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Lab 1 Requirements

Lab 1 Requirements. Local operations (at least Heapify and Sift_Root_Down) provide specs—they don't need to be formal, but you must have appropriate parameter modes, requires, and ensures Heapify must be recursive and use the algorithm discussed in class

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Lab 1 Requirements

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  1. Lab 1 Requirements • Local operations (at least Heapify and Sift_Root_Down) • provide specs—they don't need to be formal, but you must have appropriate parameter modes, requires, and ensures • Heapify must be recursive and use the algorithm discussed in class • Follow the Resolve/C++ disciplinehttp://www.cse.ohio-state.edu/sce/now/321/labs/writeups/lab_grading_hints.html • Make sure you look at and implement the specs of Sorting_Machine_Kernel • Follow the convention and correspondence • Comment your code

  2. (We were not drunk when we made it up. Seriously!) A Day of Revelations • What’s the difference between implementing an extension and a kernel? • What are convention and correspondence? What are they for? Why do we bother? • What about the rule that kernel operations cannot call other kernel operations?

  3. Extension Usually layered over a kernel Does not access representation directly Kernel Defines representation Directly accesses representation Extension vs. Kernel Op_Ext Op_1 Op_2 Rep Op_3 Op_4 Kernel Extension

  4. The Correspondence • Consider the implementation of Sorting_Machine_Kernel with Heapsort • What’s the math model of Sorting_Machine? • What’s the representation? • What’s the math model of the representation?

  5. self.contents self.inserting Math Model of Sorting_Machine Sorting_Machine_Type is modeled by ( inserting: boolean contents: multiset of Item )

  6. self.inserting_rep self.queue self.array self.heap_size self.array.lb self.array.ub self.array.table Representation Math Model Rep is modeled by ( inserting_rep: boolean queue: string of Item array: ARRAY_MODEL heap_size: integer ) math subtype ARRAY_MODEL is ( lb: integer ub: integer table: INDEXED_TABLE ) constraint … math subtype INDEXED_TABLE is finite set of ( i: integer x: Item ) constraint …

  7. abstract state space ? (true, {1, 2, 3}) concrete state space (true, <2, 1, 3>, (1, 0, {}), 0) Correspondence Continued… Sorting_Machine_Type is modeled by ( inserting: boolean contents: multiset of Item ) Rep is modeled by ( inserting_rep: boolean queue: string of Item array: ARRAY_MODEL heap_size: integer )

  8. Correspondence Continued… • Given the Sorting_Machine m with value m = (true, {1, 2, 3}), what’s the corresponding value for the representation? How do you know? • Conversely, given the representation (true, <2, 1, 3>, (1, 0, {}), 0), what Sorting_Machine value does it represent? How do you know?

  9. Correspondence Continued… • The correspondence provides the mapping between the abstract value (the sorting machine) and the concrete value (the representation)

  10. Sorting_Machine with Heapsort: Correspondence self.inserting = self.inserting_rep and ifself.inserting thenself.contents = elements (self.queue) elsefor all x: Item (x is inself.contents iff there exists i: integer (self.array.lb <= i and i <= self.heap_size and (i,x) is inself.array.table))

  11. The Convention • What Sorting Machine is represented by • (true, <2, 1, 3>, (1, 0, {}), 5) • (true, <2, 1, 3>, (1, 2, {(1, 7), (2, 8)}), 3) • (false, <>, (1, 2, {(1, 7), (2, 8)}), 3)? • Is the following a correct implementation of Size? What would you need to know to answer this question? { return self[heap_size]; }

  12. Convention Continued… • The convention states any implementation-wide assumptions the implementer makes • It restricts the space of possible representation values • It allows us to reason about the correctness of each operation independently of the others

  13. abstract state space (true, {1, 2, 3}) correspondence convention concrete state space (true, <2, 1, 3>, (1, 0, {}), 0) (true, <2, 1, 3>, (1, 0, {}), 5) Convention Continued… Sorting_Machine_Type is modeled by ( inserting: boolean contents: multiset of Item ) Rep is modeled by ( inserting_rep: boolean queue: string of Item array: ARRAY_MODEL heap_size: integer )

  14. Sorting_Machine with Heapsort: Convention if self.inserting_rep then self.heap_size = 0 and self.array = (1, 0, empty_set) else self.array.lb = 1 and 0 <= self.heap_size and self.heap_size <= self.array.ub and SUB_TREE_IS_ORDERED ( self.array, 1, self.heap_size) and self.queue = empty_string

  15. Convention: One More Thing • In implementing a kernel component, the implementer assumes that the convention holds at the beginning of each kernel operation • It is the responsibility of the implementer to ensure that the convention holds at the end of each kernel operation

  16. Convention Continued… • What happens if in the middle of a kernel operation (where the convention may not hold) we call another kernel operation?

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