Thm* n: , f:( n![](FONT/dash.png) T), i: n. (f{ n})[i] = f(i) | [select_listify_id] |
Thm* as:T List. ( i: ||as||. as[i]){ ||as||} = as | [listify_select_id] |
Thm* f:(A![](FONT/dash.png) B), as:A List, n: ||as||. map(f;as)[n] = f(as[n]) | [map_select] |
Thm* as:T List, n:{0...||as||}, i: n. firstn(n;as)[i] = as[i] | [select_firstn] |
Thm* as:T List, n:{0...||as||}, i: (||as||-n). nth_tl(n;as)[i] = as[(i+n)] | [select_nth_tl] |
Thm* as:A List, n: (||as||-1). tl(as)[n] = as[(n+1)] | [select_tl] |
Thm* as,bs:T List, i: ||as||. (as @ bs)[i] = as[i] | [select_append_front] |
Thm* as,bs:T List, i:{||as||..(||as||+||bs||) }. (as @ bs)[i] = bs[(i-||as||)] | [select_append_back] |
Thm* a:T, as:T List, i: . 0<i ![](FONT/eq.png) i ||as|| ![](FONT/eq.png) (a.as)[i] = as[(i-1)] | [select_cons_tl] |
Thm* a:T, as:T List, i: . i 0 ![](FONT/eq.png) (a.as)[i] = a | [select_cons_hd] |