| Who Cites guarded permutation? |
|
guarded_permutation | Def guarded_permutation(T;P)
Def == (L1,L2. i:(||L1||-1). P(L1,i) & L2 = swap(L1;i;i+1) T List)^* |
| | Thm* T:Type, P:(L:(T List)(||L||-1)Prop).
Thm* guarded_permutation(T;P) (T List)(T List)Prop |
|
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 |
|
permute_list | Def (L o f) == mklist(||L||;i.L[(f(i))]) |
| | Thm* T:Type, L:T List, f:(||L||||L||). (L o f) T List |
|
length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l|| |
| | Thm* ||nil|| |
|
int_seg | Def {i..j} == {k:| i k < j } |
| | Thm* m,n:. {m..n} Type |
|
rel_star | Def (R^*)(x,y) == n:. x R^n y |
| | Thm* T:Type, R:(TTProp). (R^*) TTProp |
|
flip | Def (i, j)(x) == if x=i j ; x=j i else x fi |
| | Thm* k:, i,j:k. (i, j) kk |
|
lelt | Def i j < k == ij & j<k |
|
rel_exp | Def R^n == if n=0 x,y. x = y T else x,y. z:T. (x R z) & (z R^n-1 y) fi
Def (recursive) |
| | Thm* n:, T:Type, R:(TTProp). R^n TTProp |
|
nat | Def == {i:| 0i } |
| | Thm* Type |
|
mklist | Def mklist(n;f) == primrec(n;nil;i,l. l @ [(f(i))]) |
| | Thm* T:Type, n:, f:(nT). mklist(n;f) T List |
|
primrec | Def primrec(n;b;c) == if n=0 b else c(n-1,primrec(n-1;b;c)) fi (recursive) |
| | Thm* T:Type, n:, b:T, c:(nTT). primrec(n;b;c) T |
|
eq_int | Def i=j == if i=j true ; false fi |
| | Thm* i,j:. (i=j) |
|
select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n:. 0n n<||l|| l[n] A |
|
le | Def AB == B<A |
| | Thm* i,j:. (ij) Prop |
|
nth_tl | Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive) |
| | Thm* A:Type, as:A List, i:. nth_tl(i;as) A List |
|
hd | Def hd(l) == Case of l; nil "?" ; h.t h |
| | Thm* A:Type, l:A List. ||l||1 hd(l) A |
|
append | Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
| | Thm* T:Type, as,bs:T List. (as @ bs) T List |
|
not | Def A == A False |
| | Thm* A:Prop. (A) Prop |
|
tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | Thm* A:Type, l:A List. tl(l) A List |
|
le_int | Def ij == j<i |
| | Thm* i,j:. (ij) |
|
lt_int | Def i<j == if i<j true ; false fi |
| | Thm* i,j:. (i<j) |
|
bnot | Def b == if b false else true fi |
| | Thm* b:. b |