establish the base propositions of an inductive proof.[...] At present, this is mainly theory [but] seems to show a possibility of practical results, though proving correctness is a laborious and expensive process.” Perlis: “ Much of program complexity is spurious and a number of test cases properly studied will exhaust the testing problem. The problem is to isolate the right test cases, not to prove the algorithm, for that follows after the choice of the proper test cases.” Diijkstra: “Testing shows the presence, not the absence of bugs”
easy to come up with good communication tool straightforward to implement straightforward to overlook important ones usually only cover a very small portion of your domain
o u s l y e x p e c t ( M a t h . a b s ( 0 ) ) . t o . e q u a l ( 0 ) ; / / n e g a t i v e v a l u e s b e c o m e p o s i t i v e e x p e c t ( M a t h . a b s ( - 1 ) ) . t o . e q u a l ( 1 ) ; e x p e c t ( M a t h . a b s ( - 5 ) ) . t o . e q u a l ( 5 ) ; / / w h i l e p o s i t i v e v a l u e s s t a y s p o s i t i v e e x p e c t ( M a t h . a b s ( 1 ) ) . t o . e q u a l ( 1 ) ; / / s h o u l d a l s o w o r k w i t h f l o a t i n g p o i n t n u m b e r s e x p e c t ( M a t h . a b s ( - 1 . 2 3 ) ) . t o . e q u a l ( 1 . 2 3 ) ; e x p e c t ( M a t h . a b s ( 1 . 2 3 ) ) . t o . e q u a l ( 1 . 2 3 ) ; / / o h , a n d j a v a s c r i p t k n o w s a b o u t n e g a t i v e 0 e x p e c t ( M a t h . a b s ( - 0 ) ) . t o . e q u a l ( 0 ) ;
. a b s = f u n c t i o n ( x ) { i f ( x = = = 0 ) r e t u r n 0 ; i f ( x = = = - 1 | | x = = = 1 ) r e t u r n 1 ; i f ( ( x > 1 & & x < 2 ) | | ( x > - 2 & & x < - 1 ) ) r e t u r n 1 . 2 3 ; r e t u r n 5 ; }
JavaScript objects specify a property that holds for all / specified inputs instead of finding a proof, test random inputs similar to contracts examples use jsverify, other implementations available
it should return a number greater or equal than 0.” Mathematicians: ∀ x ∈ ℝ: abs(x) ≥ 0 Programmers: v a r p = r e q u i r e ( ' j s v e r i f y ' ) ; p . c h e c k ( p . f o r a l l ( p . n u m b e r ( ) , f u n c t i o n ( x ) { v a r a c t u a l = M a t h . a b s ( x ) ; r e t u r n t y p e o f a c t u a l = = = ' n u m b e r ' & & a c t u a l > = 0 ; } ) ) ; O K , p a s s e d 1 0 0 t e s t s
h e c k ( p . f o r a l l ( p . n u m b e r ( ) , f u n c t i o n ( x ) { r e t u r n M a t h . a b s ( x ) > = x ; } ) ) ; E r r o r : F a i l e d a f t e r 3 t e s t s a n d 0 s h r i n k s . r n g S t a t e : 8 c 0 a 4 3 e f 8 5 c 7 6 1 d b 9 2 ; C o u n t e r e x a m p l e : 1 . 5 6 4 4 7 3 2 9 0 9 2 7 7 0 8 1 ;
o w S u m = f u n c t i o n ( n ) { v a r s u m = 0 , i ; f o r ( i = 1 ; i < = n ; i + + ) { s u m + = i ; } r e t u r n s u m ; } , g a u s s S u m = f u n c t i o n ( n ) { r e t u r n ( n / 2 ) * ( n + 1 ) ; } , p o s i t i v e N u m b e r = p . s u c h t h a t ( p . i n t e g e r ( ) , f u n c t i o n ( i ) { r e t u r n i > 0 ; } ) ; p . a s s e r t ( p . f o r a l l ( p o s i t i v e N u m b e r , f u n c t i o n ( i ) { r e t u r n s l o w S u m ( i ) = = = g a u s s S u m ( i ) ; } ) ) ;
u m b e r = f u n c t i o n ( ) { r e t u r n { a r b i t r a r y : f u n c t i o n ( r ) { v a r n = p . i n t e g e r ( ) . a r b i t r a r y ( r ) ; r e t u r n 2 * n + 1 ; } , s h r i n k : s h r i n k . n o o p , s h o w : s h o w . d e f } ; } ; d e s c r i b e ( ' o d d ' , f u n c t i o n ( ) { / / v a r o d d = f u n c t i o n ( n ) { r e t u r n n % 2 = = = 1 ; } ; v a r o d d = f u n c t i o n ( n ) { r e t u r n M a t h . a b s ( n ) % 2 = = = 1 ; } ; i t ( ' r e t u r n s t r u e f o r a l l o d d n u m b e r s ' , f u n c t i o n ( ) { p . a s s e r t ( p . f o r a l l ( o d d N u m b e r ( ) , o d d ) ) ; } ) ;
r i s _ i d e m p o t e n t = f u n c t i o n ( g e n e r a t o r , f n ) { r e t u r n p . f o r a l l ( g e n e r a t o r , f u n c t i o n ( x ) { r e t u r n _ . i s E q u a l ( f n ( f n ( s ) ) , f n ( s ) ) ; } ) ; } ; p . a s s e r t ( i s _ i d e m p o t e n t ( p . a r r a y ( ) , _ . c o m p a c t ) ) ; p . a s s e r t ( i s _ i d e m p o t e n t ( p . a r r a y ( ) , _ . u n i q ) ) ;
( p . f o r a l l ( p . a r r a y ( p . i n t e g e r ( ) ) , f u n c t i o n ( l ) { r e t u r n _ . a l l ( l , f u n c t i o n ( n ) { r e t u r n n ! = 3 ; } ) ; } ) ) ; E r r o r : F a i l e d a f t e r 2 7 t e s t s a n d 4 s h r i n k s . r n g S t a t e : 8 8 3 6 1 e d 7 8 2 a 9 c 0 b 4 5 f ; C o u n t e r e x a m p l e : [ 3 ] ;
/ / a s s e r t i n g t h e f u n c t i o n ' s r a n g e f ( x ) = = = f ( f ( x ) ) ; / / i d e m p o t e n c e a ( x ) = = = b ( x ) ; / / r e g r e s s i o n t e s t f o r r e i m p l e m e n t a t i o n n e w C 1 ( ) . f ( x ) = = = n e w C 2 ( ) . f ( x ) ; / / c l o s e l y r e l a t e d n e w C ( c 1 ) . f ( x ) = = = n e w C ( c 2 ) . f ( x ) ; / / c l o s e l y r e l a t e d m a x ( a , b ) = = = m a x ( b , a ) ) ; / / c o m m u t a t i v i t y z o o m ( z o o m ( i m g , n ) , - n ) = = = i m g ) ; / / i n v e r t i b i l i t y
check properties involving function valued variables, then we must be able to generate arbitrary functions. Rather surprisingly, we are able to do so.” p . a s s e r t ( p . f o r a l l ( p . a r r a y ( ) , p . f n ( ) , p . v a l u e ( ) , f u n c t i o n ( a , f , c ) { r e t u r n _ . m a p ( a , f , c ) . l e n g t h = = = a . l e n g t h ; } ) ) ;
style, but should work on testing OO code not a replacement for TDD using examples but can be used to help finding missed edge cases best for unit testing (because of high number of test cases) also good for verifying assumptions on 3dparty code
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![[horribly predictable quote] “Testing shows the presence, not the absence](https://files.speakerdeck.com/presentations/648cc5e00cf60132e45c16030f01e0df/slide_1.jpg){kind=link}
