Formalizing non-termination of recursive programs

Reinhard Kahle, Thomas Studer
2001 The Journal of Logic and Algebraic Programming  
In applicative theories the recursion theorem provides a term rec which solves recursive equations. However, it is not provable that a solution obtained by rec is minimal. In the present paper we introduce an applicative theory in which it is possible to define a least fixed point operator. Still, our theory has a standard recursion theoretic interpretation.
doi:10.1016/s1567-8326(01)00006-6 fatcat:3hzhugi4zjeohp6vmby5jgfdnq