This assignment has four problems, each worth 25% of the grade. There is a bonus problem at the end, worth an additional 10% of the grade (Note: it is discussed in class and is not harder than other problems; it is only meant to give you extra points if you do it). The assignment is due before class time on Tuesday Mar. 29; since there will be no class that day, please hand in your assignment to Jin, the TA, before that time.

Problem 1. Higher-order functions.

Winskel's book Exercise 11.3 on page 188.

Problem 2. Type inference by generating and solving constraints.

Schwartzbach's lecture notes Exercise 4.7 on page 10.

Problem 3. Curry-Howard isomorphism.

Schwartzbach's lecture notes Exercise 5.3 on page 11.

Problem 4. Polymorphic type system.

Schwartzbach's lecture notes Exercise 6.2 on page 15, but do the first half only.

Write a program, in our higher-order functional language with lazy semantics, that generates the infinite data structure <0,<2,<4,<6,...>>>>.