What do we call this (new?) higher-order function?

Question

I am trying to name what I think is a new idea for a higher-order function. To the important part, here is the code in Python and Haskell to demonstrate the concept, which will

Answer 1

Nice idiom! I just needed to use this in Perl to determine the time between sequential events. Here's what I ended up with.

sub pinch(&@) {
  my ( $f, @list ) = @_;
  no strict "refs";

  use vars qw( $a $b );

  my $caller = caller;
  local( *{$caller . "::a"} ) = \my $a;
  local( *{$caller . "::b"} ) = \my $b;

  my @res;
  for ( my $i = 0; $i < @list - 1; ++$i ) {
    $a = $list[$i];
    $b = $list[$i + 1];
    push( @res, $f->() );
  }
  wantarray ? @res : \@res;
}

print join( ",", pinch { $b - $a } qw( 1 2 3 4 5 6 7 ) ), $/;
# ==> 1,1,1,1,1,1

The implementation could probably be prettier if I'd made it dependent on List::Util, but... meh!