For reminders about Scheme syntax, see [here](/assignment8/) and [here](/week1/) and [here](/translating_between_ocaml_scheme_and_haskell). Other resources are on our [[Learning Scheme]] page.
-All of the examples assume the following preface:
+Most of the examples assume the following preface:
#lang racket
[(null? l) (k 'notfound)]
[(eq? (car l) a) (cdr l)]
[(atom? (car l)) (cons (car l) (aux (cdr l) k))]
- ; what happens when (car l) exists but isn't an atom?
- [else (let ([car2 (let/cc k2 ; now what will happen when k2 is called?
- (aux (car l) k2))])
- (cond
- ; when will the following condition be met? what happens then?
- [(eq? car2 'notfound) (cons (car l) (aux (cdr l) k))]
- [else (cons car2 (cdr l))]))]))]
+ [else
+ ; what happens when (car l) exists but isn't an atom?
+ (let ([car2 (let/cc k2 ; now what will happen when k2 is called?
+ (aux (car l) k2))])
+ (cond
+ ; when will the following condition be met? what happens then?
+ [(eq? car2 'notfound) (cons (car l) (aux (cdr l) k))]
+ [else (cons car2 (cdr l))]))]))]
[lst2 (let/cc k1 ; now what will happen when k1 is called?
(aux lst k1))])
(cond
[(eq? lst2 'notfound) lst]
[else lst2]))))
-
Here is [the answer](/hints/cps_hint_3), but try to figure it out for yourself.
Here is the hardest example. Try to figure out what this function does:
Delimited control operators
===========================
-`callcc` is what's known as an *undelimited control operator*. That is, the continuations `outk` that get bound to our `k`s behave as though they include all the code from the `call/cc ...` out to *and including* the end of the program.
+Here again is the CPS for `callcc`:
+
+ [callcc (\k. body)] = \outk. (\k. [body] outk) (\v localk. outk v)
-Often times it's more useful to use a different pattern, where we instead capture only the code from the invocation of our control operator out to a certain boundary, not including the end of the program. These are called *delimited control operators*. A variety of the latter have been formulated.
+`callcc` is what's known as an *undelimited control operator*. That is, the continuations `outk` that get bound into our `k`s include all the code from the `call/cc ...` out to *and including* the end of the program. Calling such a continuation will never return any value to the call site. (See the technique employed in the `delta` example above, with the `(begin (let/cc k2 ...) ...)`, for a work-around.)
-The most well-behaved from where we're coming from is the pair `reset` and `shift`. `reset` sets the boundary, and `shift` binds the continuation from the position where it's invoked out to that boundary.
+Often times it's more useful to use a different pattern, where we instead capture only the code from the invocation of our control operator out to a certain boundary, not including the end of the program. These are called *delimited control operators*. A variety of these have been formulated. The most well-behaved from where we're coming from is the pair `reset` and `shift`. `reset` sets the boundary, and `shift` binds the continuation from the position where it's invoked out to that boundary.
It works like this:
The above OCaml code won't work out of the box; you have to compile and install a special library that Oleg wrote. We discuss it on our [translation page](/translating_between_ocaml_scheme_and_haskell). If you can't get it working, then you can play around with `shift` and `reset` in Scheme instead. Or in the Continuation monad. Or using CPS transforms of your code, with the help of the lambda evaluator.
-The relevant CPS transforms will be performed by these helper functions:
+You can make the lambda evaluator perform the required CPS transforms with these helper functions:
let reset = \body. \outk. outk (body (\i i)) in
let shift = \k_body. \midk. (\k. (k_body k) (\i i)) (\a localk. localk (midk a)) in