<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">Disclaimer: this question is both a real question and me trying to push the type system to its limits, so I’m not really expecting to get a satisfactory answer.<div class=""> </div><div class="">I posted <a href="http://stackoverflow.com/q/28849475/465378" class="">a question on Stack Overflow here</a>, but I’m guessing that this is unfortunately far too localized to be answered there, so I’m posting it here as well. The original question is as follows:</div><div class=""> </div><div class=""><p style="margin: 0px 0px 1em; padding: 0px; border: 0px; clear: both; color: rgb(34, 34, 34); font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 19.5px; background-color: rgb(255, 255, 255);" class="">I can write a simple function in untyped Racket called <code style="margin: 0px; padding: 1px 5px; border: 0px; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, sans-serif; white-space: pre-wrap; background-color: rgb(238, 238, 238);" class="">curry-all</code> that takes a list of functions, all of which accept the same kind of value for their first argument, and produces a list of functions with their first arguments curried.<pre class="prettyprint prettyprinted lang-lisp" style="margin-top: 0px; padding: 5px; border: 0px; overflow: auto; width: auto; max-height: 600px; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, sans-serif; color: rgb(57, 51, 24); word-wrap: normal; background-color: rgb(238, 238, 238);"><code style="margin: 0px; padding: 0px; border: 0px; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, sans-serif; white-space: inherit;" class="">(define (curry-all fs arg) (map (λ (f) (curry f arg)) fs))</code></pre><p style="margin: 0px 0px 1em; padding: 0px; border: 0px; clear: both; color: rgb(34, 34, 34); font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 19.5px; background-color: rgb(255, 255, 255);" class="">For a running example of the above function, <a href="http://pasterack.org/pastes/88150" rel="nofollow" style="margin: 0px; padding: 0px; border: 0px; cursor: pointer; color: rgb(12, 101, 165);" class="">see this snippet on pasterack</a>.<p style="margin: 0px 0px 1em; padding: 0px; border: 0px; clear: both; color: rgb(34, 34, 34); font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 19.5px; background-color: rgb(255, 255, 255);" class="">This is a valid function, but I'm not sure if it's even possible to type in Typed Racket given its polymorphic typing constructs. The type of <code style="margin: 0px; padding: 1px 5px; border: 0px; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, sans-serif; white-space: pre-wrap; background-color: rgb(238, 238, 238);" class="">curry</code> itself is already fairly complex, and obviously the type of <code style="margin: 0px; padding: 1px 5px; border: 0px; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, sans-serif; white-space: pre-wrap; background-color: rgb(238, 238, 238);" class="">curry-all</code> would need to be necessarily more complex.<p style="margin: 0px 0px 1em; padding: 0px; border: 0px; clear: both; color: rgb(34, 34, 34); font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 19.5px; background-color: rgb(255, 255, 255);" class="">I made a relatively simple attempt at typing this function, though I was quite aware that it would not function as I liked:<pre class="prettyprint prettyprinted lang-lisp" style="margin-top: 0px; padding: 5px; border: 0px; overflow: auto; width: auto; max-height: 600px; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, sans-serif; color: rgb(57, 51, 24); word-wrap: normal; background-color: rgb(238, 238, 238);"><code style="margin: 0px; padding: 0px; border: 0px; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, sans-serif; white-space: inherit;" class="">(: curry-all (All [a c b ...] (Listof (-> a b ... b c)) a -> (Listof (-> b ... b c)))) (define (curry-all fs arg) (map (λ ([f : (-> a b ... b c)]) (curry f arg)) fs))</code></pre><p style="margin: 0px 0px 1em; padding: 0px; border: 0px; clear: both; color: rgb(34, 34, 34); font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 19.5px; background-color: rgb(255, 255, 255);" class="">Obviously, this works if all the functions have identical types (which isn’t worthless!), but it fails if they have different arities, even if their first arguments’ types are shared.<p style="margin: 0px 0px 1em; padding: 0px; border: 0px; clear: both; color: rgb(34, 34, 34); font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 19.5px; background-color: rgb(255, 255, 255);" class="">Is there any way to specify this function’s type so that it will work in a more general case?</div></body></html>