| Some definitions of interest. |
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int_seg | Def {i..j} == {k:| i k < j } |
| | Thm* m,n:. {m..n} Type |
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swap | Def swap(L;i;j) == (L o (i, j)) |
| | Thm* T:Type, L:T List, i,j:||L||. swap(L;i;j) T List |
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length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l|| |
| | Thm* ||nil|| |
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map | Def map(f;as) == Case of as; nil nil ; a.as' [(f(a)) / map(f;as')]
Def (recursive) |
| | Thm* A,B:Type, f:(AB), l:A List. map(f;l) B List |
| | Thm* A,B:Type, f:(AB), l:A List. map(f;l) B List |
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select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n:. 0n n<||l|| l[n] A |