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  1. (.) f g = \x -> f (g x)
  2.  
  3. Function:
  4. h = (f .) . g
  5. Substitute outer:
  6. h = \x -> (f .) (g x)
  7. Substitute section:
  8. h = \x -> (\y -> f . y) (g x)
  9. Substitute inner:
  10. h = \x -> (\y -> \z -> f (y z)) (g x)
  11. Apply (g x) to the \y lambda:
  12. h = \x -> \z -> f ((g x) z)
  13. Float z to the outer lambda:
  14. h = \x z -> f ((g x) z)
  15. Eliminate superfluous parens:
  16. h = \x z -> f (g x z)
  17. Float lambda arguments out:
  18. h x z = f (g x z)
  19.  
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