Fully parenthesize the following terms

a$.x.y.x$

b$.x$

c$.xx.$

Drop as many parentheses as possible from the following fully parenthesized terms.

The resulting term should have the same structure as the original one, but with as few

parentheses as possible.

a$.((x.())x)$

b$.((y*y)(x*(x())))$

c$.((x*(y*((xy)x)))z)$

Rename variables in the following terms so that global variables $($i$.$e$.,$ ones free in the

term$)$ have different names from local ones $($i$.$e$.,$ ones introduced by $),$ and so that

different uses of $$ introduce variables with different names. This should be done

without changing the names of global variables. For example, $xx.x$ could be renames

to $xy.y,$ but not $yx.x($because we are not allowing global variables to be renamed$).$

a$.xyx.y.z$

b$.(x.)(x.)$

c$.(x,x)y(x,xy)$

Using any reduction strategies, evaluate the provided lambda expression, and

demonstrate each step of the evaluation process.

a$.$ a$.$ b$.((c.(c**3))(a+b))52$

b$.$ m$.((x.(2**6x))(9m+8w))910$

c$.(x.y*yx)(5+2)(x.x+1)$

List all the $-$redexs $($i$.$e$.,$ terms of the form $\{$:$(x.t)t^{\text{'}})$ in each of the following terms:

a$.(x.(x.x)x)y.y$

b$.(x.(y.y)z.z)(x.x)(y.y)$

c$.(x.y.y)((x.x)(y.y))$