I tried to understand why the following (with map sentence) gives an error.

The not-very-helpful answer is: because you've created an ambiguous state in the parser.

It can be avoided by:

• Omitting the space: print @a[ map $_-1, grep { $_ > 0 and $_ <= 1 } map { $_ + 1 } -1 .. 1 ];
• Or using a unary plus prefix: print @a[ map +$_ -1, grep { $_ > 0 and $_ <= 1 } map { $_ + 1 } -1 .. 1 ];
• Or (as you've identified) using the block form: print @a[ map{ $_ -1 } grep { $_ > 0 and $_ <= 1 } map { $_ + 1 } -1 .. 1 ];

My guess is that because the parser fails to find a comma following the first argument ($_) to map, it attempts to treat that first argument as a block, and gets confused.

Under 5.10 I get: panic: ck_grep at ...; but that panic seems to have been replaced with the error message you get in later versions.