I am following this video tutorial, starting 6th minute
I would like to parse the following sentence
square blue or round yellow pillow.
For now I am interested in only how square
and blue
are combined.
In particular with start with the following representation
square -> ADJ: \lambda x. square(x)
blue -> ADJ: \lambda x. blue(x)
Next step is we raise types:
square -> N/N: \lambda f. \lambda x. f(x) /\ square (x)
blue -> N/N: \lambda f. \lambda x. f(x) /\ blue (x)
Now we create representation for square blue
. I indicate substitution by brackets
\lambda x. [ \lambda f. \lambda x. f(x) /\ blue (x) ] (x) /\ square (x)
Next I simply substitute z
for x
everywhere outside of square brackets, so that we do not confuse different x
s.
\lambda z. [ \lambda f. \lambda x. f(x) /\ blue (x) ] (z) /\ square (z)
Next I push z into square brackets
\lambda z. \lambda x. z(x) /\ blue (x) /\ square (z)
This is different from what stated in the lecture:
\lambda z. \lambda x. z(x) /\ square (x) /\ blue (x)
Where did I make a mistake?