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|
#| -*- Scheme -*-
Copyright (c) 1987, 1988, 1989, 1990, 1991, 1995, 1997, 1998,
1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006,
2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014,
2015, 2016, 2017, 2018, 2019, 2020
Massachusetts Institute of Technology
This file is part of MIT scmutils.
MIT scmutils 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 2 of the License, or (at
your option) any later version.
MIT scmutils 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 MIT scmutils; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,
USA.
|#
;;;; Operators
(declare (usual-integrations))
(define (o:type o) operator-type-tag)
(define (o:type-predicate o) operator?)
(define (o:arity o)
(operator-arity o))
#|;;; In GENERIC.SCM
(define (make-operator p #!optional name subtype arity #!rest opts)
(if (default-object? name) (set! name #f))
(if (default-object? subtype) (set! subtype #f))
(if (default-object? arity) (set! arity (procedure-arity p)))
(make-apply-hook p `(,operator-type-tag ,subtype ,name ,arity ,@opts)))
|#
(define (make-op p name subtype arity opts)
(make-apply-hook p `(,operator-type-tag ,subtype ,name ,arity ,@opts)))
(define (operator-procedure op)
(assert (operator? op))
(apply-hook-procedure op))
(define (operator-subtype op)
(assert (operator? op))
(cadr (apply-hook-extra op)))
(define (operator-name op)
(assert (operator? op))
(caddr (apply-hook-extra op)))
(define (operator-arity op)
(assert (operator? op))
(cadddr (apply-hook-extra op)))
(define (operator-optionals op)
(assert (operator? op))
(cddddr (apply-hook-extra op)))
(define (simple-operator? op)
(and (operator? op)
(not (operator-subtype op))))
(define (set-operator-optionals! op value)
(assert (operator? op))
(set-cdr! (cdddr (apply-hook-extra op)) value)
op)
(define (operator-merge-subtypes op1 op2)
(let ((t1 (operator-subtype op1))
(t2 (operator-subtype op2)))
(cond ((eq? t1 t2) t1)
((not t1) t2)
((not t2) t1)
(else
(error "Incompatible subtypes -- OPERATOR" t1 t2)))))
(define (operator-merge-arities op1 op2)
(joint-arity (operator-arity op1) (operator-arity op2)))
(define (operator-merge-optionals op1 op2)
(list-union (operator-optionals op1)
(operator-optionals op2)))
(define (o:zero-like op)
(assert (equal? (operator-arity op) *exactly-one*) "o:zero-like")
(make-op (lambda (f) (g:zero-like f))
'zero
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define (o:one-like op)
(assert (equal? (operator-arity op) *exactly-one*) "o:one-like")
(make-op g:identity
'identity
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define o:identity
(make-operator g:identity 'identity))
(define (o:+ op1 op2)
(make-op (lambda fs
(g:+ (apply op1 fs) (apply op2 fs)))
`(+ ,(operator-name op1)
,(operator-name op2))
(operator-merge-subtypes op1 op2)
(operator-merge-arities op1 op2)
(operator-merge-optionals op1 op2)))
(define (o:- op1 op2)
(make-op (lambda fs
(g:- (apply op1 fs) (apply op2 fs)))
`(- ,(operator-name op1)
,(operator-name op2))
(operator-merge-subtypes op1 op2)
(operator-merge-arities op1 op2)
(operator-merge-optionals op1 op2)))
(define (o:o+f op f)
(let ((h (coerce-to-function f)))
(make-op (lambda (g)
(g:+ (op g)
(g:compose h g)))
`(+ ,(operator-name op) ,(procedure-expression h))
(operator-subtype op)
(operator-arity op)
(operator-optionals op))))
(define (o:f+o f op)
(let ((h (coerce-to-function f)))
(make-op (lambda (g)
(g:+ (g:compose h g)
(op g)))
`(+ ,(procedure-expression h) ,(operator-name op))
(operator-subtype op)
(operator-arity op)
(operator-optionals op))))
(define (o:o-f op f)
(let ((h (coerce-to-function f)))
(make-op (lambda (g)
(g:- (op g)
(g:compose h g)))
`(- ,(operator-name op) ,(procedure-expression h))
(operator-subtype op)
(operator-arity op)
(operator-optionals op))))
(define (o:f-o f op)
(let ((h (coerce-to-function f)))
(make-op (lambda (g)
(g:- (g:compose h g)
(op g)))
`(- ,(procedure-expression h) ,(operator-name op))
(operator-subtype op)
(operator-arity op)
(operator-optionals op))))
(define (o:negate op)
(make-op (lambda fs
(g:negate (apply op fs)))
`(- ,(operator-name op))
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define (o:* op1 op2)
(let ((subtype
(operator-merge-subtypes op1 op2)))
(if (procedure? subtype)
(subtype op1 op2)
(make-op (compose op1 op2)
`(* ,(operator-name op1)
,(operator-name op2))
subtype
(operator-arity op2)
(operator-merge-optionals op1 op2)))))
(define (o:f*o f op)
(make-op (lambda gs
(g:* f (apply op gs)))
`(* ,(procedure-expression
(coerce-to-function f))
,(operator-name op))
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define (o:o*f op f)
(make-op (lambda gs
(apply op (map (lambda (g) (g:* f g)) gs)))
`(* ,(operator-name op)
,(procedure-expression
(coerce-to-function f)))
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define (o:o/n op n)
(make-op (lambda gs
(g:* (/ 1 n) (apply op gs)))
`(/ ,(operator-name op) ,n)
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define (o:expt op n)
(assert (equal? (operator-arity op) *exactly-one*) "o:expt")
(make-op (iterated op n o:identity)
`(expt ,(operator-name op) ,n)
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define (o:exp op)
(assert (equal? (operator-arity op) *exactly-one*) "o:exp")
(make-op (lambda (g)
(lambda x
(g:apply ((series:value exp-series (list op)) g) x)))
`(exp ,(operator-name op))
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define (o:cos op)
(assert (equal? (operator-arity op) *exactly-one*) "o:cos")
(make-op (lambda (g)
(lambda x
(g:apply ((series:value cos-series (list op)) g) x)))
`(cos ,(operator-name op))
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
(define (o:sin op)
(assert (equal? (operator-arity op) *exactly-one*) "o:sin")
(make-op (lambda (g)
(lambda x
(g:apply ((series:value sin-series (list op)) g) x)))
`(sin ,(operator-name op))
(operator-subtype op)
(operator-arity op)
(operator-optionals op)))
;;; Optional order argument for exponentiation of operators.
;;; (((expn D 2) g) x)
;;; = (((exp D)
;;; (lambda (eps)
;;; (((+ 1 (* (expt eps 2) D) (* 1/2 (expt eps 4) (expt D 2)) ...) g) x))
;;; 0)
;;; This is (exp (* (expt eps 2) D)) written as a power series in eps.
(define (expn op #!optional exponent)
(assert (operator? op))
(assert (equal? (operator-arity op) *exactly-one*) "o:expn")
(if (default-object? exponent)
(o:exp op)
(make-op
(lambda (g)
(lambda x
(g:apply ((series:inflate (series:value exp-series (list op))
exponent)
g)
x)))
`(exp ,(operator-name op))
(operator-subtype op)
(operator-arity op)
(operator-optionals op))))
(assign-operation 'type o:type operator?)
(assign-operation 'type-predicate o:type-predicate operator?)
(assign-operation 'arity o:arity operator?)
(assign-operation 'zero-like o:zero-like simple-operator?)
(assign-operation 'one-like o:one-like operator?)
(assign-operation 'identity-like o:one-like operator?)
(assign-operation '+ o:+ operator? operator?)
(assign-operation '+ o:o+f operator? not-operator?)
(assign-operation '+ o:f+o not-operator? operator?)
(assign-operation '- o:- operator? operator?)
(assign-operation '- o:o-f operator? not-operator?)
(assign-operation '- o:f-o not-operator? operator?)
(assign-operation '* o:* operator? operator?)
(assign-operation '* o:o*f operator? not-operator?)
(assign-operation '* o:f*o not-operator? operator?)
(assign-operation '/ o:o/n operator? numerical-quantity?)
(assign-operation 'solve-linear-right o:o/n operator? numerical-quantity?)
(assign-operation 'solve-linear-left (lambda (x y) (o:o/n y x)) numerical-quantity? operator?)
(assign-operation 'solve-linear (lambda (x y) (o:o/n y x)) numerical-quantity? operator?)
(assign-operation 'negate o:negate operator?)
(assign-operation 'expt o:expt operator? exact-integer?)
(assign-operation 'exp o:exp operator?)
(assign-operation 'sin o:sin operator?)
(assign-operation 'cos o:cos operator?)
|
