| | Some definitions of interest. |
|
| assert | Def  b == if b True else False fi |
| | | Thm*  b: . b  Prop |
|
| search | Def search(k;P) == primrec(k;0; i,j. if 0< j j ; P(i) i+1 else 0 fi) |
| | | Thm* k: , P:(k  ). search(k;P) (k+1) |
|
| 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 |
|
| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j: . (i=j) |
|
| iff | Def P   Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
|
| int_seg | Def {i..j } == {k:| i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
|
| let | Def let x = a in b(x) == (x.b(x))(a) |
| | | Thm* A,B:Type, a:A, b:(AB). let x = a in b(x) B |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
|
| not | Def  A == A False |
| | | Thm* A:Prop. (A) Prop |
|
| null | Def null(as) == Case of as; nil true ; a.as' false |
| | | Thm* T:Type, as:T List. null(as) |
| | | Thm* null(nil) |
