From: Jim Pryor Date: Tue, 26 Oct 2010 14:29:51 +0000 (-0400) Subject: ass5: move monads to end X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=ae46ef3c2cb5de4b994fc7df4a95055d03c6b867 ass5: move monads to end Signed-off-by: Jim Pryor --- diff --git a/assignment5.mdwn b/assignment5.mdwn index 5a2a488c..85ac9a18 100644 --- a/assignment5.mdwn +++ b/assignment5.mdwn @@ -123,32 +123,12 @@ and that "bool" is any boolean. Then we can try the following: [[Hint assignment 5 problem 3]] -Baby monads ------------ - -Read the lecture notes for week 6, then write a -function `lift'` that generalized the correspondence between + and -`add'`: that is, `lift'` takes any two-place operation on integers -and returns a version that takes arguments of type `int option` -instead, returning a result of `int option`. In other words, -`lift'` will have type - - (int -> int -> int) -> (int option) -> (int option) -> (int option) - -so that `lift' (+) (Some 3) (Some 4)` will evalute to `Some 7`. -Don't worry about why you need to put `+` inside of parentheses. -You should make use of `bind'` in your definition of `lift'`: - - let bind' (x: int option) (f: int -> (int option)) = - match x with None -> None | Some n -> f n;; - - Booleans, Church numbers, and Church lists in OCaml --------------------------------------------------- (These questions adapted from web materials by Umut Acar. See .) -The idea is to get booleans, Church numbers, "Church" lists, and +The idea is to get booleans, Church numbers, v3 lists, and binary trees working in OCaml. Recall from class System F, or the polymorphic λ-calculus. @@ -215,3 +195,23 @@ leaves in an int tree. Write a function `inOrder` : τ tree → τ list that computes the in-order traversal of a binary tree. You may assume the above encoding of lists; define any auxiliary functions you need. +Baby monads +----------- + +Read the lecture notes for week 6, then write a +function `lift'` that generalized the correspondence between + and +`add'`: that is, `lift'` takes any two-place operation on integers +and returns a version that takes arguments of type `int option` +instead, returning a result of `int option`. In other words, +`lift'` will have type + + (int -> int -> int) -> (int option) -> (int option) -> (int option) + +so that `lift' (+) (Some 3) (Some 4)` will evalute to `Some 7`. +Don't worry about why you need to put `+` inside of parentheses. +You should make use of `bind'` in your definition of `lift'`: + + let bind' (x: int option) (f: int -> (int option)) = + match x with None -> None | Some n -> f n;; + +