identity-monads.scm

; monads
;
; references:
;   http://onclojure.com/2009/03/05/a-monad-tutorial-for-clojure-programmers-part-1/
;   http://www.intensivesystems.net/tutorials/monads_101.html

;
; define the 'identity' monad
;
(define-class <identity> ()
  ((value :init-keyword :value :accessor value-of)))

(define-method return (monad value)
  (make monad :value value))

(define-method bind (monad function)
  (return monad (function (ref monad 'value))))

(define-method just (monad)
  (ref monad 'value))

;
; define a few functions to use on the monadic values
;
(define (f v) (* v v))    ; square the value
(define (g v) (+ v v))    ; double the value


; example
;

(just (bind (return <identity> 3) f))     ; -> 9
;
; explained
;
; The 'return' wraps the value 3 in an instance of the identity monad
;
; The 'bind' passes the function 'f' to the instance of the idenity monad
; created by return.  The function f squares values passed to it.
;
; The 'just' unwraps the monadic result of the 'bind' to get it's value
; which is 9 in this case.

;
; notice that sequence is correctly preserved
;
(just (bind (bind (return <identity> 3) f) g))     ; -> 18
(just (bind (bind (return <identity> 3) g) f))     ; -> 36

; in the first case 3 is squared then doubled 3 -> 9 -> 18
; in the second csae 3 is doubled then squared 3 > 6 -> 36

; TODO
;
; create a 'sequence' macro so we can get rid of all the parens and just write...
;
(just (sequence <identity> 3 f g))    ; -> 18
(just (sequence <identity> 3 g f))    ; -> 36