(Bindings). For each of the following expressions. determine for each variable x the \(\lambda x\). it is bound to. I have numbered
the variables and the abstractions. The variables are numbered using Arabic numerals and the abstractions are numbered
using roman numerals and you should specify which variable numbers are bound to which abstraction number. For
example, if variables 4 and 7 are bound to abstraction I, your answer should be of the form I\(\to\)4 7 to indicate that
abstaction I has variables 4, and 7 bound by it. If variable 3 is free, then your answer should have the form free \(\to\) 3.
Example.
\((\lambda y. x \; y \; \lambda x. y)\; x\
1 2 3 4
Answer free \(\to\) 1 4
I \(\to\) 2 3
II
Your answers need not be colored (look at old homework assignments for more examples. Similar questions were
covered in old HW3 or old HW4 depending on the semester)
1.1.
\(\lambda y. x \; \lambda z. z \; y \; (\lambda z. \lambda x. x \; y) \; (\lambda z. x) \; (z \; x \; y)\
1 2 3 III IV 4 5 V 6 7 8 9
1.2.
\(\lambda y. x \; (\lambda x. z \; x \; (\lambda z. \lambda x. y \; z \; x) \; \lambda y. z) \; y \; z\
1 2 3 III IV 4 5 6 7 8 9
