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Re: Types

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Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote or quoted:
>On 19/04/2026 19:51, Stefan Ram wrote:
>>-- Both types have the exact same "extension" (two Integers)
>>data Apple  = Apple Int Int
>>data Orange = Orange Int Int
>Why do you call the two integers the "extension" ?

  In set theory, two sets are considered equal if and only if
  they contain the same elements, regardless of how they were
  defined or named.

  This concept is also called "extensional equality", because
  a set is defined by the elements to which it /extends/.

  Even though Apple and Orange have different names and may have
  different conceptual purposes in the mind of the programmer,
  both have the same set of possible values (a pair of integers).

  As the author of that book claimed that types /are/ sets he must
  then accept that set theoretic equality applies to these sets.

  In set theory, two sets that both contain all pairs of integers
  and nothing else are equal, even if they were introduced using
  two different names and two different descriptions.

  So when that comment said, "both types have the exact same
  'extension'", it meant to remind the reader of the fact that if
  the types are deemed to be sets, they should be deemed to be equal.

  But Haskell does /not/ deem them to be equal, which shows that
  Haskell types are /not/ mathematical sets.

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Types ram@zedat.fu-berlin.de (Stefan Ram) - 2026-04-19 18:51 +0000
  Re: Types Jonathan Lamothe <jonathan@jlamothe.net> - 2026-04-19 17:17 -0400
    Re: Types ram@zedat.fu-berlin.de (Stefan Ram) - 2026-04-20 10:32 +0000
      Re: Types Paul Rubin <no.email@nospam.invalid> - 2026-04-20 11:19 -0700
        Re: Types ram@zedat.fu-berlin.de (Stefan Ram) - 2026-04-20 19:32 +0000
          Re: Types Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-11 22:48 +0100
      Re: Types 8128 <lambda@dr.com> - 2026-05-30 21:50 +0000
  Re: Types Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-11 22:44 +0100
    Re: Types ram@zedat.fu-berlin.de (Stefan Ram) - 2026-06-11 23:05 +0000
      Re: Types Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-12 13:42 +0100
        Re: Types ram@zedat.fu-berlin.de (Stefan Ram) - 2026-06-12 13:17 +0000
          Re: Types Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-12 15:17 +0100

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