Memory hard function (MHF) is a family of functions that costs a significant amount of memory to evaluate. It is different from memory bound functions, the latter incurs cost by slowing down computation through memory latency. MHFs find their use as a form of proof-of-work.
Memory hard measure
There are different ways to measure the memory hardness of a function. A commonly seen measure is Cumulative Memory Complexity (CMC). In a parallel model, CMC measures memory hardness by summing up all the inputs on each step.
Another popular measure is integrating memory against physical time.
Yet another measure is the memory bandwidth consumption on a memory bus.