;; Standard Library Procedures and Macros ;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-;; LISTS
+;; MISC
+
+(define (not x) (if x #f #t))
-(define (null? args)
- (eq? args ()))
+(define (list . args) args)
(define (caar l) (car (car l)))
(define (cadr l) (car (cdr l)))
(define (cdar l) (cdr (car l)))
(define (cddr l) (cdr (cdr l)))
+(define (caaar l) (car (car (car l))))
+(define (caadr l) (car (car (cdr l))))
(define (cadar l) (car (cdr (car l))))
+(define (caddr l) (car (cdr (cdr l))))
+(define (cdaar l) (cdr (car (car l))))
+(define (cdadr l) (cdr (car (cdr l))))
+(define (cddar l) (cdr (cdr (car l))))
+(define (cdddr l) (cdr (cdr (cdr l))))
+(define (cadddr l) (car (cdr (cdr (cdr l)))))
+
+;; FUNCTIONAL PROGRAMMING
+
+(define (fold-left proc init l)
+ (if (null? l)
+ init
+ (fold-left proc (proc init (car l)) (cdr l))))
+
+(define (reduce-left proc init l)
+ (if (null? l)
+ init
+ (if (null? (cdr l))
+ (car l)
+ (fold-left proc (proc (car l) (car (cdr l))) (cdr (cdr l))))))
+
+(define (map proc l)
+ (if (null? l)
+ '()
+ (cons (proc (car l)) (map proc (cdr l)))))
+
+;; NUMBERS
+
+; Rational primitives
+
+(define (numerator x)
+ (if (ratnum? x)
+ (rat:numerator x)
+ x))
+
+(define (denominator x)
+ (if (ratnum? x)
+ (rat:denominator x)
+ (if (fixnum? x)
+ 1
+ 1.0)))
+
+(define (rat:+ x y)
+ (make-rational (fix:+ (fix:* (numerator x) (denominator y))
+ (fix:* (denominator x) (numerator y)))
+ (fix:* (denominator x) (denominator y))))
+
+(define (rat:- x y)
+ (make-rational (fix:- (fix:* (numerator x) (denominator y))
+ (fix:* (denominator x) (numerator y)))
+ (fix:* (denominator x) (denominator y))))
+
+(define (rat:* x y)
+ (make-rational (fix:* (numerator x) (numerator y))
+ (fix:* (denominator x) (denominator y))))
+
+(define (rat:/ x y)
+ (make-rational (fix:* (numerator x) (denominator y))
+ (fix:* (denominator x) (numerator y))))
+
+(define (rat:1/ x)
+ (make-rational (denominator x) (numerator x)))
+
+; Type dispatch and promotion
+
+(define (type-dispatch ops x)
+ (if (flonum? x)
+ ((cdr ops) x)
+ ((car ops) x)))
+
+(define (promote-dispatch ops x y)
+ (if (flonum? x)
+ (if (flonum? y)
+ ((cdr ops) x y)
+ ((cdr ops) x (fixnum->flonum y)))
+ (if (flonum? y)
+ ((cdr ops) (fixnum->flonum x) y)
+ ((car ops) x y))))
+
+; Unary ops
+
+(define (neg x)
+ (type-dispatch (cons fix:neg flo:neg) x))
+
+(define (abs x)
+ (type-dispatch (cons fix:abs flo:abs) x))
+
+(define (flo:1+ x) (flo:+ x 1.0))
+(define (flo:1- x) (flo:- x 1.0))
+
+(define (1+ n)
+ (type-dispatch (cons fix:1+ flo:1+) n))
+
+(define (1- n)
+ (type-dispatch (cons fix:1- flo:1-) n))
+
+(define (apply-to-flonum op x)
+ (if (flonum? x) (op x) x))
+
+(define (round x)
+ (apply-to-flonum flo:round x))
+(define (floor x)
+ (apply-to-flonum flo:floor x))
+(define (ceiling x)
+ (apply-to-flonum flo:ceiling x))
+(define (truncate x)
+ (apply-to-flonum flo:truncate x))
+
+; Binary operations
+
+(define (fix:/ x y) ; Non-standard definition while we don't have rationals
+ (if (fix:= 0 (fix:remainder x y))
+ (fix:quotient x y)
+ (flo:/ (fixnum->flonum x) (fixnum->flonum y))))
+
+(define (pair+ x y) (promote-dispatch (cons fix:+ flo:+) x y))
+(define (pair- x y) (promote-dispatch (cons fix:- flo:-) x y))
+(define (pair* x y) (promote-dispatch (cons fix:* flo:*) x y))
+(define (pair/ x y) (promote-dispatch (cons fix:/ flo:/) x y))
+
+(define (pair> x y) (promote-dispatch (cons fix:> flo:>) x y))
+(define (pair< x y) (promote-dispatch (cons fix:< flo:<) x y))
+(define (pair>= x y) (promote-dispatch (cons fix:>= flo:>=) x y))
+(define (pair<= x y) (promote-dispatch (cons fix:<= flo:<=) x y))
+(define (pair= x y) (promote-dispatch (cons fix:= flo:=) x y))
+
+(define (null? arg)
+ (eq? arg '()))
+
+(define (+ . args)
+ (fold-left pair+ 0 args))
+
+(define (- first . rest)
+ (if (null? rest)
+ (neg first)
+ (pair- first (apply + rest))))
+
+(define (* . args)
+ (fold-left pair* 1 args))
+
+(define (/ first . rest)
+ (if (null? rest)
+ (pair/ 1 first)
+ (pair/ first (apply * rest))))
+
+(define (quotient n1 n2)
+ (fix:quotient n1 n2))
+
+(define (remainder n1 n2)
+ (fix:remainder n1 n2))
+
+(define modulo remainder)
+
+; Relations
+
+(define (test-relation rel l)
+ (if (null? l)
+ #t
+ (if (null? (cdr l))
+ #t
+ (if (rel (car l) (car (cdr l)))
+ (test-relation rel (cdr l))
+ #f))))
+
+(define (= . args)
+ (test-relation pair= args))
+
+(define (> . args)
+ (test-relation pair> args))
+
+(define (< . args)
+ (test-relation pair< args))
+
+(define (>= . args)
+ (test-relation pair>= args))
+
+(define (<= . args)
+ (test-relation pair<= args))
+
+; Numeric tests
+
+(define (zero? x) (pair= x 0.0))
+(define (positive x) (pair> x 0.0))
+(define (odd? n) (pair= (remainder n 2) 0))
+(define (odd? n) (not (pair= (remainder n 2) 0)))
+
+
+; Current state of the numerical tower
+(define (complex? x) #f)
+(define (real? x) #t)
+(define (rational? x) #t)
+(define (integer? x) (= x (round x)))
+(define (exact? x) (fixnum? x))
+(define (inexact? x) (flonum? x))
+(define (number? x)
+ (if (fixnum? x) #t
+ (if (flonum? x) #t
+ (if (ratnum? x) #t #f))))
+
+;; LISTS
; Return number of items in list
(define (length l)
(define (iter a count)
(if (null? a)
count
- (iter (cdr a) (+ count 1))))
+ (iter (cdr a) (fix:+ count 1))))
(iter l 0))
; Join two lists together
; let
-(define (let-vars args)
- (if (null? args)
- '()
- (cons (caar args) (let-vars (cdr args)))))
+(define-macro (let args . body)
+ `((lambda ,(map (lambda (x) (car x)) args)
+ ,@body) ,@(map (lambda (x) (cadr x)) args)))
-(define (let-inits args)
- (if (null? args)
- '()
- (cons (cadar args) (let-inits (cdr args)))))
+; let*
-(define-macro (let args . body)
- `((lambda ,(let-vars args)
- ,@body) ,@(let-inits args)))
+(define-macro (let* args . body)
+ (if (null? args)
+ `(let () ,@body)
+ `(let (,(car args))
+ (let* ,(cdr args) ,@body))))
; while
; cond
-(define (cond-predicate clause) (car clause))
-(define (cond-actions clause) (cdr clause))
-(define (cond-else-clause? clause)
- (eq? (cond-predicate clause) 'else))
-
-(define (expand-clauses clauses)
- (if (null? clauses)
- (none)
- (let ((first (car clauses))
- (rest (cdr clauses)))
- (if (cond-else-clause? first)
- (if (null? rest)
- `(begin ,@(cond-actions first))
- (error "else clause isn't last in cond expression."))
- `(if ,(cond-predicate first)
- (begin ,@(cond-actions first))
- ,(expand-clauses rest))))))
-
-(define-macro (cond . clauses)
- (if (null? clauses)
- (error "cond requires at least one clause.")
- (expand-clauses clauses)))
+((lambda ()
+ (define (cond-predicate clause) (car clause))
+ (define (cond-actions clause) (cdr clause))
+ (define (cond-else-clause? clause)
+ (eq? (cond-predicate clause) 'else))
+
+ (define (expand-clauses clauses)
+ (if (null? clauses)
+ (none)
+ (let ((first (car clauses))
+ (rest (cdr clauses)))
+ (if (cond-else-clause? first)
+ (if (null? rest)
+ `(begin ,@(cond-actions first))
+ (error "else clause isn't last in cond expression."))
+ `(if ,(cond-predicate first)
+ (begin ,@(cond-actions first))
+ ,(expand-clauses rest))))))
+
+ (define-macro (cond . clauses)
+ (if (null? clauses)
+ (error "cond requires at least one clause.")
+ (expand-clauses clauses)))
+ ))
; and
-(define (expand-and-expressions expressions)
- (let ((first (car expressions))
- (rest (cdr expressions)))
- (if (null? rest)
- first
- `(if ,first
- ,(expand-and-expressions rest)
- #f))))
-
-(define-macro (and . expressions)
- (if (null? expressions)
- #t
- (expand-and-expressions expressions)))
+((lambda ()
+ (define (expand-and-expressions expressions)
+ (let ((first (car expressions))
+ (rest (cdr expressions)))
+ (if (null? rest)
+ first
+ `(if ,first
+ ,(expand-and-expressions rest)
+ #f))))
+
+ (define-macro (and . expressions)
+ (if (null? expressions)
+ #t
+ (expand-and-expressions expressions)))
+ ))
; or
-(define (expand-or-expressions expressions)
- (if (null? expressions)
- #f
- (let ((first (car expressions))
- (rest (cdr expressions))
- (val (gensym)))
- `(let ((,val ,first))
- (if ,val
- ,val
- ,(expand-or-expressions rest))))))
+((lambda ()
+ (define (expand-or-expressions expressions)
+ (if (null? expressions)
+ #f
+ (let ((first (car expressions))
+ (rest (cdr expressions))
+ (val (gensym)))
+ `(let ((,val ,first))
+ (if ,val
+ ,val
+ ,(expand-or-expressions rest))))))
-(define-macro (or . expressions)
- (expand-or-expressions expressions))
+ (define-macro (or . expressions)
+ (expand-or-expressions expressions))
+ ))
;; TESTING
(define (sum n)
(define (sum-iter total count maxcount)
- (if (> count maxcount)
+ (if (fix:> count maxcount)
total
- (sum-iter (+ total count) (+ count 1) maxcount)))
+ (sum-iter (fix:+ total count) (fix:+ count 1) maxcount)))
(sum-iter 0 1 n))
; Recursive summation. Use this to compare with tail call
; optimized iterative algorithm.
(define (sum-recurse n)
- (if (= n 0)
+ (if (fix:= n 0)
0
- (+ n (sum-recurse (- n 1)))))
+ (fix:+ n (sum-recurse (fix:- n 1)))))
+
+;; MISC
+
+(define (license)
+ (display
+"This program 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.
+
+This program 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 this program. If not, see http://www.gnu.org/licenses/.
+"))
+
+(define (welcome)
+ (display
+"Welcome to scheme.forth.jl!
+
+Copyright (C) 2016 Tim Vaughan.
+This program comes with ABSOLUTELY NO WARRANTY; for details type '(license)'.
+Use Ctrl-D to exit.
+"))
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