{"action":"opened","number":125,"pull_request":{"url":"https://api.github.com/repos/Andromedans/andromeda/pulls/125","id":53579107,"html_url":"https://github.com/Andromedans/andromeda/pull/125","diff_url":"https://github.com/Andromedans/andromeda/pull/125.diff","patch_url":"https://github.com/Andromedans/andromeda/pull/125.patch","issue_url":"https://api.github.com/repos/Andromedans/andromeda/issues/125","number":125,"state":"open","locked":false,"title":"Abstract operation","user":{"login":"SkySkimmer","id":2461932,"avatar_url":"https://avatars.githubusercontent.com/u/2461932?v=3","gravatar_id":"","url":"https://api.github.com/users/SkySkimmer","html_url":"https://github.com/SkySkimmer","followers_url":"https://api.github.com/users/SkySkimmer/followers","following_url":"https://api.github.com/users/SkySkimmer/following{/other_user}","gists_url":"https://api.github.com/users/SkySkimmer/gists{/gist_id}","starred_url":"https://api.github.com/users/SkySkimmer/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/SkySkimmer/subscriptions","organizations_url":"https://api.github.com/users/SkySkimmer/orgs","repos_url":"https://api.github.com/users/SkySkimmer/repos","events_url":"https://api.github.com/users/SkySkimmer/events{/privacy}","received_events_url":"https://api.github.com/users/SkySkimmer/received_events","type":"User","site_admin":false},"body":"When abstracting a variable `x` from a context, if there is a variable `y` depending on it, give the user a chance to replace by emitting an operation `#abstract ('pair x y)`. It expects an option of a replacement term for `y`. Usually `x : X` and `y : Y` and the replacement is `z : Π [x_ : X] Y where x := x_ |- z y : Y`.\r\n\r\nSince we need to replace `y` in any terms under the abstraction (eg `lambda [x] ... y ...` becomes `lambda [x] ... (z x) ...`), context abstraction also returns the list of instantiations.\r\n\r\nIn a term `lambda [x : X] [y : Y] t`, `Y` needs to get any assumptions depending on `x` replaced before we evaluate `t` with `y : Y` in the environment, ie we make the context typing `Y : Type` abstractable for `x`.\r\n\r\nChecking equalities under binders also involves abstraction operations. 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