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:

< variable-name , memory-address(or location) >

2- Memory ()- Each pair: <location , value>- 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 tt’ 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