Homework 4 (25pts)
Due before class Feb 18, 2009
1. Reduce the following lambda terms to normal forms. For each reduction step, mark
the function abstraction and the parameter value being reduced.
(a) (λx. λy. y x) 5
(b) (λx. λy. y x) 5 (λz .z + 3)
(c) (λx. λy. x y) (λz .z +y) 7
(d) (λy.(λx. λy. x y) (λz.y z) 7) (λx.x + 1)
2. Translate the following C code to lambda calculus.
int apply_twice (int (*f) (...), int x) { return f(x); }
int twice (int (*g)(...), int y) { return y + apply_twice(g, y); }
int foo(int x) { return x + x; }
int main() { return twice(foo, 5); }
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