#15078: base: Customary type class laws (e.g. for Eq) and non-abiding instances (e.g. Float) should be documented -------------------------------------+------------------------------------- Reporter: sjakobi | Owner: Azel Type: feature request | Status: new Priority: normal | Milestone: 8.8.1 Component: Core Libraries | Version: 8.4.2 Resolution: | Keywords: newcomer Operating System: Unknown/Multiple | Architecture: | Unknown/Multiple Type of failure: None/Unknown | Test Case: Blocked By: | Blocking: Related Tickets: | Differential Rev(s): Phab:D4736 Wiki Page: | -------------------------------------+------------------------------------- Comment (by jpath): For `Num` I would expect `fromIntegral` to be a ring homomorphism. φ is a ring homomorphism if: 1. φ(x + y) = φ(x) + φ(y) 2. φ(x · y) = φ(x) · φ(y) 3. φ(1) = 1 We get φ(0) = 0, because φ(0) = φ(1 - 1) = φ(1) - φ(1) = 0, but we do need the “`fromIntegral 0` is addivite identity” law, to state the ring laws in the first place. In the case of dom φ = ℤ, we can also drop the second law, as φ is already uniquely defined by laws 1 and 3. So I would like to add `fromIntegral (a + b) = fromIntegral a + fromIntegral b` and maybe `fromIntegral (a * b) = fromIntegral a * fromIntegral b` even though it is redundant. Similarly I would like `fromRational` to be a ring homomorphism, again law 2 would be redundant, but we may still want it anyway. Note that these laws do not require any additional structure, as ℤ is the initial object in the category of rings and ℚ the initial object in the category of fields, so for every ring R a unique ring homomorphism φ: ℤ → R exists and for every field F a unique field homomorphism ℚ → F exists. The laws just ask that `fromIntegral` and `fromRational` are indeed these homomorphisms. Also `a / b = a * recip b`. -- Ticket URL: http://ghc.haskell.org/trac/ghc/ticket/15078#comment:23 GHC http://www.haskell.org/ghc/ The Glasgow Haskell Compiler