n
T
T:Type. array(T) 
Type
j.if j=
i
v else a[j] fi > x,n. n+f(x))n:, f:(n
). sum(f(x) | x < n) j == if i=j true ; false fii,j:. (i=j) 
} == {k:| i 
k < j }m,n:. {m..n} Type == {i:| 0i } Type| Some definitions of interest. | |
| array | Def array(T) == n:nT |
| Thm* T:Type. array(T) Type | |
| array-update | Def a[i:=v] == < |a|,j.if j=i v else a[j] fi > |
| array-length | Def |a| == 1of(a) |
| array-select | Def a[i] == 2of(a)(i) |
| sum | Def sum(f(x) | x < k) == primrec(k;0;x,n. n+f(x)) |
| Thm* n:, f:(n). sum(f(x) | x < n) | |
| eq_int | Def i=j == if i=j true ; false fi |
| Thm* i,j:. (i=j) | |
| int_seg | Def {i..j} == {k:| i k < j } |
| Thm* m,n:. {m..n} Type | |
| nat | Def == {i:| 0i } |
| Thm* Type |
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