a common problem in JsonSchema-Validation.

The JSON-Schema which is validating everything as expected looks like:

{
  "allOf": [
    {
      "type": "object",
      "properties": {
        "foo": {
          "type": "string"
        }
      },
      "required": [
        "foo"
      ],
    },
    {
      "type": "object",
      "properties": {
        "bar": {
          "type": "string"
        }
      },
      "required": [
        "bar"
      ],
    }
  ],
  "$schema": "http://json-schema.org/draft-07/schema#",
  "unevaluatedProperties": false
}

Note the unevaluatedProperties and the missing additionalProperties.

This issue was found in backstage/backstage#17721