Iam a beginner in Lambda Calculus, I have a expression saying
Here y is a free variable and x is a bound variable. My question is what would be the value of the expression (which has free variables).
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The term $\lambda x . x y$ is in normal form. It does not reduce any further.
In general, to find out these things, you can just type them into a $\lambda$-calculus calculator. One is available in my PL zoo (hmm, it is momentarily under construction):
lambda @ programming languages zoo Type Ctrl-D to exit or "#help;" for help. # #constant y ; y is a constant. # ^ x . x y ; = λ x . x y
The language wants you to declare free variables as constants, which is why we first explain that
y is a known constant.