Mathematical Techniques for Computer Science (COMP11120)
Class notes
Lecture Notes on Lists (COMP11120)
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Course
Mathematical Techniques for Computer Science (COMP11120)
Institution
The University Of Manchester (UOM)
Master the fundamentals of lists with these comprehensive lecture notes for COMP11120. Covering essential topics such as list operations, properties, and various traversal techniques, these notes provide clear explanations and practical examples to help you understand and utilize lists effectively....
= 1 + 2 + 1 + 0 be sum
Example : ForI t given by base case [l + 11 = 1
=
4 Step case (5 : 1) H = 5 : ((11 ()
Show that for all Le Lists (+ [T =
,
[J
So is unit for it
Example Define : a operation rev : Lists >
Lists that reverses a list.
Proof by induction :
L
L
base rev[] = [] base case [J + []
=
[]
case
Step case rev(s : 1) = revL #ISI Step case (5 : (15) =
5 :
((it)) #
base Case !
=
S
: step case
Example : Show summer) = sum for all Le Lists
You may use sum (1H1') =
Suml + suml Example : Show forthat all 1, 11E Lists IN
,
sum((H(1) = sum) + Sum(
Proof by induction :
base case Sumrev[] =
SumI] be nev Proof by induction :
Step case sum rev (5 : 1) =
Sum(rov1H [s]) Sc rev base case Sum([]111) = Sum I' be concat
("
=
Sum(rev() + sum(s : []) ind . hyp
.
= O + Sum
= sumY + 5 + sumI]
Sc Sum = sum[I + sumI' be sum
Suml
=
+ 5 + 0 be Sum
=
S + sum Step case Sum(15 : 1) H() =
sum(s : (1 + 1)) Sc concert
= Sum(5 : () = S + Sum(( + 1) sc sum
= S + sum) + suml' ind .
hyp .
= Sum (s : 1) + suml" sc Sum
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