{"action":"closed","issue":{"url":"https://api.github.com/repos/RedPRL/sml-redprl/issues/694","repository_url":"https://api.github.com/repos/RedPRL/sml-redprl","labels_url":"https://api.github.com/repos/RedPRL/sml-redprl/issues/694/labels{/name}","comments_url":"https://api.github.com/repos/RedPRL/sml-redprl/issues/694/comments","events_url":"https://api.github.com/repos/RedPRL/sml-redprl/issues/694/events","html_url":"https://github.com/RedPRL/sml-redprl/issues/694","id":379048871,"node_id":"MDU6SXNzdWUzNzkwNDg4NzE=","number":694,"title":"Recursor for parametric type seems broken","user":{"login":"konn","id":21860,"node_id":"MDQ6VXNlcjIxODYw","avatar_url":"https://avatars0.githubusercontent.com/u/21860?v=4","gravatar_id":"","url":"https://api.github.com/users/konn","html_url":"https://github.com/konn","followers_url":"https://api.github.com/users/konn/followers","following_url":"https://api.github.com/users/konn/following{/other_user}","gists_url":"https://api.github.com/users/konn/gists{/gist_id}","starred_url":"https://api.github.com/users/konn/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/konn/subscriptions","organizations_url":"https://api.github.com/users/konn/orgs","repos_url":"https://api.github.com/users/konn/repos","events_url":"https://api.github.com/users/konn/events{/privacy}","received_events_url":"https://api.github.com/users/konn/received_events","type":"User","site_admin":false},"labels":[],"state":"closed","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":2,"created_at":"2018-11-09T07:15:51Z","updated_at":"2018-11-10T03:19:47Z","closed_at":"2018-11-10T03:19:47Z","author_association":"NONE","body":"For a non-parametric data-type, we can use recursor instead of the `elim` tactic as follows:\r\n\r\n```redprl\r\ndata BraceInt: (U 0 kan) {\r\n  brace int\r\n} by { auto }.\r\n\r\ntheorem UnbraceInt :  (-> (.BraceInt type ) int) by {\r\n  lam b => `(.BraceInt rec [_] int b [z] z)\r\n}.\r\n```\r\n\r\nOn the other hand, it seems that recursors for parametric data-types don't work.\r\nConsider the following parametric version of the above `Brace`\r\n\r\n```redprl\r\ndata Brace [a: (U 0 coe)]: (U 0 kan) {\r\n  brace a\r\n} by { auto }.\r\n\r\ntheorem Unbrace: (-> [a: (U 0 coe)] (.Brace type a) a)\r\nby {\r\n  lam a b =>`(.Brace rec [_] a b [z] z);\r\n  ?unresolved\r\n}.\r\n```\r\n\r\nThen, RedPRL reports that there is an unresolved goal as follows:\r\n\r\n```\r\nlist.prl:14.3-14.14 [Info]:\r\n  ?unresolved.\r\n  Goal #0.\r\n    a : (U 0 coe)\r\n    b : (. Brace type a)\r\n    -----------------------------------\r\n    (mem a (. Brace rec [_] a b [z] z))\r\n\r\nlist.prl:12.3-14.14 [Warning]:\r\n  1 Remaining Obligations\r\n```\r\n\r\nThings won't change if one specialise type argument `a` in `Unbrace` theorem to `int`."}}
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