Typescript allows a type to reference another type defined further down in the same file, which can lead to rather interesting constructs.<\/p>\n
The vanilla circular reference fails:<\/p>\n
\r\ntype Foo = Bar; \/\/ error: type alias Foo circularly references itself\r\ntype Bar = Foo; \/\/ error: type alias Bar circularly references itself\r\n<\/pre>\nHowever, the following is legal, and surprisingly deep:<\/p>\n
\r\ntype Foo = Bar;\r\ntype Bar = Foo[];\r\n<\/pre>\nWhat it defines is a recursive list of empty lists:<\/p>\n
[]<\/code> is in the type.<\/li>\n- A list of any values already in the type is in the type.<\/li>\n<\/ul>\n
This is pretty close to Von Neumann construction of natural numbers<\/a>:<\/p>\n\r\n\/\/ combine two Foo lists\r\nfunction union(left: Foo, right: Foo) : Foo {\r\n return [...left, ...right];\r\n}\r\n\r\n\/\/ von Neumann definition of "next number"\r\nfunction succ(x: Foo) : Foo {\r\n return union(x, [x]);\r\n}\r\n\r\nconst zero: Foo = [];\r\nconst one: Foo = succ(zero); \/\/ [[]]\r\nconst two: Foo = succ(one); \/\/ [[],[[]]]\r\nconst three: Foo = succ(two); \/\/ [[],[[]],[[],[[]] ] ]\r\nconsole.log(JSON.stringify(three)); \/\/ prints [[],[[]],[[],[[]]]]\r\n<\/pre>\nWe can go ahead and implement addition and even multiplication of Foo<\/code>s (but it’s going to be very slow):<\/p>\n\r\nfunction isZero(x: Foo) {\r\n return x.length === 0;\r\n}\r\n\r\nfunction pred(x: Foo) : Foo {\r\n if (isZero(x)) {\r\n throw new Error("Zero has no predecessor");\r\n }\r\n return x.slice(0, -1); \/\/ all elements except the last one\r\n}\r\n\r\nfunction add(a: Foo, b: Foo): Foo {\r\n if (isZero(b)) {\r\n return a;\r\n } else {\r\n return succ(add(a, pred(b)));\r\n }\r\n}\r\n\r\nfunction multiply(a: Foo, b: Foo): Foo {\r\n if (isZero(b)) {\r\n return zero;\r\n } else {\r\n return add(a, multiply(a, pred(b)));\r\n }\r\n}\r\n\r\nconsole.log( JSON.stringify(add(one, two))); \/\/ [[],[[]],[[],[[]]]]\r\nconsole.log( JSON.stringify(multiply(two, two))); \/\/ [[],[[]],[[],[[]]],[[],[[]],[[],[[]]]]]\r\n<\/pre>\nRecursive types are definitely fun.<\/p>\n","protected":false},"excerpt":{"rendered":"
Typescript allows a type to reference another type defined further down in the same file, which can lead to rather interesting constructs. The vanilla circular reference fails: type Foo = […]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"Layout":"","footnotes":""},"categories":[29],"tags":[],"class_list":["entry","author-ikriv","post-5285","post","type-post","status-publish","format-standard","category-typescript"],"_links":{"self":[{"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/5285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5285"}],"version-history":[{"count":3,"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/5285\/revisions"}],"predecessor-version":[{"id":5288,"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/5285\/revisions\/5288"}],"wp:attachment":[{"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ikriv.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}