PURPOSE: To obtain a memory management system where the stack and local memory areas can be managed with high availability of the memories for a processor of a stack arithmetic system.

CONSTITUTION: A stack memory 40 includes the arithmetic stack areas 41 and the local variable areas 42 which are alternately arrayed. The base addresses of both areas 41 and 42 are shown by the 1st and 2nd stack base addresses 51 and 52 respectively. The size of the memory 40 used by a program under execution is calculated from an arithmetic stack pointer 61 and local variable number 62. When an interruption is produced, both addresses 51 and 52 are updated based on these addresses 51 and 52 and the calculated size of the memory 40. Then the base address of the memory 40 used by an interruption processing routine is decided.