| Who Cites permute list? |
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permute_list | Def (L o f) == mklist(||L||; i.L[(f(i))]) |
| | Thm* T:Type, L:T List, f:( ||L||![](FONT/dash.png) ![](FONT/then_med.png) ||L||). (L o f) T List |
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select |
Def l[i] == hd(nth_tl(i;l)) |
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Thm* A:Type, l:A List, n: . 0 n ![](FONT/eq.png) n < ||l|| ![](FONT/eq.png) l[n] A |
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length |
Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
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Thm* A:Type, l:A List. ||l|| ![](FONT/int.png) |
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Thm* ||nil|| ![](FONT/int.png) |
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mklist |
Def mklist(n;f) == primrec(n;nil; i,l. l @ [(f(i))]) |
| | Thm* T:Type, n: , f:( n![](FONT/dash.png) T). mklist(n;f) T List |
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nth_tl |
Def nth_tl(n;as) == if n![](FONT/le.png) 0 as else nth_tl(n-1;tl(as)) fi (recursive) |
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Thm* A:Type, as:A List, i: . nth_tl(i;as) A List |
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hd |
Def hd(l) == Case of l; nil "?" ; h.t h |
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Thm* A:Type, l:A List. ||l|| 1 ![](FONT/eq.png) hd(l) A |
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Thm* A:Type, l:A List . hd(l) A |
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append |
Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
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Thm* T:Type, as,bs:T List. (as @ bs) T List |
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primrec |
Def primrec(n;b;c) == if n= 0 b else c(n-1,primrec(n-1;b;c)) fi (recursive) |
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Thm* T:Type, n: , b:T, c:( n![](FONT/dash.png) T![](FONT/dash.png) T). primrec(n;b;c) T |
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tl |
Def tl(l) == Case of l; nil nil ; h.t t |
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Thm* A:Type, l:A List. tl(l) A List |
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le_int |
Def i![](FONT/le.png) j == ![](FONT/not.png) j < i |
| | Thm* i,j: . (i![](FONT/le.png) j) ![](FONT/bool.png) |
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eq_int |
Def i= j == if i=j true ; false fi |
| | Thm* i,j: . (i= j) ![](FONT/bool.png) |
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lt_int |
Def i < j == if i < j true ; false fi |
| | Thm* i,j: . (i < j) ![](FONT/bool.png) |
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bnot |
Def ![](FONT/not.png) b == if b false else true fi |
| | Thm* b: . ![](FONT/not.png) b ![](FONT/bool.png) |