Lecture Notes on Part II of Fundamentals of Computation (COMP11212)
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Course
Fundamentals of Computation (COMP11212)
Institution
The University Of Manchester (UOM)
Advance your understanding of computation with these in-depth lecture notes on Part II of Fundamentals of Computation (COMP11212). These notes cover: The While Programming Language, Coding and Counting Programs, Complexity and Asymptotic Analysis, and. Correctness
These lecture notes provide a s...
The while programming language, coding and counting programs, complexity and asymptomatic analysis, and correctness
Subjects
coding
big oh
notation
complexity
computability
correctness
while programming language
Written for
The University of Manchester (UOM)
Unknown
Fundamentals of Computation (COMP11212)
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The While Programming Language
he Three Cs of
-
Computer Science What is a computer ?
1. Does
program Pr and Pa that
a both compute a
function ,
f
Complexity A thing that compute...
which one is better ?
.
2 Does Correctness
a
program p correctly compute a
function fu
.
3 What functions can we compute ? i e
.
. are there functions that Computability
cannot be computed by any program ?
Do we need a
computer for Computation ?
No !
The While
Programming Language
Semantics What a
Meaning of a
program what function it
computes
:
program means
Define what it means to interpret execute programs Operational
Syntax : The
form that programs are allowed to take We
focus on these
Define a
program by what it provably does Axiomatic
All languages have will defined
a
syntax
Transform other metalanguage Denotational
Very few have a
formal semantics programs
into some
Syntax given as a
grammar Semantics of the Language
.
5 v := alskip)Seise if then Sy else Se while b do s We need : Weintroduce a relation - on
programs and states :
b : true false an = as an Ea2 it b, "be
·
Represent current values of variables (State
a : In a, +as a, -de a, a2
·
Evaluate arithmetic and logical expressions Si G
A
↓ Sid
·
program state
·
Show how program statements transform state
, [iffetiff] b is true
,
then use iffet b is false , then use iffff [while]
if two then [J] *
else [J) While (y < 1) do (y : y + 2) [y Y
1 else
~
,
z := v : = 2
,
if xx then X := 1 v : = 2 = + 2]
10
,
I
So
,
9b Si Sa 9b Si
WE While (y < 1) do (y : =
y + 2)
S2
-
↓ (v : = 1
, []Y (iftt) ↓ [v : = 2, [JY lifff) ↓ (if (y <1) than (4 :=
y +2
; W) also ship [y
,
+
2]) [while]
Rewrite ! Alternative !
[x : = 1
,
[3)][X +
1] X(x := x +1
,
[x +
1]) [ass]
[comp2]
[ : = 1 ; k : = x +1
, [])X(k := x + 1 ,
[x +
1]) ↓ [x +
2] [ass]
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