SuperPAL: Data Types & Anonymous Functions

Data Types & Anonymous Functions

Question 1

What is an abstract data type? Give two examples.

Question 2

Write a recursive data type for a list. Is this data type primitive recursive?

Question 3

Write a recursive data type for a trinary tree. That is, each node in the tree has three branches.

Question 4

Consider the following data type for temperature:

data TemperatureUnit = Kelvin | Celsius | Faren... etc..
data Temperature a = Temperature a TemperatureUnit

a) Check if a given temperature is in units of Farenheit.

b) Write a function to convert a given temperature into Kelvin. (Hint: K = C + 273, F=9/5 C + 32)

Question 5

Using anonymous functions, write the following functions:

a) Add 1 to every element of a list of integers.

b) Filter our all odd elements of a list.

c) Swap the order of the arguments of a function with two inputs.

Challenge Question

Data Types

Recall the data type for a set: Set a = Empty | Element a (Set a)

a) Write a function which calculates the intersection of two sets.

b) Write a function which finds the compliment of two sets.

Anonymous Functions

Suppose you have a list of functions of type a -> a. Using an anonymous function, can you figure out a way to generate a new function of type a->a which applies all the functions in the list together?

For example: funcFold [f,g,h,i,j,k] >> f ( g ( h ( i ( j ( k( a ))))).