CS 3723: Objectives to be Tested on Midterm I (2/26/2008)
1. Computability
(a) be able to identify partial functions and what recursive functions
(b) be able to explain what it means for a language to be Turing-complete
(c) be able explain what the Church-Turing Thesis tells us about the computational
power of lambd a-calculus, Turing Machines, partial µ-recursive functions, and
different (Turing-complete) programming languages
(d) given a description of a programming languages with recursion or general loop-
ing, be able to identify it as being Turing-complete
(e) given a description of a language that always terminates in a finite amount of
time, be able to identify it as not being Turing-complete
(f) be able to list several languages that are and are not Turing complete
(g) be able to explain why the Halting Problem is undecidable
2. Lisp/Scheme
(a) be able to read Lisp expressions and read/write Scheme expressions
i. using the define,lambda,cond quote,let,if, and eval special forms
ii. using numerical (e.g., <and equality comparison (e.g., eqv?) operators
iii. using mathematical functions (e.g., +,sqrt
iv. using list functions (e.g., cons,car,cdr,list)
(b) be able to explain some of the important contributions of Lisp to the history of
Programming Languages
(c) be able to read/write recursive functions (esp., those that recurse over lists) in
Scheme
(d) be able to read/write and use higher-order functions in Scheme
(e) be able to read/write curried functions in Scheme
3.λ-Calculus
(a) be able to explain what λ-calculus is and its theoretical significance
(b) understand λ-calculus terms
i. know what the three types of λ-calculus terms are and their closest ana-
logues in conventional programming languages (i.e., abstraction ∼function
definition, application ∼function call)
ii. be able to correctly partition λ-calculus terms into their constituent sub-
terms (e.g., by creating or identifying the ”correct” parse tree according to
precedence and associativity)
iii. be able to identify free variables in λ-calculus terms
iv. be able to determine whether two λ-calculus terms are α-equivalent
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