[bg] starter functions
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ben
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28
tapl/tests/mlish/bg/README.md
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28
tapl/tests/mlish/bg/README.md
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bg
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===
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mlish tests by Ben
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- `ps1` :
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```
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(define (fn-list [f* : (List (→ A A))] [a : A] → A)
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(define (count-letters/one [s : String] [c : Char] → Int)
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(define (count-letters [s* : (List String)] [c : Char] → Int)
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(define (map [f : (→ A B)] [x* : (List A)] → (List B))
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(define (append [x* : (List A)] [y* : (List A)] → (List A))
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(define (flatten [x** : (List (List A))] → (List A))
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(define (insert [x : A] → (→ (List A) (List (List A))))
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(define (permutations [x* : (List A)] → (List (List A)))
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(define (split [ab* : (List (** A B))] → (** (List A) (List B)))
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(define (combine [a*b* : (** (List A) (List B))] → (List (** A B)))
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(define (fst [xy : (** A B)] → A)
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(define (snd [xy : (** A B)] → B)
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(define (foldl [f : (→ A B A)] [acc : A] [x* : (List B)] → A)
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(define (sum [x* : (List Float)] → Float)
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(define (reverse [x* : (List A)] → (List A))
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(define (convolve [x* : (List Float)] [y* : (List Float)] → Float)
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(define (mc [n : Int] [f : (→ A A)] [x : A] → A)
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(define (square [n : Int] → Int)
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(define (successor [mcn : (→ (→ A A) A A)] → (→ (→ A A) A A))
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```
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-
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248
tapl/tests/mlish/bg/ps1.mlish
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248
tapl/tests/mlish/bg/ps1.mlish
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#lang s-exp "../../../mlish.rkt"
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(require "../../rackunit-typechecking.rkt")
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;; =============================================================================
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(define-type (List X)
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Nil
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(Cons X (List X)))
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;; =============================================================================
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;; http://www.cs.cornell.edu/courses/cs3110/2011fa/hw/ps1/ps1.html
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(define (fn-list [f* : (List (→ A A))] [a : A] → A)
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(match f* with
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[Nil -> a]
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[Cons f f* -> (fn-list f* (f a))]))
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(check-type
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(fn-list (Cons (λ ([x : Int]) (+ x 1)) (Cons (λ ([x : Int]) (* x 2)) Nil)) 4)
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: Int
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⇒ 10)
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;; -----------------------------------------------------------------------------
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(define (count-letters/one [s : String] [c : Char] → Int)
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(for/sum ([i (in-range (string-length s))])
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(if (equal? (string-ref s i) c)
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1
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0)))
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(define (count-letters [s* : (List String)] [c : Char] → Int)
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(match s* with
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[Nil -> 0]
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[Cons s s* -> (+ (count-letters/one s c)
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(count-letters s* c))]))
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(check-type
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(count-letters (Cons "OCaml" (Cons "Is" (Cons "Alot" (Cons "Better" (Cons "Than" (Cons "Java" Nil)))))) (string-ref "a" 0))
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: Int
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⇒ 4)
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;; -----------------------------------------------------------------------------
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(define (map [f : (→ A B)] [x* : (List A)] → (List B))
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(match x* with
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[Nil -> Nil]
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[Cons x x* -> (Cons (f x) (map f x*))]))
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(define (append [x* : (List A)] [y* : (List A)] → (List A))
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(match x* with
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[Nil -> y*]
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[Cons x x* -> (Cons x (append x* y*))]))
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(define (flatten [x** : (List (List A))] → (List A))
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(match x** with
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[Nil -> Nil]
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[Cons x* x** -> (append x* (flatten x**))]))
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(define (insert [x : A] → (→ (List A) (List (List A))))
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(λ ([x* : (List A)])
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(Cons (Cons x x*)
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(match x* with
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[Nil -> Nil]
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[Cons y y* -> (map (λ ([z* : (List A)]) (Cons y z*))
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((insert x) y*))]))))
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(define (permutations [x* : (List A)] → (List (List A)))
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(match x* with
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[Nil -> (Cons Nil Nil)]
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[Cons x x* -> (flatten (map (insert x) (permutations x*)))]))
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(check-type
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(permutations (Nil {Int}))
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: (List (List Int))
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⇒ (Cons (Nil {(List Int)}) Nil))
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(check-type
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(permutations (Cons 1 Nil))
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: (List (List Int))
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⇒ (Cons (Cons 1 Nil) Nil))
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(check-type
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(permutations (Cons 1 (Cons 2 Nil)))
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: (List (List Int))
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⇒ (Cons (Cons 1 (Cons 2 Nil)) (Cons (Cons 2 (Cons 1 Nil)) Nil)))
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(check-type
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(permutations (Cons 1 (Cons 2 (Cons 3 Nil))))
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: (List (List Int))
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⇒ (Cons (Cons 1 (Cons 2 (Cons 3 Nil)))
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(Cons (Cons 2 (Cons 1 (Cons 3 Nil)))
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(Cons (Cons 2 (Cons 3 (Cons 1 Nil)))
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(Cons (Cons 1 (Cons 3 (Cons 2 Nil)))
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(Cons (Cons 3 (Cons 1 (Cons 2 Nil)))
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(Cons (Cons 3 (Cons 2 (Cons 1 Nil)))
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Nil)))))))
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;; =============================================================================
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;; http://www.cs.cornell.edu/courses/cs3110/2011sp/hw/ps1/ps1.htm
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(define-type (** X Y)
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(Pair X Y))
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(define (split [ab* : (List (** A B))] → (** (List A) (List B)))
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(match ab* with
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[Nil -> (Pair Nil Nil)]
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[Cons ab ab* ->
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(match ab with
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[Pair a b ->
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(match (split ab*) with
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[Pair a* b* ->
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(Pair (Cons a a*)
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(Cons b b*))])])]))
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(check-type
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(split (Nil {(** Int Int)}))
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: (** (List Int) (List Int))
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⇒ (Pair (Nil {Int}) (Nil {Int})))
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(check-type
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(split (Cons (Pair 1 2) (Cons (Pair 3 4) Nil)))
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: (** (List Int) (List Int))
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⇒ (Pair (Cons 1 (Cons 3 Nil))
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(Cons 2 (Cons 4 Nil))))
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(check-type
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(split (Cons (Pair 1 "one") (Cons (Pair 2 "two") (Cons (Pair 3 "three") Nil))))
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: (** (List Int) (List String))
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⇒ (Pair (Cons 1 (Cons 2 (Cons 3 Nil)))
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(Cons "one" (Cons "two" (Cons "three" Nil)))))
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;; -----------------------------------------------------------------------------
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(define (combine [a*b* : (** (List A) (List B))] → (List (** A B)))
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(match a*b* with
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[Pair a* b* ->
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(match a* with
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[Nil ->
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(match b* with
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[Nil ->
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Nil]
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[Cons b b* ->
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Nil])] ;; Error
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[Cons a a* ->
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(match b* with
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[Nil ->
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Nil] ;; Error
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[Cons b b* ->
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(Cons (Pair a b) (combine (Pair a* b*)))])])]))
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(check-type
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(combine (Pair (Nil {Int}) (Nil {Int})))
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: (List (** Int Int))
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⇒ (Nil {(** Int Int)}))
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(check-type
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(combine (Pair (Cons 1 (Cons 2 Nil)) (Cons 3 (Cons 4 Nil))))
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: (List (** Int Int))
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⇒ (Cons (Pair 1 3) (Cons (Pair 2 4) Nil)))
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(check-type
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(combine (split (Cons (Pair 1 "one") (Cons (Pair 2 "two") (Cons (Pair 3 "three") Nil)))))
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: (List (** Int String))
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⇒ (Cons (Pair 1 "one") (Cons (Pair 2 "two") (Cons (Pair 3 "three") Nil))))
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;; -----------------------------------------------------------------------------
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(define (fst [xy : (** A B)] → A)
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(match xy with
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[Pair x y -> x]))
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(define (snd [xy : (** A B)] → B)
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(match xy with
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[Pair x y -> y]))
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(define (foldl [f : (→ A B A)] [acc : A] [x* : (List B)] → A)
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(match x* with
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[Nil -> acc]
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[Cons x x* -> (foldl f (f acc x) x*)]))
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(define (sum [x* : (List Float)] → Float)
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(foldl fl+ (exact->inexact 0) x*))
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(define (reverse [x* : (List A)] → (List A))
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(foldl (λ ([x* : (List A)] [x : A]) (Cons x x*)) Nil x*))
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(define (convolve [x* : (List Float)] [y* : (List Float)] → Float)
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(sum
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(map (λ ([xy : (** Float Float)]) (fl* (fst xy) (snd xy)))
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(combine (Pair x* (reverse y*))))))
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(check-type
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(convolve (Cons 1.0 (Cons 2.0 (Cons 3.0 Nil))) (Cons 1.0 (Cons 2.0 (Cons 3.0 Nil))))
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: Float
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⇒ (fl+ (fl+ (fl* 1.0 3.0) (fl* 2.0 2.0)) (fl* 3.0 1.0)))
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;; -----------------------------------------------------------------------------
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(define (mc [n : Int] [f : (→ A A)] [x : A] → A)
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(for/fold ([x x])
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([_i (in-range n)])
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(f x)))
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(check-type
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(mc 3000 (λ ([n : Int]) (+ n 1)) 3110)
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: Int
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⇒ 6110)
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(define (square [n : Int] → Int)
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(* n n))
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(check-type
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(mc 0 square 2)
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: Int
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⇒ 2)
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(check-type
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(mc 2 square 2)
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: Int
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⇒ 16)
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(check-type
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(mc 3 square 2)
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: Int
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⇒ 256)
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;; -----------------------------------------------------------------------------
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(define (successor [mcn : (→ (→ A A) A A)] → (→ (→ A A) A A))
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(λ ([f : (→ A A)] [x : A])
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(f (mcn f x))))
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(check-type
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((successor (λ ([f : (→ Int Int)] [x : Int]) (mc 0 f x))) square 2)
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: Int
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⇒ 4)
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(check-type
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((successor (successor (λ ([f : (→ Int Int)] [x : Int]) (mc 0 f x)))) square 2)
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: Int
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⇒ 16)
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(check-type
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((successor (successor (successor (λ ([f : (→ Int Int)] [x : Int]) (mc 0 f x))))) square 2)
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: Int
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⇒ 256)
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;; # (mc 3 successor) (mc 0) square 2;;
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