guix/guix/monads.scm

;;; GNU Guix --- Functional package management for GNU
;;; Copyright © 2013, 2014, 2015 Ludovic Courtès <ludo@gnu.org>
;;;
;;; This file is part of GNU Guix.
;;;
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;;; under the terms of the GNU General Public License as published by
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;;; your option) any later version.
;;;
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;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
;;; GNU General Public License for more details.
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;;; You should have received a copy of the GNU General Public License
;;; along with GNU Guix.  If not, see <http://www.gnu.org/licenses/>.

(define-module (guix monads)
  #:use-module ((system syntax)
                #:select (syntax-local-binding))
  #:use-module (ice-9 match)
  #:use-module (srfi srfi-1)
  #:use-module (srfi srfi-9)
  #:use-module (srfi srfi-26)
  #:export (;; Monads.
            define-monad
            monad?
            monad-bind
            monad-return

            ;; Syntax.
            >>=
            return
            with-monad
            mlet
            mlet*
            mbegin
            mwhen
            munless
            lift0 lift1 lift2 lift3 lift4 lift5 lift6 lift7 lift
            listm
            foldm
            mapm
            sequence
            anym

            ;; Concrete monads.
            %identity-monad))

;;; Commentary:
;;;
;;; This module implements the general mechanism of monads, and provides in
;;; particular an instance of the "store" monad.  The API was inspired by that
;;; of Racket's "better-monads" module (see
;;; <http://planet.racket-lang.org/package-source/toups/functional.plt/1/1/planet-docs/better-monads-guide/index.html>).
;;; The implementation and use case were influenced by Oleg Kysielov's
;;; "Monadic Programming in Scheme" (see
;;; <http://okmij.org/ftp/Scheme/monad-in-Scheme.html>).
;;;
;;; The store monad allows us to (1) build sequences of operations in the
;;; store, and (2) make the store an implicit part of the execution context,
;;; rather than a parameter of every single function.
;;;
;;; Code:

;; Record type for monads manipulated at run time.
(define-record-type <monad>
  (make-monad bind return)
  monad?
  (bind   monad-bind)
  (return monad-return))                         ; TODO: Add 'plus' and 'zero'

(define-syntax define-monad
  (lambda (s)
    "Define the monad under NAME, with the given bind and return methods."
    (define prefix (string->symbol "% "))
    (define (make-rtd-name name)
      (datum->syntax name
                     (symbol-append prefix (syntax->datum name) '-rtd)))

    (syntax-case s (bind return)
      ((_ name (bind b) (return r))
       (with-syntax ((rtd (make-rtd-name #'name)))
         #`(begin
             (define rtd
               ;; The record type, for use at run time.
               (make-monad b r))

             (define-syntax name
               ;; An "inlined record", for use at expansion time.  The goal is
               ;; to allow 'bind' and 'return' to be resolved at expansion
               ;; time, in the common case where the monad is accessed
               ;; directly as NAME.
               (lambda (s)
                 (syntax-case s (%bind %return)
                   ((_ %bind)   #'b)
                   ((_ %return) #'r)
                   (_           #'rtd))))))))))

(define-syntax-parameter >>=
  ;; The name 'bind' is already taken, so we choose this (obscure) symbol.
  (lambda (s)
    (syntax-violation '>>= ">>= (bind) used outside of 'with-monad'" s)))

(define-syntax-parameter return
  (lambda (s)
    (syntax-violation 'return "return used outside of 'with-monad'" s)))

(define-syntax with-monad
  (lambda (s)
    "Evaluate BODY in the context of MONAD, and return its result."
    (syntax-case s ()
      ((_ monad body ...)
       (eq? 'macro (syntax-local-binding #'monad))
       ;; MONAD is a syntax transformer, so we can obtain the bind and return
       ;; methods by directly querying it.
       #'(syntax-parameterize ((>>=    (identifier-syntax (monad %bind)))
                               (return (identifier-syntax (monad %return))))
           body ...))
      ((_ monad body ...)
       ;; MONAD refers to the <monad> record that represents the monad at run
       ;; time, so use the slow method.
       #'(syntax-parameterize ((>>=    (identifier-syntax
                                        (monad-bind monad)))
                               (return (identifier-syntax
                                        (monad-return monad))))
           body ...)))))

(define-syntax mlet*
  (syntax-rules (->)
    "Bind the given monadic values MVAL to the given variables VAR.  When the
form is (VAR -> VAL), bind VAR to the non-monadic value VAL in the same way as
'let'."
    ;; Note: the '->' symbol corresponds to 'is:' in 'better-monads.rkt'.
    ((_ monad () body ...)
     (with-monad monad body ...))
    ((_ monad ((var mval) rest ...) body ...)
     (with-monad monad
       (>>= mval
            (lambda (var)
              (mlet* monad (rest ...)
                body ...)))))
    ((_ monad ((var -> val) rest ...) body ...)
     (let ((var val))
       (mlet* monad (rest ...)
         body ...)))))

(define-syntax mlet
  (lambda (s)
    (syntax-case s ()
      ((_ monad ((var mval ...) ...) body ...)
       (with-syntax (((temp ...) (generate-temporaries #'(var ...))))
         #'(mlet* monad ((temp mval ...) ...)
             (let ((var temp) ...)
               body ...)))))))

(define-syntax mbegin
  (syntax-rules (%current-monad)
    "Bind the given monadic expressions in sequence, returning the result of
the last one."
    ((_ %current-monad mexp)
     mexp)
    ((_ %current-monad mexp rest ...)
     (>>= mexp
          (lambda (unused-value)
            (mbegin %current-monad rest ...))))
    ((_ monad mexp)
     (with-monad monad
       mexp))
    ((_ monad mexp rest ...)
     (with-monad monad
       (>>= mexp
            (lambda (unused-value)
              (mbegin monad rest ...)))))))

(define-syntax mwhen
  (syntax-rules ()
    "When CONDITION is true, evaluate EXP0..EXP* as in an 'mbegin'.  When
CONDITION is false, return *unspecified* in the current monad."
    ((_ condition exp0 exp* ...)
     (if condition
         (mbegin %current-monad
           exp0 exp* ...)
         (return *unspecified*)))))

(define-syntax munless
  (syntax-rules ()
    "When CONDITION is false, evaluate EXP0..EXP* as in an 'mbegin'.  When
CONDITION is true, return *unspecified* in the current monad."
    ((_ condition exp0 exp* ...)
     (if condition
         (return *unspecified*)
         (mbegin %current-monad
           exp0 exp* ...)))))

(define-syntax define-lift
  (syntax-rules ()
    ((_ liftn (args ...))
     (define (liftn proc monad)
       "Lift PROC to MONAD---i.e., return a monadic function in MONAD."
       (lambda (args ...)
         (with-monad monad
           (return (proc args ...))))))))

(define-lift lift0 ())
(define-lift lift1 (a))
(define-lift lift2 (a b))
(define-lift lift3 (a b c))
(define-lift lift4 (a b c d))
(define-lift lift5 (a b c d e))
(define-lift lift6 (a b c d e f))
(define-lift lift7 (a b c d e f g))

(define (lift proc monad)
  "Lift PROC, a procedure that accepts an arbitrary number of arguments, to
MONAD---i.e., return a monadic function in MONAD."
  (lambda args
    (with-monad monad
      (return (apply proc args)))))

(define (foldm monad mproc init lst)
  "Fold MPROC over LST, a list of monadic values in MONAD, and return a
monadic value seeded by INIT."
  (with-monad monad
    (let loop ((lst    lst)
               (result init))
      (match lst
        (()
         (return result))
        ((head tail ...)
         (mlet* monad ((item   head)
                       (result (mproc item result)))
           (loop tail result)))))))

(define (mapm monad mproc lst)
  "Map MPROC over LST, a list of monadic values in MONAD, and return a monadic
list.  LST items are bound from left to right, so effects in MONAD are known
to happen in that order."
  (mlet monad ((result (foldm monad
                              (lambda (item result)
                                (mlet monad ((item (mproc item)))
                                  (return (cons item result))))
                              '()
                              lst)))
    (return (reverse result))))

(define-inlinable (sequence monad lst)
  "Turn the list of monadic values LST into a monadic list of values, by
evaluating each item of LST in sequence."
  (with-monad monad
    (mapm monad return lst)))

(define (anym monad proc lst)
  "Apply PROC to the list of monadic values LST; return the first value,
lifted in MONAD, for which PROC returns true."
  (with-monad monad
    (let loop ((lst lst))
      (match lst
        (()
         (return #f))
        ((head tail ...)
         (mlet* monad ((value  head)
                       (result -> (proc value)))
           (if result
               (return result)
               (loop tail))))))))

(define-syntax listm
  (lambda (s)
    "Return a monadic list in MONAD from the monadic values MVAL."
    (syntax-case s ()
      ((_ monad mval ...)
       (with-syntax (((val ...) (generate-temporaries #'(mval ...))))
         #'(mlet monad ((val mval) ...)
             (return (list val ...))))))))



;;;
;;; Identity monad.
;;;

(define-inlinable (identity-return value)
  value)

(define-inlinable (identity-bind mvalue mproc)
  (mproc mvalue))

(define-monad %identity-monad
  (bind   identity-bind)
  (return identity-return))

;;; monads.scm end here