Recursive type system fails unexpectedly

[TheOnlyTails]

I've written the parser for the type definitions in my language like so:

type_def     = { (type_primary ~ "|")* ~ type_primary }
type_primary = { type_term | closure_type | "(" ~ type_def ~ ")" }
type_term    = { "int" | "float" | "string" | "char" | "boolean" | "void" | list_type | map_type | tuple_type | object_type }

list_type         = { "#[" ~ type_def ~ "]" }
map_type          = { "#{" ~ type_def ~ ":" ~ type_def ~ "}" }
tuple_type        = { "#(" ~ (type_def* ~ ",") ~ type_def? ~ ")" }
object_type       = { "@{" ~ (object_type_entry ~ ",")* ~ object_type_entry? ~ "}" }
object_type_entry = { identifier ~ ":" ~ type_def }
closure_type      = { "(" ~ (type_def* ~ ",") ~ type_def? ~ ")" ~ "->" ~ closure_term }

closure_term = { type_term | "(" ~ (closure_type | type_def) ~ ")" }

However, trying to parse a simple closure type such as this: (int) -> void produces the wrong result:

- type_def > type_primary > type_def > type_primary > type_term: "int"

Why is this happening? I would imagine that it should hit the closure_type parser before the parenthesized type parser.
Thanks in advance

pest editor link

[TheOnlyTails]

Update: I was a bit silly, I applied the 0-or-more operator to the first type_def instead of the type_def and comma, making the first comma mandatory!