Homework 2 Problem 1 Sample Solution

(a) 

           ------------@----------------------
           |                                 |
           |                                 |
           \h                         -------@-------
           |                          |             |    
       ----@------                   \a          ---@---
       |         |                    |          |     |     
      \x        \x                   \b          @     5
       |         |                    |         / \
       @         @                    a        +   1
      / \       / \
     h   @     h   @
        / \       / \
       x   x     x   x




(b,c)

(\h.(\x.h(xx))(\x.h(xx)))((\a.\b.a)(+ 1 5))
                                   -delta-
    -------beta(LI)-----  -----beta------            
-------------beta(LO)---------------------


(d) Normal form and weak-head normal form are the same:

(\h.(\x.h(xx))(\x.h(xx)))((\a.\b.a)(+ 1 5)) ->
(\x.((\a.\b.a)(+ 1 5))(xx))(\x.((\a\b.a)(+ 1 5))(xx)) ->
((\a.\b.a)(+ 1 5))((\x.((\a\b.a)(+ 1 5))(xx))(\x.((\a\b.a)(+ 1 5))(xx))) ->
(\b.(+ 1 5))((\x.((\a\b.a)(+ 1 5))(xx))(\x.((\a\b.a)(+ 1 5))(xx))) ->
(+ 1 5)