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+;;; -*- mode: scheme; coding: utf-8; -*-
+
+;;; Copyright (C) 2010 Free Software Foundation, Inc.
+;;; Copyright (c) 2005 Sebastian Egner and Jens Axel S{\o}gaard.
+;;;
+;;; This code is based on the file examples.scm in the reference
+;;; implementation of SRFI-67, provided under the following license:
+;;;
+;;; Permission is hereby granted, free of charge, to any person obtaining
+;;; a copy of this software and associated documentation files (the
+;;; ``Software''), to deal in the Software without restriction, including
+;;; without limitation the rights to use, copy, modify, merge, publish,
+;;; distribute, sublicense, and/or sell copies of the Software, and to
+;;; permit persons to whom the Software is furnished to do so, subject to
+;;; the following conditions:
+;;;
+;;; The above copyright notice and this permission notice shall be
+;;; included in all copies or substantial portions of the Software.
+;;;
+;;; THE SOFTWARE IS PROVIDED ``AS IS'', WITHOUT WARRANTY OF ANY KIND,
+;;; EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+;;; MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+;;; NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
+;;; LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+;;; OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+;;; WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+;;;
+
+(define-module (test-srfi-67)
+ #:use-module (test-suite lib)
+ #:use-module (srfi srfi-42)
+ #:use-module (srfi srfi-67))
+
+; =============================================================================
+
+; Test engine
+; ===========
+;
+; We use an extended version of the checker of SRFI-42 (with
+; Felix' reduction on codesize) for running a batch of tests for
+; the various procedures of 'compare.scm'. Moreover, we use the
+; comprehensions of SRFI-42 to generate examples systematically.
+
+; (my-check expr => desired-result)
+; evaluates expr and compares the value with desired-result.
+
+(define-syntax my-check
+ (syntax-rules (=>)
+ ((my-check expr => desired-result)
+ (my-check-proc 'expr (lambda () expr) desired-result))))
+
+(define (my-check-proc expr thunk desired-result)
+ (pass-if expr (equal? (thunk) desired-result)))
+
+; (my-check-ec <qualifier>* <ok?> <expr>)
+; runs (every?-ec <qualifier>* <ok?>), counting the times <ok?>
+; is evaluated as a correct example, and stopping at the first
+; counter example for which <expr> provides the argument.
+
+(define-syntax my-check-ec
+ (syntax-rules (nested)
+ ((my-check-ec (nested q1 ...) q etc1 etc2 etc ...)
+ (my-check-ec (nested q1 ... q) etc1 etc2 etc ...))
+ ((my-check-ec q1 q2 etc1 etc2 etc ...)
+ (my-check-ec (nested q1 q2) etc1 etc2 etc ...))
+ ((my-check-ec ok? expr)
+ (my-check-ec (nested) ok? expr))
+ ((my-check-ec (nested q ...) ok? expr)
+ (my-check-ec-proc
+ '(every?-ec q ... ok?)
+ (lambda ()
+ (first-ec
+ 'ok
+ (nested q ...)
+ (:let ok ok?)
+ (if (not ok))
+ (list expr)))
+ 'expr))
+ ((my-check-ec q ok? expr)
+ (my-check-ec (nested q) ok? expr))))
+
+(define (my-check-ec-proc expr thunk arg-counter-example)
+ (pass-if expr (eqv? (thunk) 'ok)))
+
+; =============================================================================
+
+; Abstractions etc.
+; =================
+
+(define ci integer-compare) ; very frequently used
+
+; (result-ok? actual desired)
+; tests if actual and desired specify the same ordering.
+
+(define (result-ok? actual desired)
+ (eqv? actual desired))
+
+; (my-check-compare compare increasing-elements)
+; evaluates (compare x y) for x, y in increasing-elements
+; and checks the result against -1, 0, or 1 depending on
+; the position of x and y in the list increasing-elements.
+
+(define-syntax my-check-compare
+ (syntax-rules ()
+ ((my-check-compare compare increasing-elements)
+ (my-check-ec
+ (:list x (index ix) increasing-elements)
+ (:list y (index iy) increasing-elements)
+ (result-ok? (compare x y) (ci ix iy))
+ (list x y)))))
+
+; sorted lists
+
+(define my-booleans '(#f #t))
+(define my-chars '(#\a #\b #\c))
+(define my-chars-ci '(#\a #\B #\c #\D))
+(define my-strings '("" "a" "aa" "ab" "b" "ba" "bb"))
+(define my-strings-ci '("" "a" "aA" "Ab" "B" "bA" "BB"))
+(define my-symbols '(a aa ab b ba bb))
+
+(define my-reals
+ (append-ec (:range xn -6 7)
+ (:let x (/ xn 3))
+ (list x (+ x (exact->inexact (/ 1 100))))))
+
+(define my-rationals
+ (list-ec (:list x my-reals)
+ (and (exact? x) (rational? x))
+ x))
+
+(define my-integers
+ (list-ec (:list x my-reals)
+ (if (and (exact? x) (integer? x)))
+ x))
+
+(define my-complexes
+ (list-ec (:list re-x my-reals)
+ (if (inexact? re-x))
+ (:list im-x my-reals)
+ (if (inexact? im-x))
+ (make-rectangular re-x im-x)))
+
+(define my-lists
+ '(() (1) (1 1) (1 2) (2) (2 1) (2 2)))
+
+(define my-vector-as-lists
+ (map list->vector my-lists))
+
+(define my-list-as-vectors
+ '(() (1) (2) (1 1) (1 2) (2 1) (2 2)))
+
+(define my-vectors
+ (map list->vector my-list-as-vectors))
+
+(define my-null-or-pairs
+ '(()
+ (1) (1 1) (1 2) (1 . 1) (1 . 2)
+ (2) (2 1) (2 2) (2 . 1) (2 . 2)))
+
+(define my-objects
+ (append my-null-or-pairs
+ my-booleans
+ my-chars
+ my-strings
+ my-symbols
+ my-integers
+ my-vectors))
+
+; =============================================================================
+
+; The checks
+; ==========
+
+(define (check:if3)
+
+ ; basic functionality
+
+ (my-check (if3 -1 'n 'z 'p) => 'n)
+ (my-check (if3 0 'n 'z 'p) => 'z)
+ (my-check (if3 1 'n 'z 'p) => 'p)
+
+ ; check arguments are evaluated only once
+
+ (my-check
+ (let ((x -1))
+ (if3 (let ((x0 x)) (set! x (+ x 1)) x0) 'n 'z 'p))
+ => 'n)
+
+ (my-check
+ (let ((x -1) (y 0))
+ (if3 (let ((x0 x)) (set! x (+ x 1)) x0)
+ (begin (set! y (+ y 1)) y)
+ (begin (set! y (+ y 10)) y)
+ (begin (set! y (+ y 100)) y)))
+ => 1)
+
+ (my-check
+ (let ((x 0) (y 0))
+ (if3 (let ((x0 x)) (set! x (+ x 1)) x0)
+ (begin (set! y (+ y 1)) y)
+ (begin (set! y (+ y 10)) y)
+ (begin (set! y (+ y 100)) y)))
+ => 10)
+
+ (my-check
+ (let ((x 1) (y 0))
+ (if3 (let ((x0 x)) (set! x (+ x 1)) x0)
+ (begin (set! y (+ y 1)) y)
+ (begin (set! y (+ y 10)) y)
+ (begin (set! y (+ y 100)) y)))
+ => 100)
+
+ ) ; check:if3
+
+(define-syntax my-check-if2
+ (syntax-rules ()
+ ((my-check-if2 if-rel? rel)
+ (begin
+ ; check result
+ (my-check (if-rel? -1 'yes 'no) => (if (rel -1 0) 'yes 'no))
+ (my-check (if-rel? 0 'yes 'no) => (if (rel 0 0) 'yes 'no))
+ (my-check (if-rel? 1 'yes 'no) => (if (rel 1 0) 'yes 'no))
+
+ ; check result of 'laterally challenged if'
+ (my-check (let ((x #f)) (if-rel? -1 (set! x #t)) x) => (rel -1 0))
+ (my-check (let ((x #f)) (if-rel? 0 (set! x #t)) x) => (rel 0 0))
+ (my-check (let ((x #f)) (if-rel? 1 (set! x #t)) x) => (rel 1 0))
+
+ ; check that <c> is evaluated exactly once
+ (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) -1) #t #f) n) => 1)
+ (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) 0) #t #f) n) => 1)
+ (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) 1) #t #f) n) => 1)
+ (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) -1) #t) n) => 1)
+ (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) 0) #t) n) => 1)
+ (my-check (let ((n 0)) (if-rel? (begin (set! n (+ n 1)) 1) #t) n) => 1)
+ ))))
+
+(define (check:ifs)
+
+ (my-check-if2 if=? =)
+ (my-check-if2 if<? <)
+ (my-check-if2 if>? >)
+ (my-check-if2 if<=? <=)
+ (my-check-if2 if>=? >=)
+ (my-check-if2 if-not=? (lambda (x y) (not (= x y))))
+
+ ) ; check:if2
+
+; <? etc. macros
+
+(define-syntax my-check-chain2
+ (syntax-rules ()
+ ((my-check-chain2 rel? rel)
+ (begin
+ ; all chains of length 2
+ (my-check (rel? ci 0 0) => (rel 0 0))
+ (my-check (rel? ci 0 1) => (rel 0 1))
+ (my-check (rel? ci 1 0) => (rel 1 0))
+
+ ; using default-compare
+ (my-check (rel? 0 0) => (rel 0 0))
+ (my-check (rel? 0 1) => (rel 0 1))
+ (my-check (rel? 1 0) => (rel 1 0))
+
+ ; as a combinator
+ (my-check ((rel? ci) 0 0) => (rel 0 0))
+ (my-check ((rel? ci) 0 1) => (rel 0 1))
+ (my-check ((rel? ci) 1 0) => (rel 1 0))
+
+ ; using default-compare as a combinator
+ (my-check ((rel?) 0 0) => (rel 0 0))
+ (my-check ((rel?) 0 1) => (rel 0 1))
+ (my-check ((rel?) 1 0) => (rel 1 0))
+ ))))
+
+(define (list->set xs) ; xs a list of integers
+ (if (null? xs)
+ '()
+ (let ((max-xs
+ (let max-without-apply ((m 1) (xs xs))
+ (if (null? xs)
+ m
+ (max-without-apply (max m (car xs)) (cdr xs))))))
+ (let ((in-xs? (make-vector (+ max-xs 1) #f)))
+ (do-ec (:list x xs) (vector-set! in-xs? x #t))
+ (list-ec (:vector in? (index x) in-xs?)
+ (if in?)
+ x)))))
+
+(define-syntax arguments-used ; set of arguments (integer, >=0) used in compare
+ (syntax-rules ()
+ ((arguments-used (rel1/rel2 compare arg ...))
+ (let ((used '()))
+ (rel1/rel2 (lambda (x y)
+ (set! used (cons x (cons y used)))
+ (compare x y))
+ arg ...)
+ (list->set used)))))
+
+(define-syntax my-check-chain3
+ (syntax-rules ()
+ ((my-check-chain3 rel1/rel2? rel1 rel2)
+ (begin
+ ; all chains of length 3
+ (my-check (rel1/rel2? ci 0 0 0) => (and (rel1 0 0) (rel2 0 0)))
+ (my-check (rel1/rel2? ci 0 0 1) => (and (rel1 0 0) (rel2 0 1)))
+ (my-check (rel1/rel2? ci 0 1 0) => (and (rel1 0 1) (rel2 1 0)))
+ (my-check (rel1/rel2? ci 1 0 0) => (and (rel1 1 0) (rel2 0 0)))
+ (my-check (rel1/rel2? ci 1 1 0) => (and (rel1 1 1) (rel2 1 0)))
+ (my-check (rel1/rel2? ci 1 0 1) => (and (rel1 1 0) (rel2 0 1)))
+ (my-check (rel1/rel2? ci 0 1 1) => (and (rel1 0 1) (rel2 1 1)))
+ (my-check (rel1/rel2? ci 0 1 2) => (and (rel1 0 1) (rel2 1 2)))
+ (my-check (rel1/rel2? ci 0 2 1) => (and (rel1 0 2) (rel2 2 1)))
+ (my-check (rel1/rel2? ci 1 2 0) => (and (rel1 1 2) (rel2 2 0)))
+ (my-check (rel1/rel2? ci 1 0 2) => (and (rel1 1 0) (rel2 0 2)))
+ (my-check (rel1/rel2? ci 2 0 1) => (and (rel1 2 0) (rel2 0 1)))
+ (my-check (rel1/rel2? ci 2 1 0) => (and (rel1 2 1) (rel2 1 0)))
+
+ ; using default-compare
+ (my-check (rel1/rel2? 0 0 0) => (and (rel1 0 0) (rel2 0 0)))
+ (my-check (rel1/rel2? 0 0 1) => (and (rel1 0 0) (rel2 0 1)))
+ (my-check (rel1/rel2? 0 1 0) => (and (rel1 0 1) (rel2 1 0)))
+ (my-check (rel1/rel2? 1 0 0) => (and (rel1 1 0) (rel2 0 0)))
+ (my-check (rel1/rel2? 1 1 0) => (and (rel1 1 1) (rel2 1 0)))
+ (my-check (rel1/rel2? 1 0 1) => (and (rel1 1 0) (rel2 0 1)))
+ (my-check (rel1/rel2? 0 1 1) => (and (rel1 0 1) (rel2 1 1)))
+ (my-check (rel1/rel2? 0 1 2) => (and (rel1 0 1) (rel2 1 2)))
+ (my-check (rel1/rel2? 0 2 1) => (and (rel1 0 2) (rel2 2 1)))
+ (my-check (rel1/rel2? 1 2 0) => (and (rel1 1 2) (rel2 2 0)))
+ (my-check (rel1/rel2? 1 0 2) => (and (rel1 1 0) (rel2 0 2)))
+ (my-check (rel1/rel2? 2 0 1) => (and (rel1 2 0) (rel2 0 1)))
+ (my-check (rel1/rel2? 2 1 0) => (and (rel1 2 1) (rel2 1 0)))
+
+ ; as a combinator
+ (my-check ((rel1/rel2? ci) 0 0 0) => (and (rel1 0 0) (rel2 0 0)))
+ (my-check ((rel1/rel2? ci) 0 0 1) => (and (rel1 0 0) (rel2 0 1)))
+ (my-check ((rel1/rel2? ci) 0 1 0) => (and (rel1 0 1) (rel2 1 0)))
+ (my-check ((rel1/rel2? ci) 1 0 0) => (and (rel1 1 0) (rel2 0 0)))
+ (my-check ((rel1/rel2? ci) 1 1 0) => (and (rel1 1 1) (rel2 1 0)))
+ (my-check ((rel1/rel2? ci) 1 0 1) => (and (rel1 1 0) (rel2 0 1)))
+ (my-check ((rel1/rel2? ci) 0 1 1) => (and (rel1 0 1) (rel2 1 1)))
+ (my-check ((rel1/rel2? ci) 0 1 2) => (and (rel1 0 1) (rel2 1 2)))
+ (my-check ((rel1/rel2? ci) 0 2 1) => (and (rel1 0 2) (rel2 2 1)))
+ (my-check ((rel1/rel2? ci) 1 2 0) => (and (rel1 1 2) (rel2 2 0)))
+ (my-check ((rel1/rel2? ci) 1 0 2) => (and (rel1 1 0) (rel2 0 2)))
+ (my-check ((rel1/rel2? ci) 2 0 1) => (and (rel1 2 0) (rel2 0 1)))
+ (my-check ((rel1/rel2? ci) 2 1 0) => (and (rel1 2 1) (rel2 1 0)))
+
+ ; as a combinator using default-compare
+ (my-check ((rel1/rel2?) 0 0 0) => (and (rel1 0 0) (rel2 0 0)))
+ (my-check ((rel1/rel2?) 0 0 1) => (and (rel1 0 0) (rel2 0 1)))
+ (my-check ((rel1/rel2?) 0 1 0) => (and (rel1 0 1) (rel2 1 0)))
+ (my-check ((rel1/rel2?) 1 0 0) => (and (rel1 1 0) (rel2 0 0)))
+ (my-check ((rel1/rel2?) 1 1 0) => (and (rel1 1 1) (rel2 1 0)))
+ (my-check ((rel1/rel2?) 1 0 1) => (and (rel1 1 0) (rel2 0 1)))
+ (my-check ((rel1/rel2?) 0 1 1) => (and (rel1 0 1) (rel2 1 1)))
+ (my-check ((rel1/rel2?) 0 1 2) => (and (rel1 0 1) (rel2 1 2)))
+ (my-check ((rel1/rel2?) 0 2 1) => (and (rel1 0 2) (rel2 2 1)))
+ (my-check ((rel1/rel2?) 1 2 0) => (and (rel1 1 2) (rel2 2 0)))
+ (my-check ((rel1/rel2?) 1 0 2) => (and (rel1 1 0) (rel2 0 2)))
+ (my-check ((rel1/rel2?) 2 0 1) => (and (rel1 2 0) (rel2 0 1)))
+ (my-check ((rel1/rel2?) 2 1 0) => (and (rel1 2 1) (rel2 1 0)))
+
+ ; test if all arguments are type checked
+ (my-check (arguments-used (rel1/rel2? ci 0 1 2)) => '(0 1 2))
+ (my-check (arguments-used (rel1/rel2? ci 0 2 1)) => '(0 1 2))
+ (my-check (arguments-used (rel1/rel2? ci 1 2 0)) => '(0 1 2))
+ (my-check (arguments-used (rel1/rel2? ci 1 0 2)) => '(0 1 2))
+ (my-check (arguments-used (rel1/rel2? ci 2 0 1)) => '(0 1 2))
+ (my-check (arguments-used (rel1/rel2? ci 2 1 0)) => '(0 1 2))
+ ))))
+
+(define-syntax my-check-chain
+ (syntax-rules ()
+ ((my-check-chain chain-rel? rel)
+ (begin
+ ; the chain of length 0
+ (my-check (chain-rel? ci) => #t)
+
+ ; a chain of length 1
+ (my-check (chain-rel? ci 0) => #t)
+
+ ; all chains of length 2
+ (my-check (chain-rel? ci 0 0) => (rel 0 0))
+ (my-check (chain-rel? ci 0 1) => (rel 0 1))
+ (my-check (chain-rel? ci 1 0) => (rel 1 0))
+
+ ; all chains of length 3
+ (my-check (chain-rel? ci 0 0 0) => (rel 0 0 0))
+ (my-check (chain-rel? ci 0 0 1) => (rel 0 0 1))
+ (my-check (chain-rel? ci 0 1 0) => (rel 0 1 0))
+ (my-check (chain-rel? ci 1 0 0) => (rel 1 0 0))
+ (my-check (chain-rel? ci 1 1 0) => (rel 1 1 0))
+ (my-check (chain-rel? ci 1 0 1) => (rel 1 0 1))
+ (my-check (chain-rel? ci 0 1 1) => (rel 0 1 1))
+ (my-check (chain-rel? ci 0 1 2) => (rel 0 1 2))
+ (my-check (chain-rel? ci 0 2 1) => (rel 0 2 1))
+ (my-check (chain-rel? ci 1 2 0) => (rel 1 2 0))
+ (my-check (chain-rel? ci 1 0 2) => (rel 1 0 2))
+ (my-check (chain-rel? ci 2 0 1) => (rel 2 0 1))
+ (my-check (chain-rel? ci 2 1 0) => (rel 2 1 0))
+
+ ; check if all arguments are used
+ (my-check (arguments-used (chain-rel? ci 0)) => '(0))
+ (my-check (arguments-used (chain-rel? ci 0 1)) => '(0 1))
+ (my-check (arguments-used (chain-rel? ci 1 0)) => '(0 1))
+ (my-check (arguments-used (chain-rel? ci 0 1 2)) => '(0 1 2))
+ (my-check (arguments-used (chain-rel? ci 0 2 1)) => '(0 1 2))
+ (my-check (arguments-used (chain-rel? ci 1 2 0)) => '(0 1 2))
+ (my-check (arguments-used (chain-rel? ci 1 0 2)) => '(0 1 2))
+ (my-check (arguments-used (chain-rel? ci 2 0 1)) => '(0 1 2))
+ (my-check (arguments-used (chain-rel? ci 2 1 0)) => '(0 1 2))
+ ))))
+
+(define (check:predicates-from-compare)
+
+ (my-check-chain2 =? =)
+ (my-check-chain2 <? <)
+ (my-check-chain2 >? >)
+ (my-check-chain2 <=? <=)
+ (my-check-chain2 >=? >=)
+ (my-check-chain2 not=? (lambda (x y) (not (= x y))))
+
+ (my-check-chain3 </<? < <)
+ (my-check-chain3 </<=? < <=)
+ (my-check-chain3 <=/<? <= <)
+ (my-check-chain3 <=/<=? <= <=)
+
+ (my-check-chain3 >/>? > >)
+ (my-check-chain3 >/>=? > >=)
+ (my-check-chain3 >=/>? >= >)
+ (my-check-chain3 >=/>=? >= >=)
+
+ (my-check-chain chain=? =)
+ (my-check-chain chain<? <)
+ (my-check-chain chain>? >)
+ (my-check-chain chain<=? <=)
+ (my-check-chain chain>=? >=)
+
+ ) ; check:predicates-from-compare
+
+; pairwise-not=?
+
+(define pairwise-not=?:long-sequences
+ (let ()
+
+ (define (extremal-pivot-sequence r)
+ ; The extremal pivot sequence of order r is a
+ ; permutation of {0..2^(r+1)-2} such that the
+ ; middle element is minimal, and this property
+ ; holds recursively for each binary subdivision.
+ ; This sequence exposes a naive implementation of
+ ; pairwise-not=? chosing the middle element as pivot.
+ (if (zero? r)
+ '(0)
+ (let* ((s (extremal-pivot-sequence (- r 1)))
+ (ns (length s)))
+ (append (list-ec (:list x s) (+ x 1))
+ '(0)
+ (list-ec (:list x s) (+ x ns 1))))))
+
+ (list (list-ec (: i 4096) i)
+ (list-ec (: i 4097 0 -1) i)
+ (list-ec (: i 4099) (modulo (* 1003 i) 4099))
+ (extremal-pivot-sequence 11))))
+
+(define pairwise-not=?:short-sequences
+ (let ()
+
+ (define (combinations/repeats n l)
+ ; return list of all sublists of l of size n,
+ ; the order of the elements occur in the sublists
+ ; of the output is the same as in the input
+ (let ((len (length l)))
+ (cond
+ ((= n 0) '())
+ ((= n 1) (map list l))
+ ((= len 1) (do ((r '() (cons (car l) r))
+ (i n (- i 1)))
+ ((= i 0) (list r))))
+ (else (append (combinations/repeats n (cdr l))
+ (map (lambda (c) (cons (car l) c))
+ (combinations/repeats (- n 1) l)))))))
+
+ (define (permutations l)
+ ; return a list of all permutations of l
+ (let ((len (length l)))
+ (cond
+ ((= len 0) '(()))
+ ((= len 1) (list l))
+ (else (apply append
+ (map (lambda (p) (insert-every-where (car l) p))
+ (permutations (cdr l))))))))
+
+ (define (insert-every-where x xs)
+ (let loop ((result '()) (before '()) (after xs))
+ (let ((new (append before (cons x after))))
+ (cond
+ ((null? after) (cons new result))
+ (else (loop (cons new result)
+ (append before (list (car after)))
+ (cdr after)))))))
+
+ (define (sequences n max)
+ (apply append
+ (map permutations
+ (combinations/repeats n (list-ec (: i max) i)))))
+
+ (append-ec (: n 5) (sequences n 5))))
+
+(define (colliding-compare x y)
+ (ci (modulo x 3) (modulo y 3)))
+
+(define (naive-pairwise-not=? compare . xs)
+ (let ((xs (list->vector xs)))
+ (every?-ec (:range i (- (vector-length xs) 1))
+ (:let xs-i (vector-ref xs i))
+ (:range j (+ i 1) (vector-length xs))
+ (:let xs-j (vector-ref xs j))
+ (not=? compare xs-i xs-j))))
+
+(define (check:pairwise-not=?)
+
+ ; 0-ary, 1-ary
+ (my-check (pairwise-not=? ci) => #t)
+ (my-check (pairwise-not=? ci 0) => #t)
+
+ ; 2-ary
+ (my-check (pairwise-not=? ci 0 0) => #f)
+ (my-check (pairwise-not=? ci 0 1) => #t)
+ (my-check (pairwise-not=? ci 1 0) => #t)
+
+ ; 3-ary
+ (my-check (pairwise-not=? ci 0 0 0) => #f)
+ (my-check (pairwise-not=? ci 0 0 1) => #f)
+ (my-check (pairwise-not=? ci 0 1 0) => #f)
+ (my-check (pairwise-not=? ci 1 0 0) => #f)
+ (my-check (pairwise-not=? ci 1 1 0) => #f)
+ (my-check (pairwise-not=? ci 1 0 1) => #f)
+ (my-check (pairwise-not=? ci 0 1 1) => #f)
+ (my-check (pairwise-not=? ci 0 1 2) => #t)
+ (my-check (pairwise-not=? ci 0 2 1) => #t)
+ (my-check (pairwise-not=? ci 1 2 0) => #t)
+ (my-check (pairwise-not=? ci 1 0 2) => #t)
+ (my-check (pairwise-not=? ci 2 0 1) => #t)
+ (my-check (pairwise-not=? ci 2 1 0) => #t)
+
+ ; n-ary, n large: [0..n-1], [n,n-1..1], 5^[0..96] mod 97
+ (my-check (apply pairwise-not=? ci (list-ec (: i 10) i)) => #t)
+ (my-check (apply pairwise-not=? ci (list-ec (: i 100) i)) => #t)
+ (my-check (apply pairwise-not=? ci (list-ec (: i 1000) i)) => #t)
+
+ (my-check (apply pairwise-not=? ci (list-ec (: i 10 0 -1) i)) => #t)
+ (my-check (apply pairwise-not=? ci (list-ec (: i 100 0 -1) i)) => #t)
+ (my-check (apply pairwise-not=? ci (list-ec (: i 1000 0 -1) i)) => #t)
+
+ (my-check (apply pairwise-not=? ci
+ (list-ec (: i 97) (modulo (* 5 i) 97)))
+ => #t)
+
+ ; bury another copy of 72 = 5^50 mod 97 in 5^[0..96] mod 97
+ (my-check (apply pairwise-not=? ci
+ (append (list-ec (: i 0 23) (modulo (* 5 i) 97))
+ '(72)
+ (list-ec (: i 23 97) (modulo (* 5 i) 97))))
+ => #f)
+ (my-check (apply pairwise-not=? ci
+ (append (list-ec (: i 0 75) (modulo (* 5 i) 97))
+ '(72)
+ (list-ec (: i 75 97) (modulo (* 5 i) 97))))
+ => #f)
+
+ ; check if all arguments are used
+ (my-check (arguments-used (pairwise-not=? ci 0)) => '(0))
+ (my-check (arguments-used (pairwise-not=? ci 0 1)) => '(0 1))
+ (my-check (arguments-used (pairwise-not=? ci 1 0)) => '(0 1))
+ (my-check (arguments-used (pairwise-not=? ci 0 2 1)) => '(0 1 2))
+ (my-check (arguments-used (pairwise-not=? ci 1 2 0)) => '(0 1 2))
+ (my-check (arguments-used (pairwise-not=? ci 1 0 2)) => '(0 1 2))
+ (my-check (arguments-used (pairwise-not=? ci 2 0 1)) => '(0 1 2))
+ (my-check (arguments-used (pairwise-not=? ci 2 1 0)) => '(0 1 2))
+ (my-check (arguments-used (pairwise-not=? ci 0 0 0 1 0 0 0 2 0 0 0 3))
+ => '(0 1 2 3))
+
+ ; Guess if the implementation is O(n log n):
+ ; The test is run for 2^e pairwise unequal inputs, e >= 1,
+ ; and the number of calls to the compare procedure is counted.
+ ; all pairs: A = Binomial[2^e, 2] = 2^(2 e - 1) * (1 - 2^-e).
+ ; divide and conquer: D = e 2^e.
+ ; Since an implementation can be randomized, the actual count may
+ ; be a random number. We put a threshold at 100 e 2^e and choose
+ ; e such that A/D >= 150, i.e. e >= 12.
+ ; The test is applied to several inputs that are known to cause
+ ; trouble in simplistic sorting algorithms: (0..2^e-1), (2^e+1,2^e..1),
+ ; a pseudo-random permutation, and a sequence with an extremal pivot
+ ; at the center of each subsequence.
+
+ (my-check-ec
+ (:list input pairwise-not=?:long-sequences)
+ (let ((compares 0))
+ (apply pairwise-not=?
+ (lambda (x y)
+ (set! compares (+ compares 1))
+ (ci x y))
+ input)
+ ; (display compares) (newline)
+ (< compares (* 100 12 4096)))
+ (length input))
+
+ ; check many short sequences
+
+ (my-check-ec
+ (:list input pairwise-not=?:short-sequences)
+ (eq?
+ (apply pairwise-not=? colliding-compare input)
+ (apply naive-pairwise-not=? colliding-compare input))
+ input)
+
+ ; check if the arguments are used for short sequences
+
+ (my-check-ec
+ (:list input pairwise-not=?:short-sequences)
+ (let ((args '()))
+ (apply pairwise-not=?
+ (lambda (x y)
+ (set! args (cons x (cons y args)))
+ (colliding-compare x y))
+ input)
+ (equal? (list->set args) (list->set input)))
+ input)
+
+ ) ; check:pairwise-not=?
+
+
+; min/max
+
+(define min/max:sequences
+ (append pairwise-not=?:short-sequences
+ pairwise-not=?:long-sequences))
+
+(define (check:min/max)
+
+ ; all lists of length 1,2,3
+ (my-check (min-compare ci 0) => 0)
+ (my-check (min-compare ci 0 0) => 0)
+ (my-check (min-compare ci 0 1) => 0)
+ (my-check (min-compare ci 1 0) => 0)
+ (my-check (min-compare ci 0 0 0) => 0)
+ (my-check (min-compare ci 0 0 1) => 0)
+ (my-check (min-compare ci 0 1 0) => 0)
+ (my-check (min-compare ci 1 0 0) => 0)
+ (my-check (min-compare ci 1 1 0) => 0)
+ (my-check (min-compare ci 1 0 1) => 0)
+ (my-check (min-compare ci 0 1 1) => 0)
+ (my-check (min-compare ci 0 1 2) => 0)
+ (my-check (min-compare ci 0 2 1) => 0)
+ (my-check (min-compare ci 1 2 0) => 0)
+ (my-check (min-compare ci 1 0 2) => 0)
+ (my-check (min-compare ci 2 0 1) => 0)
+ (my-check (min-compare ci 2 1 0) => 0)
+
+ (my-check (max-compare ci 0) => 0)
+ (my-check (max-compare ci 0 0) => 0)
+ (my-check (max-compare ci 0 1) => 1)
+ (my-check (max-compare ci 1 0) => 1)
+ (my-check (max-compare ci 0 0 0) => 0)
+ (my-check (max-compare ci 0 0 1) => 1)
+ (my-check (max-compare ci 0 1 0) => 1)
+ (my-check (max-compare ci 1 0 0) => 1)
+ (my-check (max-compare ci 1 1 0) => 1)
+ (my-check (max-compare ci 1 0 1) => 1)
+ (my-check (max-compare ci 0 1 1) => 1)
+ (my-check (max-compare ci 0 1 2) => 2)
+ (my-check (max-compare ci 0 2 1) => 2)
+ (my-check (max-compare ci 1 2 0) => 2)
+ (my-check (max-compare ci 1 0 2) => 2)
+ (my-check (max-compare ci 2 0 1) => 2)
+ (my-check (max-compare ci 2 1 0) => 2)
+
+ ; check that the first minimal value is returned
+ (my-check (min-compare (pair-compare-car ci)
+ '(0 1) '(0 2) '(0 3))
+ => '(0 1))
+ (my-check (max-compare (pair-compare-car ci)
+ '(0 1) '(0 2) '(0 3))
+ => '(0 1))
+
+ ; check for many inputs
+ (my-check-ec
+ (:list input min/max:sequences)
+ (= (apply min-compare ci input)
+ (apply min (apply max input) input))
+ input)
+ (my-check-ec
+ (:list input min/max:sequences)
+ (= (apply max-compare ci input)
+ (apply max (apply min input) input))
+ input)
+ ; Note the stupid extra argument in the apply for
+ ; the standard min/max makes sure the elements are
+ ; identical when apply truncates the arglist.
+
+ ) ; check:min/max
+
+
+; kth-largest
+
+(define kth-largest:sequences
+ pairwise-not=?:short-sequences)
+
+(define (naive-kth-largest compare k . xs)
+ (let ((vec (list->vector xs)))
+ ; bubble sort: simple, stable, O(|xs|^2)
+ (do-ec (:range n (- (vector-length vec) 1))
+ (:range i 0 (- (- (vector-length vec) 1) n))
+ (if>? (compare (vector-ref vec i)
+ (vector-ref vec (+ i 1)))
+ (let ((vec-i (vector-ref vec i)))
+ (vector-set! vec i (vector-ref vec (+ i 1)))
+ (vector-set! vec (+ i 1) vec-i))))
+ (vector-ref vec (modulo k (vector-length vec)))))
+
+(define (check:kth-largest)
+
+ ; check extensively against naive-kth-largest
+ (my-check-ec
+ (:list input kth-largest:sequences)
+ (: k (- -2 (length input)) (+ (length input) 2))
+ (= (apply naive-kth-largest colliding-compare k input)
+ (apply kth-largest colliding-compare k input))
+ (list input k))
+
+ ) ;check:kth-largest
+
+; compare-by< etc. procedures
+
+(define (check:compare-from-predicates)
+
+ (my-check-compare
+ (compare-by< <)
+ my-integers)
+
+ (my-check-compare
+ (compare-by> >)
+ my-integers)
+
+ (my-check-compare
+ (compare-by<= <=)
+ my-integers)
+
+ (my-check-compare
+ (compare-by>= >=)
+ my-integers)
+
+ (my-check-compare
+ (compare-by=/< = <)
+ my-integers)
+
+ (my-check-compare
+ (compare-by=/> = >)
+ my-integers)
+
+ ; with explicit arguments
+
+ (my-check-compare
+ (lambda (x y) (compare-by< < x y))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y) (compare-by> > x y))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y) (compare-by<= <= x y))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y) (compare-by>= >= x y))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y) (compare-by=/< = < x y))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y) (compare-by=/> = > x y))
+ my-integers)
+
+ ) ; check:compare-from-predicates
+
+
+(define (check:atomic)
+
+ (my-check-compare boolean-compare my-booleans)
+
+ (my-check-compare char-compare my-chars)
+
+ (my-check-compare char-compare-ci my-chars-ci)
+
+ (my-check-compare string-compare my-strings)
+
+ (my-check-compare string-compare-ci my-strings-ci)
+
+ (my-check-compare symbol-compare my-symbols)
+
+ (my-check-compare integer-compare my-integers)
+
+ (my-check-compare rational-compare my-rationals)
+
+ (my-check-compare real-compare my-reals)
+
+ (my-check-compare complex-compare my-complexes)
+
+ (my-check-compare number-compare my-complexes)
+
+ ) ; check:atomic
+
+(define (check:refine-select-cond)
+
+ ; refine-compare
+
+ (my-check-compare
+ (lambda (x y) (refine-compare))
+ '(#f))
+
+ (my-check-compare
+ (lambda (x y) (refine-compare (integer-compare x y)))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y)
+ (refine-compare (integer-compare (car x) (car y))
+ (symbol-compare (cdr x) (cdr y))))
+ '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c)))
+
+ (my-check-compare
+ (lambda (x y)
+ (refine-compare (integer-compare (car x) (car y))
+ (symbol-compare (cadr x) (cadr y))
+ (string-compare (caddr x) (caddr y))))
+ '((1 a "a") (1 b "a") (1 b "b") (2 b "c") (2 c "a") (3 a "b") (3 c "b")))
+
+ ; select-compare
+
+ (my-check-compare
+ (lambda (x y) (select-compare x y))
+ '(#f))
+
+ (my-check-compare
+ (lambda (x y)
+ (select-compare x y
+ (integer? (ci x y))))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y)
+ (select-compare x y
+ (pair? (integer-compare (car x) (car y))
+ (symbol-compare (cdr x) (cdr y)))))
+ '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c)))
+
+ (my-check-compare
+ (lambda (x y)
+ (select-compare x y
+ (else (integer-compare x y))))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y)
+ (select-compare x y
+ (else (integer-compare (car x) (car y))
+ (symbol-compare (cdr x) (cdr y)))))
+ '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c)))
+
+ (my-check-compare
+ (lambda (x y)
+ (select-compare x y
+ (symbol? (symbol-compare x y))
+ (string? (string-compare x y))))
+ '(a b c "a" "b" "c" 1)) ; implicit (else 0)
+
+ (my-check-compare
+ (lambda (x y)
+ (select-compare x y
+ (symbol? (symbol-compare x y))
+ (else (string-compare x y))))
+ '(a b c "a" "b" "c"))
+
+ ; test if arguments are only evaluated once
+
+ (my-check
+ (let ((nx 0) (ny 0) (nt 0))
+ (select-compare (begin (set! nx (+ nx 1)) 1)
+ (begin (set! ny (+ ny 1)) 2)
+ ((lambda (z) (set! nt (+ nt 1)) #f) 0)
+ ((lambda (z) (set! nt (+ nt 10)) #f) 0)
+ ((lambda (z) (set! nt (+ nt 100)) #f) 0)
+ (else 0))
+ (list nx ny nt))
+ => '(1 1 222))
+
+ ; cond-compare
+
+ (my-check-compare
+ (lambda (x y) (cond-compare))
+ '(#f))
+
+ (my-check-compare
+ (lambda (x y)
+ (cond-compare
+ (((integer? x) (integer? y)) (integer-compare x y))))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y)
+ (cond-compare
+ (((pair? x) (pair? y)) (integer-compare (car x) (car y))
+ (symbol-compare (cdr x) (cdr y)))))
+ '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c)))
+
+ (my-check-compare
+ (lambda (x y)
+ (cond-compare
+ (else (integer-compare x y))))
+ my-integers)
+
+ (my-check-compare
+ (lambda (x y)
+ (cond-compare
+ (else (integer-compare (car x) (car y))
+ (symbol-compare (cdr x) (cdr y)))))
+ '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a) (3 . c)))
+
+ (my-check-compare
+ (lambda (x y)
+ (cond-compare
+ (((symbol? x) (symbol? y)) (symbol-compare x y))
+ (((string? x) (string? y)) (string-compare x y))))
+ '(a b c "a" "b" "c" 1)) ; implicit (else 0)
+
+ (my-check-compare
+ (lambda (x y)
+ (cond-compare
+ (((symbol? x) (symbol? y)) (symbol-compare x y))
+ (else (string-compare x y))))
+ '(a b c "a" "b" "c"))
+
+ ) ; check:refine-select-cond
+
+
+; We define our own list/vector data structure
+; as '(my-list x[1] .. x[n]), n >= 0, in order
+; to make sure the default ops don't work on it.
+
+(define (my-list-checked obj)
+ (if (and (list? obj) (eqv? (car obj) 'my-list))
+ obj
+ (error "expected my-list but received" obj)))
+
+(define (list->my-list list) (cons 'my-list list))
+(define (my-empty? x) (null? (cdr (my-list-checked x))))
+(define (my-head x) (cadr (my-list-checked x)))
+(define (my-tail x) (cons 'my-list (cddr (my-list-checked x))))
+(define (my-size x) (- (length (my-list-checked x)) 1))
+(define (my-ref x i) (list-ref (my-list-checked x) (+ i 1)))
+
+(define (check:data-structures)
+
+ (my-check-compare
+ (pair-compare-car ci)
+ '((1 . b) (2 . a) (3 . c)))
+
+ (my-check-compare
+ (pair-compare-cdr ci)
+ '((b . 1) (a . 2) (c . 3)))
+
+ ; pair-compare
+
+ (my-check-compare pair-compare my-null-or-pairs)
+
+ (my-check-compare
+ (lambda (x y) (pair-compare ci x y))
+ my-null-or-pairs)
+
+ (my-check-compare
+ (lambda (x y) (pair-compare ci symbol-compare x y))
+ '((1 . a) (1 . b) (2 . b) (2 . c) (3 . a)))
+
+ ; list-compare
+
+ (my-check-compare list-compare my-lists)
+
+ (my-check-compare
+ (lambda (x y) (list-compare ci x y))
+ my-lists)
+
+ (my-check-compare
+ (lambda (x y) (list-compare x y my-empty? my-head my-tail))
+ (map list->my-list my-lists))
+
+ (my-check-compare
+ (lambda (x y) (list-compare ci x y my-empty? my-head my-tail))
+ (map list->my-list my-lists))
+
+ ; list-compare-as-vector
+
+ (my-check-compare list-compare-as-vector my-list-as-vectors)
+
+ (my-check-compare
+ (lambda (x y) (list-compare-as-vector ci x y))
+ my-list-as-vectors)
+
+ (my-check-compare
+ (lambda (x y) (list-compare-as-vector x y my-empty? my-head my-tail))
+ (map list->my-list my-list-as-vectors))
+
+ (my-check-compare
+ (lambda (x y) (list-compare-as-vector ci x y my-empty? my-head my-tail))
+ (map list->my-list my-list-as-vectors))
+
+ ; vector-compare
+
+ (my-check-compare vector-compare my-vectors)
+
+ (my-check-compare
+ (lambda (x y) (vector-compare ci x y))
+ my-vectors)
+
+ (my-check-compare
+ (lambda (x y) (vector-compare x y my-size my-ref))
+ (map list->my-list my-list-as-vectors))
+
+ (my-check-compare
+ (lambda (x y) (vector-compare ci x y my-size my-ref))
+ (map list->my-list my-list-as-vectors))
+
+ ; vector-compare-as-list
+
+ (my-check-compare vector-compare-as-list my-vector-as-lists)
+
+ (my-check-compare
+ (lambda (x y) (vector-compare-as-list ci x y))
+ my-vector-as-lists)
+
+ (my-check-compare
+ (lambda (x y) (vector-compare-as-list x y my-size my-ref))
+ (map list->my-list my-lists))
+
+ (my-check-compare
+ (lambda (x y) (vector-compare-as-list ci x y my-size my-ref))
+ (map list->my-list my-lists))
+
+ ) ; check:data-structures
+
+
+(define (check:default-compare)
+
+ (my-check-compare default-compare my-objects)
+
+ ; check if default-compare refines pair-compare
+
+ (my-check-ec
+ (:list x (index ix) my-objects)
+ (:list y (index iy) my-objects)
+ (:let c-coarse (pair-compare x y))
+ (:let c-fine (default-compare x y))
+ (or (eqv? c-coarse 0) (eqv? c-fine c-coarse))
+ (list x y))
+
+ ; check if default-compare passes on debug-compare
+
+ (my-check-compare (debug-compare default-compare) my-objects)
+
+ ) ; check:default-compare
+
+
+(define (sort-by-less xs pred) ; trivial quicksort
+ (if (or (null? xs) (null? (cdr xs)))
+ xs
+ (append
+ (sort-by-less (list-ec (:list x (cdr xs))
+ (if (pred x (car xs)))
+ x)
+ pred)
+ (list (car xs))
+ (sort-by-less (list-ec (:list x (cdr xs))
+ (if (not (pred x (car xs))))
+ x)
+ pred))))
+
+(define (check:more-examples)
+
+ ; define recursive order on tree type (nodes are dotted pairs)
+
+ (my-check-compare
+ (letrec ((c (lambda (x y)
+ (cond-compare (((null? x) (null? y)) 0)
+ (else (pair-compare c c x y))))))
+ c)
+ (list '() (list '()) (list '() '()) (list (list '())))
+ ;'(() (() . ()) (() . (() . ())) ((() . ()) . ())) ; Chicken can't parse this ?
+ )
+
+ ; redefine default-compare using select-compare
+
+ (my-check-compare
+ (letrec ((c (lambda (x y)
+ (select-compare x y
+ (null? 0)
+ (pair? (pair-compare c c x y))
+ (boolean? (boolean-compare x y))
+ (char? (char-compare x y))
+ (string? (string-compare x y))
+ (symbol? (symbol-compare x y))
+ (number? (number-compare x y))
+ (vector? (vector-compare c x y))
+ (else (error "unrecognized type in c" x y))))))
+ c)
+ my-objects)
+
+ ; redefine default-compare using cond-compare
+
+ (my-check-compare
+ (letrec ((c (lambda (x y)
+ (cond-compare
+ (((null? x) (null? y)) 0)
+ (((pair? x) (pair? y)) (pair-compare c c x y))
+ (((boolean? x) (boolean? y)) (boolean-compare x y))
+ (((char? x) (char? y)) (char-compare x y))
+ (((string? x) (string? y)) (string-compare x y))
+ (((symbol? x) (symbol? y)) (symbol-compare x y))
+ (((number? x) (number? y)) (number-compare x y))
+ (((vector? x) (vector? y)) (vector-compare c x y))
+ (else (error "unrecognized type in c" x y))))))
+ c)
+ my-objects)
+
+ ; compare strings with character order reversed
+
+ (my-check-compare
+ (lambda (x y)
+ (vector-compare-as-list
+ (lambda (x y) (char-compare y x))
+ x y string-length string-ref))
+ '("" "b" "bb" "ba" "a" "ab" "aa"))
+
+ ; examples from SRFI text for <? etc.
+
+ (my-check (>? "laugh" "LOUD") => #t)
+ (my-check (<? string-compare-ci "laugh" "LOUD") => #t)
+ (my-check (sort-by-less '(1 a "b") (<?)) => '("b" a 1))
+ (my-check (sort-by-less '(1 a "b") (>?)) => '(1 a "b"))
+
+ ) ; check:more-examples
+
+
+; Real life examples
+; ==================
+
+; (update/insert compare x s)
+; inserts x into list s, or updates an equivalent element by x.
+; It is assumed that s is sorted with respect to compare,
+; i.e. (apply chain<=? compare s). The result is a list with x
+; replacing the first element s[i] for which (=? compare s[i] x),
+; or with x inserted in the proper place.
+; The algorithm uses linear insertion from the front.
+
+(define (insert/update compare x s) ; insert x into list s, or update
+ (if (null? s)
+ (list x)
+ (if3 (compare x (car s))
+ (cons x s)
+ (cons x (cdr s))
+ (cons (car s) (insert/update compare x (cdr s))))))
+
+; (index-in-vector compare vec x)
+; an index i such that (=? compare vec[i] x), or #f if there is none.
+; It is assumed that s is sorted with respect to compare,
+; i.e. (apply chain<=? compare (vector->list s)). If there are
+; several elements equivalent to x then it is unspecified which
+; these is chosen.
+; The algorithm uses binary search.
+
+(define (index-in-vector compare vec x)
+ (let binary-search ((lo -1) (hi (vector-length vec)))
+ ; invariant: vec[lo] < x < vec[hi]
+ (if (=? (- hi lo) 1)
+ #f
+ (let ((mi (quotient (+ lo hi) 2)))
+ (if3 (compare x (vector-ref vec mi))
+ (binary-search lo mi)
+ mi
+ (binary-search mi hi))))))
+
+
+; Run the checks
+; ==============
+
+; comment in/out as needed
+(with-test-prefix "atomic" (check:atomic))
+(with-test-prefix "if3" (check:if3))
+(with-test-prefix "ifs" (check:ifs))
+(with-test-prefix "predicates-form-compare"
+ (check:predicates-from-compare))
+(with-test-prefix "pairwise-not=?"
+ (check:pairwise-not=?))
+(with-test-prefix "min/max"
+ (check:min/max))
+(with-test-prefix "kth-largest"
+ (check:kth-largest))
+(with-test-prefix "compare-from-predicates"
+ (check:compare-from-predicates))
+(with-test-prefix "refine-select-cond"
+ (check:refine-select-cond))
+(with-test-prefix "data-structures"
+ (check:data-structures))
+(with-test-prefix "default-compare"
+ (check:default-compare))
+(with-test-prefix "more-examples"
+ (check:more-examples))
+