# Questions tagged [combinatory-logic]

Combinatory logic, combinatorial calculi, and other questions about combinators and variable-free variants of the $\lambda$-calculus.

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### How to count the ways to fill a pyramid in 2d [closed]

I am trying to count the ways to fill a 2D pyramid of base $n$. We have a base already placed of $n$ squares and we try to fill the pyramid with squares (we can place a square only if the two below ...
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### Line follower robot using max 8 NAND gates

So I have to figure out the logic for a line follower robot using at maximum 8 NAND gates (2 7400HC series NAND circuits). The robot has 3 sensors, which give 1 on a black surface and 0 on a white ...
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### Is it possible to do abstraction elimination on the strict fixed point combinator Z?

In lambda calculus, the strict fixed point combinator Z is given by: \f.(\x.f(\v.x(x)(v)))(\x.f(\v.x(x)(v))) Is it possible to eliminate all abstractions from the Z ...
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### Proving a combinator is a fixed point

Show that the term ZZ where Z is λz.λx. x(z z x) satisfies the requirement for fixed point combinators that ZZM =β M(ZZM).