Mirror of GNU Guix
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;;; GNU Guix --- Functional package management for GNU
;;; Copyright © 2013, 2014, 2015 Ludovic Courtès <ludo@gnu.org>
;;;
;;; This file is part of GNU Guix.
;;;
;;; GNU Guix is free software; you can redistribute it and/or modify it
;;; under the terms of the GNU General Public License as published by
;;; the Free Software Foundation; either version 3 of the License, or (at
;;; your option) any later version.
;;;
;;; GNU Guix is distributed in the hope that it will be useful, but
;;; WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;;; GNU General Public License for more details.
;;;
;;; 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
%state-monad
state-return
state-bind
current-state
set-current-state
state-push
state-pop
run-with-state))
;;; Commentary:
;;;
;;; This module implements the general mechanism of monads, and provides in
;;; particular an instance of the "state" 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>).
;;;
;;; 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-rule (bind-syntax bind)
"Return a macro transformer that handles the expansion of '>>=' expressions
using BIND as the binary bind operator.
This macro exists to allow the expansion of n-ary '>>=' expressions, even
though BIND is simply binary, as in:
(with-monad %state-monad
(>>= (return 1)
(lift 1+ %state-monad)
(lift 1+ %state-monad)))
"
(lambda (stx)
(define (expand body)
(syntax-case body ()
((_ mval mproc)
#'(bind mval mproc))
((x mval mproc0 mprocs (... ...))
(expand #'(>>= (>>= mval mproc0)
mprocs (... ...))))))
(expand stx)))
(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 ((>>= (bind-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 ((>>= (bind-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-syntax liftn
(lambda (s)
"Lift PROC to MONAD---i.e., return a monadic function in MONAD."
(syntax-case s ()
((liftn proc monad)
;; Inline the result of lifting PROC, such that 'return' can in
;; turn be open-coded.
#'(lambda (args ...)
(with-monad monad
(return (proc args ...)))))
(id
(identifier? #'id)
;; Slow path: Return a closure-returning procedure (we don't
;; guarantee (eq? LIFTN LIFTN), but that's fine.)
#'(lambda (proc 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 and return a monadic value seeded by INIT.
(foldm %state-monad (lift2 cons %state-monad) '() '(a b c))
=> '(c b a) ;monadic
"
(with-monad monad
(let loop ((lst lst)
(result init))
(match lst
(()
(return result))
((head tail ...)
(>>= (mproc head result)
(lambda (result)
(loop tail result))))))))
(define (mapm monad mproc lst)
"Map MPROC over LST and return a monadic list.
(mapm %state-monad (lift1 1+ %state-monad) '(0 1 2))
=> (1 2 3) ;monadic
"
(mlet monad ((result (foldm monad
(lambda (item result)
(>>= (mproc item)
(lambda (item)
(return (cons item result)))))
'()
lst)))
(return (reverse result))))
(define-syntax-rule (sequence monad lst)
"Turn the list of monadic values LST into a monadic list of values, by
evaluating each item of LST in sequence."
;; XXX: Making it a macro is a bit brutal as it leads to a lot of code
;; duplication. However, it allows >>= and return to be open-coded, which
;; avoids struct-ref's to MONAD and a few closure allocations when using
;; %STATE-MONAD.
(with-monad monad
(let seq ((lstx lst)
(result '()))
(match lstx
(()
(return (reverse result)))
((head . tail)
(>>= head
(lambda (item)
(seq tail (cons item result)))))))))
(define (anym monad mproc lst)
"Apply MPROC to the list of values LST; return as a monadic value the first
value for which MPROC returns a true monadic value or #f. For example:
(anym %state-monad (lift1 odd? %state-monad) '(0 1 2))
=> #t ;monadic
"
(with-monad monad
(let loop ((lst lst))
(match lst
(()
(return #f))
((head tail ...)
(>>= (mproc head)
(lambda (result)
(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))
;;;
;;; State monad.
;;;
(define-inlinable (state-return value)
(lambda (state)
(values value state)))
(define-inlinable (state-bind mvalue mproc)
"Bind MVALUE, a value in the state monad, and pass it to MPROC."
(lambda (state)
(call-with-values
(lambda ()
(mvalue state))
(lambda (value state)
;; Note: as of Guile 2.0.11, declaring a variable to hold the result
;; of (mproc value) prevents a bit of unfolding/inlining.
((mproc value) state)))))
(define-monad %state-monad
(bind state-bind)
(return state-return))
(define* (run-with-state mval #:optional (state '()))
"Run monadic value MVAL starting with STATE as the initial state. Return
two values: the resulting value, and the resulting state."
(mval state))
(define-inlinable (current-state)
"Return the current state as a monadic value."
(lambda (state)
(values state state)))
(define-inlinable (set-current-state value)
"Set the current state to VALUE and return the previous state as a monadic
value."
(lambda (state)
(values state value)))
(define (state-pop)
"Pop a value from the current state and return it as a monadic value. The
state is assumed to be a list."
(lambda (state)
(match state
((head . tail)
(values head tail)))))
(define (state-push value)
"Push VALUE to the current state, which is assumed to be a list, and return
the previous state as a monadic value."
(lambda (state)
(values state (cons value state))))
;;; monads.scm end here