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.