Minimum specification for Haskell library type classes?

Question

The Haskell prelude and Standard Library define a number of useful type classes.

Is there a page somewhere that lists the minimum complete definition for all these classes?

Answer 1

This information can be found scattered around the Haskell language report as well as the GHC documentation, but in the interest of having an overview, I'm starting a CW answer for this.

Comparison

• Eq: == or /=.
• Ord: compare or <=.

Numbers

• Num: All except either - or negate.
• Real: toRational.
• Integral: quotRem and toInteger.
• Bits: .&., .|., xor, complement, either shift or both shiftL and shiftR, either rotate or both rotateL and rotateR, bitSize and isSigned.
• Fractional: fromRational and either / or recip.
• Floating: pi, exp, log, sin, cos, sinh, cosh, asin, acos, atan, asinh, acosh and atanh.
• RealFrac: properFraction.
• RealFloat: All except exponent, significand, scaleFloat and atan2.

Functors

• Functor: fmap.
• Applicative: pure and <*>.
• Monad: >>= and return.
• MonadPlus: mplus and mzero.
• MonadFix: mfix.
• Foldable: foldMap or foldr.
• Traversable: traverse or sequenceA.

Arrows

• Category: . and id.
• Arrow: arr and first.
• ArrowZero: zeroArrow.
• ArrowPlus: <+>.
• ArrowChoice: left.
• ArrowApply: app.
• ArrowLoop: loop.

Serialization

• Read: readsPrec (or, for GHC only, readPrec).
• Show: show or showsPrec.

Misc

• Enum: toEnum and fromEnum.
• Bounded: Both minBound and maxBound.
• Ix: range, index, inRange.
• Monoid: mempty and mappend.

Answer 2

The section in the Haskell Report about standard classes describes what you need to implement for each type class.