Borrowed from CSE340 at Arizona State University and CMSC 330 at the University of Maryland
Use parentheses to make the order of evaluation explicit in the following expressions.
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λx. x z λy. x y -
(λx. x z) λy. w λw. w y z x -
λx. x y λx. y x
Identify all the free variables in the following expressions.
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λx. x z λy. x y -
(λx. x z) λy. w λw. w y z x -
λx. x y λx. y x
Reduce the following expressions as much as possible.
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(λx. x λy. λz. z y x)(y z) -
(λn. λf. λx. f(n f x))(λx. λf. x x x x f) -
(λx. x(λx. λy. y)(λy. λx. y))(λx. λy. y) -
(λx. λy. xy)(λz. (λc. y) z) -
(λx. λy. x y)(λz. (λc. c y) z) -
(λx. x q)(λy. y y y) -
(λc. c(λx. (λx. λy. y))(λx. λy. x))(λq. q) -
(λz. z)(λy. y y)(λx. x a) -
(λz. z)(λz. z z)(λz. z y) -
(λx. λy. x y y)(λa. a) b -
(λx. λy. x y y)(λy. y) y -
(λx. x x)(λy. y x) z -
(λx. (λy. (x y)) y) z -
((λx. x x)(λy. y))(λy. y) -
(((λx. λy. (x y))(λy. y)) w) -
(λx. y)((λy. y y y)(λx. x x x))