all2

Lib.all2 : ('a -> 'b -> bool) -> 'a list -> 'b list -> bool

Tests whether a predicate holds pairwise throughout two lists.

An invocation

   all2 P [x1,...,xn] [y1,...,yn]

equals

   P x1 y1 andalso .... andalso P xn yn

Also, all2 P [] [] yields true.

Failure

If P x0,...,P x(j-1) all evaluate to true and P xj raises an exception e, then

   all2 P [x0,...,x(j-1),xj,...,xn]

raises e. An invocation all2 P l1 l2 will also raise an exception if the length of l1 is not equal to the length of l2.

Example

- all2 equal [1,2,3] [1,2,3];
> val it = true : bool

- all2 equal [1,2,3] [1,2,3,4] handle e => Raise e;

Exception raised at Lib.all2:
different length lists
! Uncaught exception:
! HOL_ERR

- all2 (fn _ => fn _ => raise Fail "") [] [];
> val it = true : bool

- all2 (fn _ => fn _ => raise Fail "") [1] [1];
! Uncaught exception:
! Fail  ""

See also

Lib.all