6 ms·

Interesting. The bug in the proof is in the assumption that ints contain any integer and addition operates the same in normal mathematics, when in fact they're

by efaref 11y ago

Interesting. The bug in the proof is in the assumption that ints contain any integer and addition operates the same in normal mathematics, when in fact they're the set of values in [INT_MIN, INT_MAX] and addition has overflow behaviour. Arguably addition (or any operation) that overflows with signed integers ought to cause some kind of SignedIntegerOverflow exception. If you want to do modulo mathematics in the set of [0, 2^n) then you should explictly use unsigned integers, which are defined to work that way.

pjc50 11y ago
I've been seriously considering doing a mini programming language where you can type-decorate numbers with exactly what behaviour you want and what their range is. So you could have "integer, range [a-b), exception on overflow" or "integer, 32-bit, unsigned, wrap" or "integer, 8-bit, signed, saturates" (the latter is useful in codecs and often available in assembly).
- revelation 11y ago
  I think they call that Ada. (not sure on the overflow behavior, but ranges are in)
  - AndyMcConachie 11y ago
    You might also argue that SQL shares some of these characteristics.
    - creshal 11y ago
      It does. It also makes for a rather… clumsy general-purpose language.
  - vidarh 11y ago
    Pascal also has ranges. "VAR foo : 42...56;" Don't remember how it handled overflow.
  - reacweb 11y ago
    Yes, Ada is a marvellous language. The exception is not named overflow, but constraint error. When used correctly, its typing system is very effective to avoid mistakes. The problem is that Ada types can become very annoying in bad code like the one produced by people with a very weak knowledge of the language. It is really too sad this language is almost not teached anymore in school.
  - david-given 11y ago
    Ha ha. I'd been reading HN on my phone, saw the parent comment, thought 'I should write a post about Ada', and when I got back to my computer, saw this... Yes, ranges work. They (and ordinary integers) throw exceptions on overflow: type NonoverflowingByte is integer range 0..255; If you want modulus arithmetic, you specify it: type OverflowingByte is mod 256; Modulus types seem to be always unsigned and are always 0-based. Anyone know different? For saturating arithmetic, there doesn't seem to be built-in language support. (There isn't even a standard library package. That seems to be a bit of an omission. Isn't saturating arithmetic common in the kind of real-time environment where Ada is used?) Ada so totally deserves to be better known.
    - pjc50 11y ago
      > Ada so totally deserves to be better known I do wonder why it isn't. It's probably handicapped by its history: once people have written off a language they'll never look at it again, despite improvements to fix the very problems they fled. As an Ada advocate, what does it do badly? String processing? Networking?
      - david-given 11y ago
        It's got a lot of historic warts. e.g. the OO system is a retrofit with invisible syntax: functions defined immediately after the type representing the object are methods, but you can't interleave them with other statements. It desperately needs an explicit `class...end` structure. The OO model is kinda weird, too, although once you've beaten your head against it it makes sense. Another wart is that you can only define an expression function in a module specification and not in a module body. Huh? Likewise, you can only define pre- or post-conditions on public data, so you can't have a module assert on its private state; you must export the state first. String processing is both really nice and a pain. Built-in strings are fixed size, but the `array<>` magic means you do string processing using functional style without needing to explicitly size anything. The string libraries are a bit of a mess, with `Wide_String` and `Wide_Wide_String`, because they made the same mistake as Java and Windows about UCS-2 vs Unicode. The standard library is mostly really cool, but it makes the same mistake C++ does in that entries in collections are always initialised by copying, so you can't have collections of non-copyable objects. I forget the details but I think the last time I tried to do collections of pointers I couldn't make it work properly. Ada's generics are awesome. Nested functions that work properly are awesome. The compilation time is awesome. Access semantics that prevent you leaking pointers to inner stack frames are awesome. in-out parameters are awesome (they mostly replace pointers). Being unable to pass a nested function to a procedure as a callback parameter is less awesome; the access semantics forbid it. To my mind, though, the biggest showstopper in Ada is a technically fairly trivial thing: it's case insensitive. This means that any programmer used to case sensitive languages, which is basically any programmer, will have to drastically revamp their coding style to work with Ada, because none of the usual conventions about separating locals from globals by capitalisation work any more. It also makes Ada code look ugly to the untrained eye. It's hard to convert people when the first thing they say when looking at code is 'ugh'.
- andy_ppp 11y ago
  While not integer/number specific I like the idea of Guards in Elixir: def sum(a, b) when is_integer(a) and is_integer(b) do a + b end def sum(a, b) when is_list(a) and is_list(b) do a ++ b end def sum(a, b) when is_binary(a) and is_binary(b) do a <> b end sum 1, 2 #=> 3 sum [1], [2] #=> [1,2] sum "a", "b" #=> "ab"
  - lifeisstillgood 11y ago
    That's it - going to set aside some time for getting Elixr on my bare competence skill set. I love that
  - arethuza 11y ago
    That's pretty nice - like CLOS multiple dispatch with arbitrary predicates rather than types. Are there any restriction on what the code in the guards can do?
    - lectrick 11y ago
      Yes. But the guard code are just macros, so... ;) But I do believe that Erlang underneath does have actual limits.
- CyberDildonics 11y ago
  Look at Ada first and see if there is anything missing.

by efaref 11y ago

pjc50 11y ago

I've been seriously considering doing a mini programming language where you can type-decorate numbers with exactly what behaviour you want and what their range is. So you could have "integer, range [a-b), exception on overflow" or "integer, 32-bit, unsigned, wrap" or "integer, 8-bit, signed, saturates" (the latter is useful in codecs and often available in assembly).

revelation 11y ago
I think they call that Ada. (not sure on the overflow behavior, but ranges are in)
- AndyMcConachie 11y ago
  You might also argue that SQL shares some of these characteristics.
  - creshal 11y ago
    It does. It also makes for a rather… clumsy general-purpose language.
- vidarh 11y ago
  Pascal also has ranges. "VAR foo : 42...56;" Don't remember how it handled overflow.
- reacweb 11y ago
  Yes, Ada is a marvellous language. The exception is not named overflow, but constraint error. When used correctly, its typing system is very effective to avoid mistakes. The problem is that Ada types can become very annoying in bad code like the one produced by people with a very weak knowledge of the language. It is really too sad this language is almost not teached anymore in school.
- david-given 11y ago
  Ha ha. I'd been reading HN on my phone, saw the parent comment, thought 'I should write a post about Ada', and when I got back to my computer, saw this... Yes, ranges work. They (and ordinary integers) throw exceptions on overflow: type NonoverflowingByte is integer range 0..255; If you want modulus arithmetic, you specify it: type OverflowingByte is mod 256; Modulus types seem to be always unsigned and are always 0-based. Anyone know different? For saturating arithmetic, there doesn't seem to be built-in language support. (There isn't even a standard library package. That seems to be a bit of an omission. Isn't saturating arithmetic common in the kind of real-time environment where Ada is used?) Ada so totally deserves to be better known.
  - pjc50 11y ago
    > Ada so totally deserves to be better known I do wonder why it isn't. It's probably handicapped by its history: once people have written off a language they'll never look at it again, despite improvements to fix the very problems they fled. As an Ada advocate, what does it do badly? String processing? Networking?
    - david-given 11y ago
      It's got a lot of historic warts. e.g. the OO system is a retrofit with invisible syntax: functions defined immediately after the type representing the object are methods, but you can't interleave them with other statements. It desperately needs an explicit `class...end` structure. The OO model is kinda weird, too, although once you've beaten your head against it it makes sense. Another wart is that you can only define an expression function in a module specification and not in a module body. Huh? Likewise, you can only define pre- or post-conditions on public data, so you can't have a module assert on its private state; you must export the state first. String processing is both really nice and a pain. Built-in strings are fixed size, but the `array<>` magic means you do string processing using functional style without needing to explicitly size anything. The string libraries are a bit of a mess, with `Wide_String` and `Wide_Wide_String`, because they made the same mistake as Java and Windows about UCS-2 vs Unicode. The standard library is mostly really cool, but it makes the same mistake C++ does in that entries in collections are always initialised by copying, so you can't have collections of non-copyable objects. I forget the details but I think the last time I tried to do collections of pointers I couldn't make it work properly. Ada's generics are awesome. Nested functions that work properly are awesome. The compilation time is awesome. Access semantics that prevent you leaking pointers to inner stack frames are awesome. in-out parameters are awesome (they mostly replace pointers). Being unable to pass a nested function to a procedure as a callback parameter is less awesome; the access semantics forbid it. To my mind, though, the biggest showstopper in Ada is a technically fairly trivial thing: it's case insensitive. This means that any programmer used to case sensitive languages, which is basically any programmer, will have to drastically revamp their coding style to work with Ada, because none of the usual conventions about separating locals from globals by capitalisation work any more. It also makes Ada code look ugly to the untrained eye. It's hard to convert people when the first thing they say when looking at code is 'ugh'.
andy_ppp 11y ago
While not integer/number specific I like the idea of Guards in Elixir: def sum(a, b) when is_integer(a) and is_integer(b) do a + b end def sum(a, b) when is_list(a) and is_list(b) do a ++ b end def sum(a, b) when is_binary(a) and is_binary(b) do a <> b end sum 1, 2 #=> 3 sum [1], [2] #=> [1,2] sum "a", "b" #=> "ab"
- lifeisstillgood 11y ago
  That's it - going to set aside some time for getting Elixr on my bare competence skill set. I love that
- arethuza 11y ago
  That's pretty nice - like CLOS multiple dispatch with arbitrary predicates rather than types. Are there any restriction on what the code in the guards can do?
  - lectrick 11y ago
    Yes. But the guard code are just macros, so... ;) But I do believe that Erlang underneath does have actual limits.
CyberDildonics 11y ago
Look at Ada first and see if there is anything missing.