api.hs

-- I am designing an API. This is not real haskell code, but it is accepted by my tool.

-- I can define type sigs as usual
query :: Query a -> System -> [a]

-- I can also write laws that the eventual implementation must satisfy.
-- lines that begin with a string are laws.
-- notice that these are _not even_ haskell definitions, because the LHS is not a pattern.
"1" queryEntity ix (refine (const False) q) s = Nothing
"2" queryEntity ix (refine (const True) q) = queryEntity ix q
"3" queryEntity ix (mapQ f q) = fmap f . queryEntity ix q

-- the tool will gather these laws, and construct the following:

properties :: [Property]
properties =
  [ (queryEntity ix (refine (const False) q) s) =-= (Nothing)
  , (queryEntity ix (refine (const True) q)) =-= (queryEntity ix q)
  , (queryEntity ix (mapQ f q)) =-= (fmap f . queryEntity ix q)
  ]
  
-- (=-=) :: EqProp a => a -> a -> Property
--
-- because (=-=) consumes polymorphic inputs, and because `queryEntity` _produces_ polymorphic 
-- outputs, these expressions are ambiguous in `a`. But it can't possibly matter, so defaulting 
-- is a very reasonable thing to do