In a blender or food processor, puree papaya.
Add lime juice, cream, half and half, and sugar and whirl until blended.
Pour puree into a bowl and cover with plastic wrap.
Freeze until mixture hardens around edge With an electric mixer, beat mixture until smooth.
Place plastic wrap directly on mixture and return to freezer until firm.
One hour before serving, beat or whirl again until soft.
Return to freezer until firm.