# Tag Info

Accepted

### How does the Y combinator exemplify "Lambda calculus inconsistency"?

It's inspired from real events, but the way it's stated is barely recognizable and “should be regarded with suspicion” is nonsense. Consistency has a precise meaning in logic: a consistent theory is ...
Accepted

### Is the SK2 calculus a complete basis, where K2 is the flipped K combinator?

Consider the terms of the $S,K_2,I$ calculus as trees (with binary nodes representing applications, and $S, K_2$ leaves representing the combinators. For example, the term $S(SS)K_2$ would be ...
• 355

### What is the purpose of the SKI combinator calculus(or even lambda calculus)? What are some real life examples of its use?

The obvious application of the lambda calculus is any functional programming language (e.g., Lisp, ML, Haskell), and any language that supports anonymous functions. As for combinator calculus, does ...
• 81.9k
Accepted

### Why are combinators important in lambda calculus?

The word "combinator" has some connotations that you don't seem to be intending here and sometimes a stricter definition. Another term for the definition you gave is a closed term. The opposite is ...
• 12.1k

### Why do combinators look this way?

The combinators $K$ and $S$ first appear in Moses Schönfinkel, Über die Bausteine der mathematischen Logik, though he calls them $C$ and $S$. He actually defines five combinators, $I,C,T,Z,S$, and ...
• 278k

• 2,157

### What is the purpose of the SKI combinator calculus(or even lambda calculus)? What are some real life examples of its use?

Have a look at Microsoft's LINQ (Language INtegrated Query). It makes extensive and quite direct use of lambda calculus to manipulate and transform expression trees. Probably the most complete and ...
• 171

### Why are combinators important in lambda calculus?

A combinator is a lambda expression with no free variables. So, λx.x is a combinator but λx.y is not a combinator. Consider the following: (λxy.xy)(λx.y) = (λy.xy)[x := λx.y] = (λy.(λx.y)y) Notice ...

### What is the name of the operator that translates from $X\rightarrow(Y\rightarrow Z)$ to $Y\rightarrow(X\rightarrow Z)$?

Given the tag combinatory-logic, the answer in combinatory logic is C, i.e. "the C combinator". Obviously, this name is not self-documenting or going to be obvious in even a slightly more general ...
• 12.1k
Accepted

### Coding max as an interaction net

Rules for agents in interaction nets are defined by what the principal port of that agent is connected to and each agent has exactly one principal port. In the "max" example, for the top ...
• 56