dds/utils.rkt

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#lang typed/racket
(require typed/graph typed-compose typed/racket/stream syntax/parse/define
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(for-syntax syntax/parse racket/syntax racket/list))
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(provide
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Variable VariableMapping GeneralPair NonemptyListof
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assert-type for/first/typed for*/first/typed define/abstract/error
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relax-arg-type/any
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eval-with eval1-with auto-hash-ref/explicit auto-hash-ref/:
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lambda/: λ/: define/:
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extract-symbols any->string stringify-variable-mapping string->any
handle-org-booleans map-sexp read-org-sexp unorg unstringify-pairs
read-org-variable-mapping unorgv read-symbol-list drop-first-last
list-sets->list-strings pretty-print-set pretty-print-set-sets
update-vertices/unweighted update-graph dotit collect-by-key
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collect-by-key/sets ht-values/list->set hash->list/ordered hash-replace-keys/ordered
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multi-split-at lists-transpose append-lists in-random cartesian-product-2/stream
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cartesian-product/stream boolean-power boolean-power/stream any->01
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01->boolean)
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(module+ test
(require typed/rackunit))
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(define-type Variable Symbol)
(define-type (VariableMapping A) (Immutable-HashTable Variable A))
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(define-type (NonemptyListof a) (Pairof a (Listof a)))
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(define-syntax-parse-rule (assert-type e:expr type:expr)
(assert e (make-predicate type)))
(define-for-syntax (make-for/first/typed-variant folder)
(syntax-parser
#:literals (:)
[(_ :
ty:expr ; These should probably be more specific.
clauses:expr
c ...)
#`(#,folder : ty
([result : ty #f])
clauses
#:break (not (equal? result #f))
c ...)]))
(define-syntax for/first/typed (make-for/first/typed-variant 'for/fold))
(define-syntax for*/first/typed (make-for/first/typed-variant 'for*/fold))
(module+ test
(test-case "for/first/typed, for/first/typed*"
(check-equal? (for/first/typed : (Option Integer)
([i (in-range 1 10)]
#:when (zero? (modulo i 5)))
(* i 3))
15)
(check-equal? (for*/first/typed : (Option (Pairof Integer Integer))
([i (in-range 1 10)]
[j (in-range 1 10)]
#:when (> (+ i j) 5)
#:when (even? i)
#:when (even? j))
(cons i j))
'(2 . 4))))
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(define-syntax-parser define/abstract/error
[(_ (name:id args:id ...))
#`(define/public (name args ...) (error 'name "abstract method"))])
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(define-syntax-parse-rule (relax-arg-type/any name:id arg-type:expr)
(λ ([x : Any]) (name (assert-type x arg-type))))
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(: eval-with (-> (VariableMapping Any) Any AnyValues))
(define (eval-with ht expr)
(parameterize ([current-namespace (make-base-namespace)])
(for ([(x val) (in-hash ht)]) (namespace-set-variable-value! x val))
(eval expr)))
(: eval1-with (-> (VariableMapping Any) Any Any))
(define (eval1-with ht expr)
(call-with-values (λ () (eval-with ht expr))
(λ args (car args))))
(module+ test
(test-case "eval-with"
(check-equal? (eval1-with (hash 'a 1 'b 2) '(+ a b 1))
4)
(define ht : (VariableMapping Integer) (hash 'a 1 'b 2))
(define expr : Any '(+ a b 1))
(check-equal? (eval1-with ht expr)
4)))
(define-syntax-parser auto-hash-ref/explicit
[(_ (ht:id keys:id ...) body:expr)
#`(let #,(for/list ([key (syntax->list #'(keys ...))])
`[,key (hash-ref ,#'ht ',key)])
body)])
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(module+ test
(test-case "auto-hash-ref/explicit"
(define mytable #hash((a . 3) (b . 4)))
(check-equal? (auto-hash-ref/explicit (mytable b a)
(* a b))
12)
(define ht #hash((a . #t) (b . #f)))
(check-equal? (auto-hash-ref/explicit (ht a b)
(and (not a) b))
#f)))
;;; Helper functions for auto-hash-ref/:.
(begin-for-syntax
(define (colon? s)
(and (symbol? s)
(eq? (string-ref (symbol->string s) 0) #\:)))
(define (collect-colons datum)
(cond [(colon? datum) (list datum)]
[(list? datum)
(remove-duplicates (flatten (for/list ([el (in-list datum)])
(collect-colons el))))]
[else '()]))
(define (strip-colon s)
(string->symbol (substring (symbol->string s) 1))))
(define-syntax (auto-hash-ref/: stx)
(syntax-parse stx
[(_ ht:id body:expr)
(define colons (collect-colons (syntax->datum stx)))
(define bindings (for/list ([key colons])
`[,key (hash-ref ,#'ht ',(strip-colon key))]))
(with-syntax ([bindings-stx (datum->syntax #'ht bindings)])
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#'(let bindings-stx body))]))
(module+ test
(test-case "auto-hash-ref/:"
(define ht1 #hash((x . #t) (y . #t) (t . #f)))
(define z #t)
(check-equal? (auto-hash-ref/: ht1
(and :x (not :y) z (or (and :t) :x)))
#f)
(define ht2 #hash((a . 1) (b . 2)))
(check-equal? (auto-hash-ref/: ht2 (+ :a (* 2 :b)))
5)))
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(define-syntax-parser lambda/:
[(_ body:expr)
#:with ht (format-id #'body "ht")
#'(lambda (ht) (auto-hash-ref/: ht body))]
[(_ type:expr body:expr)
#:with ht (format-id #'body "ht")
#'(lambda ([ht : type]) (auto-hash-ref/: ht body))])
(define-syntax-parser λ/:
[(_ body:expr) #'(lambda/: body)]
[(_ type:expr body:expr) #'(lambda/: type body)])
(define-syntax-parser define/:
[(_ name:id body:expr) #'(define name (λ/: body))]
[(_ name:id type:expr body:expr) #'(define name (λ/: type body))])
(module+ test
(test-case "lambda/:, λ/:, define/:"
(define st : (HashTable Symbol Integer) (hash 'a 1 'b 2))
(check-equal? ((lambda/: (+ :a :b)) st) 3)
(check-equal? ((lambda/: (HashTable Symbol Integer) (+ :a :b)) st) 3)
(check-equal? ((λ/: (HashTable Symbol Integer) (+ :a :b)) st) 3)
(: f1 (-> (HashTable Symbol Integer) Integer))
(define/: f1 (+ :a :b))
(check-equal? (f1 st) 3)
(define/: f2 (HashTable Symbol Integer) (+ :a :b))
(check-equal? (f2 st) 3)))
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(: extract-symbols (-> Any (Listof Symbol)))
(define (extract-symbols form)
(: extract-rec (-> Any (Listof Any)))
(define (extract-rec form)
(match form
[(? symbol?) (list form)]
[(? list?)
(flatten (for/list : (Listof Any)
([x form])
(extract-symbols x)))]
[else '()]))
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(assert-type (extract-rec form) (Listof Symbol)))
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(module+ test
(test-case "extract-symbols"
(check-equal? (extract-symbols '(1 (2 3) x (y z 3)))
'(x y z))))
(: any->string (-> Any String))
(define (any->string x)
(with-output-to-string (λ () (display x))))
(module+ test
(test-case "any->string"
(check-equal? (any->string 'a) "a")
(check-equal? (any->string '(a 1 (x y))) "(a 1 (x y))")
(check-equal? (any->string "hello") "hello")))
(: stringify-variable-mapping (-> (VariableMapping Any) (VariableMapping String)))
(define (stringify-variable-mapping ht)
(for/hash : (VariableMapping String)
([(key val) (in-hash ht)]) (values key (any->string val))))
(module+ test
(test-case "stringify-variable-mapping"
(define mp (stringify-variable-mapping #hash((a . (and a b)) (b . (not b)))))
(check-equal? (hash-ref mp 'a) "(and a b)")
(check-equal? (hash-ref mp 'b) "(not b)")))
(: string->any (-> String Any))
(define (string->any str)
(with-input-from-string str (λ () (read))))
(module+ test
(test-case "string->any"
(check-equal? (string->any "(or b (not a))") '(or b (not a)))
(check-equal? (string->any "14") 14)))
;;; Given a sexp, converts all "#f" to #f and "#t" to #t.
;;;
;;; When I read Org-mode tables, I pump them through a call to the
;;; prin1 because the Elisp sexps seems incompatible with Racket.
;;; On the other hand, Racket Booleans seem to upset Elisp a little,
;;; so prin1 wraps them in additional double quotes. This function
;;; removes those quotes.
(: handle-org-booleans (-> Any Any))
(define/match (handle-org-booleans datum)
[("#t") #t]
[("#f") #f]
[((? list?)) (map handle-org-booleans datum)]
[(_) datum])
(module+ test
(test-case "handle-org-booleans"
(check-equal? (handle-org-booleans "#t") #t)
(check-equal? (handle-org-booleans "#f") #f)
(check-equal? (handle-org-booleans '("#t" "#f")) '(#t #f))
(check-equal? (handle-org-booleans "t") "t")))
(: map-sexp (-> (-> Any Any) Any Any))
(define (map-sexp func sexp)
(match sexp
[(? list?) (map ((curry map-sexp) func) sexp)]
[datum (func datum)]))
(module+ test
(test-case "map-sexp"
(check-equal? (map-sexp (λ (x)
(assert x number?)
(add1 x))
'(1 2 (4 10) 3))
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'(2 3 (5 11) 4))))
(: read-org-sexp (-> String Any))
(define read-org-sexp
(compose ((curry map-sexp) (match-lambda
[(and (? string?) str) (string->any str)]
[x x]))
string->any))
(define unorg read-org-sexp)
(module+ test
(test-case "read-org-sexp"
(check-equal? (read-org-sexp "((\"a\" \"(and a b)\") (\"b\" \"(or b (not a))\"))")
'((a (and a b)) (b (or b (not a)))))
(check-equal? (unorg "(#t \"#t\" \"#t \" '(1 2 \"#f\"))")
'(#t #t #t '(1 2 #f)))))
(define-type (GeneralPair A B) (U (Pair A B) (List A B)))
(: unstringify-pairs (-> (Listof (GeneralPair String Any))
(Listof (GeneralPair Symbol Any))))
(define (unstringify-pairs pairs)
(for/list ([p pairs])
(match p
[(list key val)
(cons (string->symbol key) (if (string? val)
(string->any val)
val))]
[(cons key val)
(cons (string->symbol key) (if (string? val)
(string->any val)
val))])))
(module+ test
(test-case "unstringify-pairs"
(check-equal? (unstringify-pairs '(("a" . "1") ("b" . "(and a (not b))")))
'((a . 1) (b . (and a (not b)))))
(check-equal? (unstringify-pairs '(("a" . 1) ("b" . "(and a (not b))")))
'((a . 1) (b . (and a (not b)))))))
(: read-org-variable-mapping (-> String (VariableMapping Any)))
(define read-org-variable-mapping
(multi-compose
(λ ([pairs : (Listof (Pair Symbol Any))])
(make-immutable-hash pairs))
(λ (sexp)
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(assert-type sexp (Listof (GeneralPair String Any)))
(unstringify-pairs sexp))
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string->any))
;;; A synonym for read-org-variable-mapping.
(define unorgv read-org-variable-mapping)
(module+ test
(test-case "read-org-variable-mapping"
(define m1 (read-org-variable-mapping "((\"a\" \"(and a b)\") (\"b\" \"(or b (not a))\"))"))
(define m2 (read-org-variable-mapping "((\"a\" . \"(and a b)\") (\"b\" . \"(or b (not a))\"))"))
(define m3 (unorgv "((\"a\" . \"(and a b)\") (\"b\" . \"(or b (not a))\"))"))
(check-equal? (hash-ref m1 'a) '(and a b))
(check-equal? (hash-ref m2 'a) '(and a b))
(check-equal? (hash-ref m3 'a) '(and a b))
(check-equal? (hash-ref m1 'b) '(or b (not a)))
(check-equal? (hash-ref m2 'b) '(or b (not a)))
(check-equal? (hash-ref m3 'b) '(or b (not a)))))
(: read-symbol-list (-> String (Listof Symbol)))
(define (read-symbol-list str)
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(assert-type (string->any (string-append "(" str ")")) (Listof Symbol)))
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(module+ test
(test-case "read-symbol-list"
(check-equal? (read-symbol-list "a b c") '(a b c))))
(: drop-first-last (-> String String))
(define (drop-first-last str)
(substring str 1 (- (string-length str) 1)))
(module+ test
(test-case "drop-first-last"
(check-equal? (drop-first-last "(a b)") "a b")))
(: list-sets->list-strings (-> (Listof (Setof Any)) (Listof String)))
(define (list-sets->list-strings lst)
(map (multi-compose drop-first-last
any->string
(λ ([x : (Setof Any)])
(set->list x))) lst))
(module+ test
(test-case "list-sets->list-strings"
(check-equal? (list-sets->list-strings (list (set 'x 'y) (set 'z) (set) (set 't)))
'("x y" "z" "" "t"))))
(: pretty-print-set (-> (U (Setof Any) (Listof Any)) String))
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(define (pretty-print-set s)
(string-join (sort (set-map s any->string) string<?)))
(module+ test
(test-case "pretty-print-set"
(check-equal? (pretty-print-set (set 'a 'b 1)) "1 a b")
(check-equal? (pretty-print-set (list 'a 'b 1)) "1 a b")))
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(: pretty-print-set-sets (-> (U (Setof (Setof Any))
(Listof (Setof Any)))
String))
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(define (pretty-print-set-sets ms)
(string-join (for/list ([m ms]) : (Listof String)
(format "{~a}" (pretty-print-set m))) ""))
(module+ test
(test-case "pretty-print-set-sets"
(check-equal? (pretty-print-set-sets (set (set 'a 'b) (set 'c))) "{a b}{c}")
(check-equal? (pretty-print-set-sets (list (set 'a 'b) (set 'c))) "{a b}{c}")))
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(define dotit (compose display graphviz))
(: update-vertices/unweighted (-> Graph (-> Any Any) Graph))
(define (update-vertices/unweighted gr func)
(unweighted-graph/directed
(for/list ([e (in-edges gr)])
(match-let ([(list u v) e])
(list (func u) (func v))))))
(module+ test
(test-case "update-vertices/unweighted"
(define gr1 (directed-graph '((a b) (b c))))
(define gr2 (undirected-graph '((a b) (b c))))
(define (dbl [x : Any])
(assert x symbol?)
(define x-str (symbol->string x))
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(string->symbol (string-append x-str x-str)))
(define new-gr1 (update-vertices/unweighted gr1 dbl))
(define new-gr2 (update-vertices/unweighted gr2 dbl))
(check-false (has-vertex? new-gr1 'a))
(check-true (has-vertex? new-gr1 'aa))
(check-false (has-vertex? new-gr1 'b))
(check-true (has-vertex? new-gr1 'bb))
(check-false (has-vertex? new-gr1 'c))
(check-true (has-vertex? new-gr1 'cc))
(check-true (has-edge? new-gr1 'aa 'bb))
(check-true (has-edge? new-gr1 'bb 'cc))
(check-true (has-edge? new-gr2 'aa 'bb))
(check-true (has-edge? new-gr2 'bb 'aa))
(check-true (has-edge? new-gr2 'bb 'cc))
(check-true (has-edge? new-gr2 'cc 'bb))))
(: update-graph (->* (Graph) (#:v-func (-> Any Any) #:e-func (-> Any Any)) Graph))
(define (update-graph gr #:v-func [v-func identity] #:e-func [e-func identity])
(cond
[(unweighted-graph? gr)
(unweighted-graph/directed
(for/list ([e (in-edges gr)]) : (Listof (List Any Any))
(match-let ([(list u v) e])
(list (v-func u) (v-func v)))))]
[else
(weighted-graph/directed
(for/list ([e (in-edges gr)]) : (Listof (List Any Any Any))
(match-let ([(list u v) e])
(list (e-func (edge-weight gr u v))
(v-func u) (v-func v)))))]))
(module+ test
(test-case "update-graph"
(define gr1 (directed-graph '((a b) (b c))))
(define gr2 (undirected-graph '((a b) (b c))))
(define (dbl [x : Any])
(assert x symbol?)
(define x-str (symbol->string x))
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(string->symbol (string-append x-str x-str)))
(define new-gr1-ug (update-graph gr1 #:v-func dbl))
(define new-gr2-ug (update-graph gr2 #:v-func dbl))
(define gr3 (weighted-graph/directed '((10 a b) (11 b c))))
(define new-gr3 (update-graph gr3
#:v-func dbl
#:e-func (λ (x)
(assert x number?)
(* 2 x))))
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(check-false (has-vertex? new-gr1-ug 'a))
(check-true (has-vertex? new-gr1-ug 'aa))
(check-false (has-vertex? new-gr1-ug 'b))
(check-true (has-vertex? new-gr1-ug 'bb))
(check-false (has-vertex? new-gr1-ug 'c))
(check-true (has-vertex? new-gr1-ug 'cc))
(check-true (has-edge? new-gr1-ug 'aa 'bb))
(check-true (has-edge? new-gr1-ug 'bb 'cc))
(check-true (has-edge? new-gr2-ug 'aa 'bb))
(check-true (has-edge? new-gr2-ug 'bb 'aa))
(check-true (has-edge? new-gr2-ug 'bb 'cc))
(check-true (has-edge? new-gr2-ug 'cc 'bb))
(check-true (has-edge? new-gr3 'aa 'bb))
(check-false (has-edge? new-gr3 'bb 'aa))
(check-true (has-edge? new-gr3 'bb 'cc))
(check-false (has-edge? new-gr3 'cc 'bb))
(check-equal? (edge-weight new-gr3 'aa 'bb) 20)
(check-equal? (edge-weight new-gr3 'bb 'cc) 22)))
(: collect-by-key (All (a b) (-> (Listof a) (Listof b)
(Values (Listof a) (Listof (Listof b))))))
(define (collect-by-key keys vals)
(for/fold ([ht : (HashTable a (Listof b))
(make-immutable-hash)]
#:result (values (hash-keys ht) (hash-values ht)))
([e keys]
[l vals])
((inst hash-update a (Listof b)) ht e (λ (ls) (cons l ls)) (λ () empty))))
(module+ test
(test-case "collect-by-key"
(define-values (e1 l1) (collect-by-key '((1 2) (1 3)) '(a b)))
(define-values (e2 l2) (collect-by-key '((1 2) (1 2)) '(a b)))
(check-equal? e1 '((1 2) (1 3))) (check-equal? l1 '((a) (b)))
(check-equal? e2 '((1 2))) (check-equal? l2 '((b a)))))
(: collect-by-key/sets (All (a b) (-> (Listof a) (Listof b)
(Values (Listof a) (Listof (Setof b))))))
(define (collect-by-key/sets edges labels)
(define-values (es ls) (collect-by-key edges labels))
(values es ((inst map (Setof b) (Listof b)) list->set ls)))
(module+ test
(test-case "collect-by-key/sets"
(define-values (e3 l3) (collect-by-key/sets '(a b a) '(1 2 1)))
(check-equal? e3 '(b a)) (check-equal? l3 (list (set 2) (set 1)))))
;;; Converts the values of a hash table from lists to sets.
(: ht-values/list->set (All (a b) (-> (HashTable a (Listof b)) (HashTable a (Setof b)))))
(define (ht-values/list->set ht)
(for/hash ([(k v) (in-hash ht)]) : (HashTable a (Setof b))
(values k (list->set v))))
(module+ test
(test-case "ht-values/list->set"
(check-equal? (ht-values/list->set #hash((a . (1 1))))
(hash 'a (set 1)))))
;; TODO: Remove after Typed Racket has caught up with Racket 8.4.
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(: hash->list/ordered (All (a b) (-> (HashTable a b) (Listof (Pairof a b)))))
(define (hash->list/ordered ht)
((inst hash-map a b (Pairof a b)) ht cons #t))
(module+ test
(test-case "hash->list/ordered"
(check-equal? (hash->list/ordered #hash((b . 1) (a . 1)))
'((a . 1) (b . 1)))))
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(: hash-replace-keys/ordered (All (K1 K2 V) (-> (Immutable-HashTable K1 V) (Listof K2)
(Immutable-HashTable K2 V))))
(define (hash-replace-keys/ordered ht new-keys)
(make-immutable-hash (map (λ ([new-k : K2] [pair : (Pairof K1 V)])
(cons new-k (cdr pair)))
new-keys
(hash->list/ordered ht))))
(module+ test
(test-case "hash-replace-keys/ordered"
(check-equal? (hash-replace-keys/ordered (hash 'a 1 'b 2) '(x y))
'#hash((x . 1) (y . 2)))))
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(: multi-split-at (All (a) (-> (Listof (Listof a)) Integer
(Values (Listof (Listof a)) (Listof (Listof a))))))
(define (multi-split-at lists pos)
(for/fold ([lefts : (Listof (Listof a)) '()]
[rights : (Listof (Listof a)) '()]
#:result (values (reverse lefts) (reverse rights)))
([lst (in-list lists)])
(define-values (left right) ((inst split-at a) lst pos))
(values (cons left lefts) (cons right rights))))
(module+ test
(test-case "multi-split-at"
(define-values (l1 l2) (multi-split-at '((1 2 3) (a b c)) 2))
(check-equal? l1 '((1 2) (a b))) (check-equal? l2 '((3) (c)))))
;; https://racket.discourse.group/t/get-to-type-apply-in-parallel-lst/683
;;
;; Same thread: (apply ((curry map) list) lsts), however I don't
;; feel like typing this right now (2022-02-18).
(: lists-transpose (All (a ...) (-> (List (Listof a) ... a) (Listof (List a ... a)))))
(define (lists-transpose lists)
(sequence->list (in-values-sequence (apply in-parallel lists))))
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(module untyped racket
(provide (contract-out [lists-transpose (-> (listof (listof any/c)) (listof (listof any/c)))]))
(define (lists-transpose lists)
(sequence->list (in-values-sequence (apply in-parallel lists)))))
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(module+ test
(test-case "lists-transpose"
(check-equal? (lists-transpose '((1 2) (a b))) '((1 a) (2 b)))))
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(: append-lists (All (a) (-> (Listof (List (Listof a) (Listof a))) (Listof (Listof a)))))
(define (append-lists lsts)
(for/list ([pr lsts])
(append (car pr) (cadr pr))))
(module+ test
(test-case "append-lists"
(check-equal? (append-lists '(((1 2) (a b))
((3 4) (c d))))
'((1 2 a b)
(3 4 c d)))))
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(: in-random (case->
(-> (Sequenceof Flonum))
(-> Integer (Sequenceof Nonnegative-Fixnum))
(-> Integer Integer (Sequenceof Nonnegative-Fixnum))))
(define in-random
(case-lambda
[() (stream-cons
(assert-type (random) Flonum)
(in-random))]
[(k) (stream-cons
(assert-type (random k) Nonnegative-Fixnum)
(in-random k))]
[(min max) (stream-cons
(assert-type (random min max) Nonnegative-Fixnum)
(in-random min max))]))
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(module+ test
(test-case "in-random"
(random-seed 1)
(check-equal? (stream->list (stream-take (in-random 100) 10))
'(50 84 10 99 94 88 43 41 63 50))
(check-equal? (stream->list (stream-take (in-random 50 100) 10))
'(57 98 82 83 61 53 73 82 50 80))
(check-equal? (stream->list (stream-take (in-random) 10))
'(0.2718099186980313
0.7319496826374751
0.17365244033739616
0.5593031443038616
0.3345256691289459
0.9845704615094365
0.05753824253751768
0.22552976312818723
0.21646500425988832
0.15188352823997242))))
(: cartesian-product-2/stream (All (a b) (-> (Sequenceof a) (Sequenceof b) (Sequenceof (Pair a b)))))
(define (cartesian-product-2/stream s1 s2)
(: cp2-store (All (a b) (-> (Sequenceof a) (Sequenceof b) (Sequenceof b)
(Sequenceof (Pair a b)))))
;; The recursive implementation using s2-store as an accumulator.
;; Main idea: combine the elements of s1 with the element of s2
;; until they are exhausted, then restart with the next element of
;; s1 and the original content of s2.
(define (cp2-store s1 s2 s2-store)
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(cond
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[(stream-empty? s1) (stream)]
[(stream-empty? s2) (cp2-store (stream-rest s1) s2-store s2-store)]
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[else
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(stream-cons (cons (stream-first s1) (stream-first s2))
(cp2-store s1 (stream-rest s2) s2-store))]))
(cp2-store s1 s2 s2))
(module+ test
(test-case "cartesian-product-2/stream"
(check-equal? (stream->list (cartesian-product-2/stream (in-range 1 5) '(a b)))
'((1 . a) (1 . b) (2 . a) (2 . b) (3 . a) (3 . b) (4 . a) (4 . b)))
(check-equal?
(stream->list (stream-take (cartesian-product-2/stream '(a b) (in-naturals)) 10))
'((a . 0) (a . 1) (a . 2) (a . 3) (a . 4) (a . 5) (a . 6) (a . 7) (a . 8) (a . 9)))))
(: cartesian-product/stream (All (a) (-> (Listof (Sequenceof a)) (Sequenceof (Listof a)))))
(define (cartesian-product/stream ss)
(for/foldr ([prod (stream (list))])
([s (in-list ss)])
(cartesian-product-2/stream s prod)))
(module+ test
(test-case "cartesian-product/stream"
(check-equal? (stream->list (cartesian-product/stream '())) '(()))
(check-equal? (stream->list (cartesian-product/stream '((a b c))))
'((a) (b) (c)))
(check-equal? (stream->list (cartesian-product/stream (list (in-range 3) (in-range 4 6) '(a b))))
'((0 4 a)
(0 4 b)
(0 5 a)
(0 5 b)
(1 4 a)
(1 4 b)
(1 5 a)
(1 5 b)
(2 4 a)
(2 4 b)
(2 5 a)
(2 5 b)))))
(: boolean-power (-> Integer (Listof (Listof Boolean))))
(define (boolean-power n)
(apply cartesian-product (make-list n '(#f #t))))
(module+ test
(test-case "boolean-power"
(check-equal? (boolean-power 2) '((#f #f) (#f #t) (#t #f) (#t #t)))))
(: boolean-power/stream (-> Integer (Sequenceof (Listof Boolean))))
(define (boolean-power/stream n) (cartesian-product/stream (make-list n '(#f #t))))
(module+ test
(test-case "boolean-power/stream"
(check-equal? (stream->list (boolean-power/stream 2)) '((#f #f) (#f #t) (#t #f) (#t #t)))))
(: any->01 (-> Any (U Zero One)))
(define (any->01 x)
(if x 1 0))
(module+ test
(test-case "any->01"
(check-equal? (any->01 #t) 1)
(check-equal? (any->01 #f) 0)))
(: 01->boolean (-> (U Zero One) Boolean))
(define (01->boolean x)
(case x [(0) #f] [else #t]))
(module+ test
(test-case "01->boolean"
(check-equal? (01->boolean 0) #f)
(check-equal? (01->boolean 1) #t)))