Suppose M decides a language L Sigma.
  Let w_1, w_2, ... be all strings over Sigma, in canonical order.

  The following program enumerates L in canonical order.

  for all i from 0 to infinity
    If M accepts w_i$ // M cannot run forever
      write w_i

  By the Church-Turing thesis, some Turing machine decides L.

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  Suppose M enumerates a language L over Sigma in canonical order.
  Let w_1, w_2, ... be the enumeration of L in canonical order.


  If L is finite, L is trivially recursive.

  If L is infinite, the following program decides L.

  Read a string w in Sigma*
  for all i from 1 to infinity
    if w = w_i
      write "Yes"
  
  By the Church-Turing thesis, some Turing machine enumerates L in canonical
  order.