整数和整数有什么区别？

Question

In Haskell, what is the difference between an Int and an Integer ? Where is the answer documented?

Answer 1

"Integer" is an arbitrary precision type: it will hold any number no matter how big, up to the limit of your machine's memory…. This means you never have arithmetic overflows. On the other hand it also means your arithmetic is relatively slow. Lisp users may recognise the "bignum" type here.

"Int" is the more common 32 or 64 bit integer. Implementations vary, although it is guaranteed to be at least 30 bits.

Source: The Haskell Wikibook . Also, you may find the Numbers section of A Gentle Introduction to Haskell useful.

Answer 2

Int is Bounded , which means that you can use minBound and maxBound to find out the limits, which are implementation-dependent but guaranteed to hold at least [-2 ²⁹ .. 2 ²⁹ -1].

For example:

Prelude> (minBound, maxBound) :: (Int, Int)
(-9223372036854775808,9223372036854775807)

However, Integer is arbitrary precision, and not Bounded .

Prelude> (minBound, maxBound) :: (Integer, Integer)

<interactive>:3:2:
    No instance for (Bounded Integer) arising from a use of `minBound'
    Possible fix: add an instance declaration for (Bounded Integer)
    In the expression: minBound
    In the expression: (minBound, maxBound) :: (Integer, Integer)
    In an equation for `it':
        it = (minBound, maxBound) :: (Integer, Integer)

Answer 3

Int is the type of machine integers, with guaranteed range at least -2 ²⁹ to 2 ²⁹ - 1, while Integer is arbitrary precision integers, with range as large as you have memory for.

https://mail.haskell.org/pipermail/haskell-cafe/2005-May/009906.html

Answer 4

Int is the C int, which means its values range from -2147483647 to 2147483647, while an Integer range from the whole Z set, that means, it can be arbitrarily large.

$ ghci
Prelude> (12345678901234567890 :: Integer, 12345678901234567890 :: Int)
(12345678901234567890,-350287150)

Notice the value of the Int literal.

Answer 5

The Prelude defines only the most basic numeric types: fixed sized integers (Int), arbitrary precision integers (Integer), ...

...

The finite-precision integer type Int covers at least the range [ - 2^29, 2^29 - 1].

from the Haskell report: http://www.haskell.org/onlinereport/basic.html#numbers

Answer 6

An Integer is implemented as an Int# until it gets larger than the maximum value an Int# can store. At that point, it's a GMP number.

Answer 7

Integer allows for more aggressive optimizations because it is not as constrained by undefined behavior as a result of overflows.

ie, the compiler must assume the expression as written won't ever experience undefined behavior, and that any potential optimizations the compiler introduces won't also introduce new undefined behavior.

or another way

the expression a - (b - c) is algebraically equivalent to (a + c) - b but the compiler can not do that rearrangement because it is possible that the intermediate value a + c will overflow with inputs which would not cause an overflow in the original.