Assignment $5-$ Functional Programming

Lambda Calculus

Apply beta reduction to the following expressions. Solve it on paper and upload a scanned version.

a$)$ y$)(x*x$ a$)$

b$)(z*z)(z*z,z)(z*zy)$

c$)(x*y*x$ y y$)(a*a$ b

d$)$ y y$)(y*y$

e$)$ x$)$ x$)z$

f$)$ y$)z$

g$)$ x$)(y*y)$

h$)(((x*y*(xy))(y*y)),w)$

i$)$ y y$)(x*x$ x x$))$

Prove the following using lambda calculus encodings.

Refer to the paper I have uploaded on Google Classroom for the encodings.

Solve it on paper and upload a scanned version.

a$)$ or false true $=$ true

b$)+22=4$

c$)$ succ$2=3$

Use a recursive definition to define a function that adds up the first n natural numbers. Refer to Recursion section $($section $4)$ in the paper I have provided. Encode the Y combinator in Python and then find the sum. For the most part, you have to read the paper and write Python code verbatim, just make sure your solution works. Upload a Python file.

Haskell Programming

Solve the following exercises in Haskell and upload only $.$hs files.

Exercises $1-5$ are supposed to be solved after Week $11.$

Exercises $6-14$ are supposed to be solved after Week $12.$

Exercise $14$ and $15$ are supposed to be solved after Week $13.$