Aiming at the possible fixed parameters and computational side- effects of the recursive operations oninductive data types,the authors define the strong monadic inductive data type and presents proofs of strong monadicinitiality by combining the notions of monads in functional programming languages with the adjoint in the categorytheory.Furthermore,we propose a kind of recursion with fixed parameters and computational side- effects.It isproved that this kind of recursion can provide better abstraction and encapsulation in comparison with normal recur-sions.Meanwhile,we discuss the corresponding categorical properties and calculation laws.