![\"f\equiv\lambda x.(y+x)\"](\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-eeecf3741e9dd48da050f9719eb91808_l3.png\" "\\"Rendered")
. It is:<\/p>\n\n\n\n<\/p>\n\n\n\n
Start with an example lambda calculus expression . It is:<\/p>\n\n\n\n
![\"x\"](\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" "\\"Rendered")
as an input argument and it uses ![\"y\"](\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" "\\"Rendered")
from the outer workspace (called a free-variable<\/em>). f(var x) { return y+x; }<\/code><\/li>- [mathematical view] can also be written as
![\"f(x) = y+x\"](\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-8def04f354d64f85a37b390460cfa335_l3.png\" "\\"Rendered")
where is seen as a fixed\/snapshotted value relative to the expression.<\/li><\/ul>\n\n\n\ng(int y) => (int x) => y + x<\/pre>\n\n\n\nLambda calculus is right-associative<\/p>\n\n\n\n
g(int y) => ( (int x) => y + x )<\/pre>\n\n\n\nUnrolling in C-style it will give better insights to the relationships between layers<\/p>\n\n\n\n
g(int y) {\n return (int x) { return y + x; };\n}<\/pre>\n\n\n\nNote that (int x) { return y + x; }<\/code><\/code> is a functor. To emphasize this, the same code can be rewritten by assigning the name f<\/code> to it and returning f<\/code>:<\/p>\n\n\n\ng(int y) {\n f(int x) { return y + x; };\n return f;\n}<\/pre>\n\n\n\nUse the C++11 style syntax so that it doesn’t look like nested function implementation body instead of a functor nested inside a function:<\/p>\n\n\n\n
g(int y) {\n var f = (int x) { return y + x; };\n return f;\n}<\/pre>\n\n\n\nNote that conceptually what we are doing with the wrapper cascade is indeed nested functions. However, in the wrapper, we spit out a functor (which did most of the partial work) so the user can endow\/evaluating it with the last piece of needed info\/input:<\/p>\n\n\n\n
g(int y) {\n f(int x) { \n return y + x;\n };\n return f;\n}<\/pre>\n\n\n\nMore commonly as seen in Dart docs, this formatting shows a (binder\/capturing) wrapper function returning its own nested function:<\/p>\n\n\n\n
g(int y) {\n return (int x) { \n return y + x;\n };\n}<\/pre>\n<\/div>