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+ Some notes:
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+ * When you're talking to the interactive OCaml program, you have to finish complete statements with a ";;". Sometimes these aren't necessary, but rather than learn the rules yet about when you can get away without them, it's easiest to just use them consistently, like a period at the end of a sentence.
+ * The expressions inside the << and >> are an expression in the pure untyped lambda calculus. The stuff outside the angle brackets is regular OCaml syntax. Here you only need to use a very small part of that syntax: "let var = some_value;;" assigns a value to a variable, and "function_foo arg1 arg2" applies the specified function to the specified arguments. "church_to_int" is a function that takes a single argument --- the lambda expression that follows it, << $add$ $one$ $two$ >> -- and, if that expression has the form of a "Church numeral", it converts it into an "int", which is OCaml's (and most language's) primitive way to represent small numbers. The line "- : int = 3" is OCaml telling you that the expression you just had it evaluate simplifies to a value whose type is "int" and which in particular is the int 3.
+ * If you call church_to_int with a lambda expression that doesn't have the form of a Church numeral, it will complain. If you call it with something that's not even a lambda expression, it will complain in a different way.
+ * The $s inside the << and >> are essentially corner quotes. If we do this: "let a = << x >>;; let b = << a >>;; let c = << $a$ >>;;" then the OCaml variable b will have as its value an (atomic) lambda expression, consisting just of the variable "a" in the untyped lambda calculus. On the other hand, the OCaml variable c will have as its value a lambda expression consisting just of the variable "*x*". That is, here the OCaml variable "a" is spliced into the lambda expression << $a$ >>.
+ * The expression that's spliced in is done so as a single syntactic unit. In other words, the lambda expression << w x y z >> is parsed via usual conventions as << (((w x) y) z) >>. Here << x y >> is not any single syntactic constituent. But if you do instead "let a = << x y >>;; let b = << w $a$ z >>", then what you get *will* have << x y >> as a constituent, and will be parsed as << ((w (x y)) z) >>.
+ * << fun x y -> something >> is equivalent to << fun x -> fun y -> something >>, which is parsed as << fun x -> (fun y -> something) >> (everything to the right of the arrow as far as possible is considered together). At the moment, this only works for up to five variables, as in << fun x1 x2 x3 x4 x5 -> something >>.
+ * The << >> and $-quotes aren't part of standard OCaml syntax, they're provided by this add-on bundle. For the most part it doesn't matter if other expressions are run together with the << and >>: you can do either << fun x -> x >> or <<fun x->x>>. But the $s *must* be separated from the << >> brackets with spaces or ( )s.
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