Semantics of Arrays and Pointers By: M. Reza Heydarian Introduction Pointers Arrays Semantics of Arrays Semantics of Pointers

Introduction (Memory Management Overview) -Three Categories of Memory 1- Static Memory For values whose storage requirement:. Are known before runtime. Remain constant during running program 2- Run-time Stack - For dispatching active methods: Their local variables and parameter-argument linkages - Structure of stack is predictable and regular 3- Heap

Heap -Least structured of the three memory categories -Contain all other values that are dynamically allocated during run-time -Structure is far less predictable and regular -Becomes fragmented -Active memory blocks are not contiguous -Heap blocks are accessed indirectly using pointers (pointers are located in stack or heap)

Figure of Memory -addresses {0,…,n} called the program’s address space -h and n are initially defined at the beginning of run-time

Using two sets to manage Memory 1- Environment (  m ): - m is a method.-  m is set of pairs: 2- Memory (  ) -Each pair: -Non-allocate locations are marked unused -Allocated location without value are marked undefined -Use overriding union to change this set

An Example of Sets

Pointers -Memory address (reference) -Indirection in referencing a value or a collection of value -Bane of reliable software development -Programmer must restore heap blocks -Some language(e.g.Java) remove explicit pointers

Arrays -Ordered sequences of values with same type -May have any number of dimensions -Its memory is dynamically allocated -Share the same scope rules as simple variables -In different language may be:.allocated space in either static, stack, or heap area.different indexing (e.g. C,C++,Java all use 0-origin indexing).different way to locate element in memory (e.g. row major order)

A semantic view of Memory in definition of Array

Semantic of arrays -By Jay semantic function.one dimensional array.heap allocation strategies.are accessed by a pointer in the stack -Using two functions:.new: find a contiguous unused block.delete

new and delete functions

allocate function

deallocate function

Semantic of expression evaluation

Denotational semantics of Array Hoare’s view: Array values are functions (Assume values of elements are Nat. Type)

Denotational semantics of Array(cont’) A new semantic function: Some semantic equations: - Array Variables

Denotational semantics of Array(cont’) - Array Application - Array Assignment - Array Declaration

Semantics of Pointers -Basic operations on references (Pointers):. Allocation r = ref 5; |> r : Ref Nat. Dereferencing !r;|> 5 : Nat. Assignment r := 7;|> unit : Unit

Pointers and Aliasing r = s = r => s = 13

Pointers and Compound Types We can create references to any type. Including function. e.g. Array of numbers (use references to function). e.g. Type is: Ref (Nat  Nat)

Operational Semantics Typing Evaluation Store Typing

Typing

Evaluation Change relation from t  t’ to t|  t’|  ’ Where  and  ’ are the starting and ending states of the store

Set of values and terms

Rules

Rules (cont’)

Store Typing

References 1- Programming Languages: Principles and Paradigms Allen Tucker and Robert Noonan. 2- Types and Programming Languages Benjamin C. Pierce 3- Theory of Programming Languages John C. Reynolds