Implemented builder-f, cleanup.
This commit is contained in:
Georges Dupéron
parent
e3074a37e4
commit
8f13786bf0
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@ -1,100 +1,13 @@
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#lang type-expander
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(require (lib "phc-graph/flexible-with-generalized-ctor.hl.rkt"))
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(define-type τ-4-2 (builder-τ 4 2))
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(provide f g)
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#;(τ (U (Pairof Any (None (Listof (Some Any))))
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(Some Any))
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(Some0 Any) Number (Some1 Any) String)
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#|
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(: f τ-4-2)
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(define (f kx x ky y)
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(error "Not Yet"))
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(define-syntax-rule (F KX X KY Y)
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(inst f propagate-τ
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KX X KY Y))
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(ann (F 0 Number 1 String)
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(-> 0 Number 1 String
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(List
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(Pairof Any (Some Number))
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(Pairof Any (Some String))
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(Pairof Any (None (List Zero One)))
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(Pairof Any (None (List Zero One))))))
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|#
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(builder-f f 4 2)
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#|
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(: g (∀ (A) (case→ [→ (Some A) A]
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[→ (None Any) 'none])))
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(define (g a)
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(if (Some? a)
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(Some-f a)
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'none))
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|#
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#;((inst f propagate-τ '|1| Number '|3| String)
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oracle '|1| 100 '|3| "bee")
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(builder-f g 8 3)
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Actual good implementation:
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;(struct (A) Some ([f : A]) #:transparent)
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;(struct (A) Some0 Some () #:transparent)
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;(struct (A) Some1 Some () #:transparent)
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;(struct (A) Some2 Some () #:transparent)
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;(struct (A) Some3 Some () #:transparent)
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;(struct (A) None ([f : A]) #:transparent)
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;; A is:
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#;(Pairof Any (U (Some Any) (None (Listof Any))))
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(: f (builder-τ 4 2))
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(define (f oracle kx x ky y)
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(list (cond
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[((make-predicate '|0|) kx)
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(ann ((inst oracle (∩ (Pairof 0/K (Some 0/X)) (Pairof '|0| Any))) (cons kx (Some x)))
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(∩ (Pairof 0/K (Some 0/X)) (Pairof '|0| Any) A))]
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[((make-predicate '|0|) ky)
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(ann ((inst oracle (∩ (Pairof 1/K (Some 1/X)) (Pairof '|0| Any))) (cons ky (Some y)))
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(∩ (Pairof 1/K (Some 1/X)) (Pairof '|0| Any) A))]
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[else
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((inst oracle (Pairof '|0| (None (List (∩ 0/K (U '|1| '|2| '|3|)) (∩ 1/K (U '|1| '|2| '|3|))))))
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(cons '|0| (None (list kx ky))))])
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(cond
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[((make-predicate '|1|) kx)
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(ann ((inst oracle (∩ (Pairof 0/K (Some 0/X)) (Pairof '|1| Any))) (cons kx (Some x)))
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(∩ (Pairof 0/K (Some 0/X)) (Pairof '|1| Any) A))]
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[((make-predicate '|1|) ky)
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(ann ((inst oracle (∩ (Pairof 1/K (Some 1/X)) (Pairof '|1| Any))) (cons ky (Some y)))
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(∩ (Pairof 1/K (Some 1/X)) (Pairof '|1| Any) A))]
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[else
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((inst oracle (Pairof '|1| (None (List (∩ 0/K (U '|0| '|2| '|3|)) (∩ 1/K (U '|0| '|2| '|3|))))))
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(cons '|1| (None (list kx ky))))])
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(cond
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[((make-predicate '|2|) kx)
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(ann ((inst oracle (∩ (Pairof 0/K (Some 0/X)) (Pairof '|2| Any))) (cons kx (Some x)))
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(∩ (Pairof 0/K (Some 0/X)) (Pairof '|2| Any) A))]
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[((make-predicate '|2|) ky)
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(ann ((inst oracle (∩ (Pairof 1/K (Some 1/X)) (Pairof '|2| Any))) (cons ky (Some y)))
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(∩ (Pairof 1/K (Some 1/X)) (Pairof '|2| Any) A))]
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[else
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((inst oracle (Pairof '|2| (None (List (∩ 0/K (U '|0| '|1| '|3|)) (∩ 1/K (U '|0| '|1| '|3|))))))
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(cons '|2| (None (list kx ky))))])
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(cond
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[((make-predicate '|3|) kx)
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(ann ((inst oracle (∩ (Pairof 0/K (Some 0/X)) (Pairof '|3| Any))) (cons kx (Some x)))
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(∩ (Pairof 0/K (Some 0/X)) (Pairof '|3| Any) A))]
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[((make-predicate '|3|) ky)
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(ann ((inst oracle (∩ (Pairof 1/K (Some 1/X)) (Pairof '|3| Any))) (cons ky (Some y)))
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(∩ (Pairof 1/K (Some 1/X)) (Pairof '|3| Any) A))]
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[else
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((inst oracle (Pairof '|3| (None (List (∩ 0/K (U '|0| '|1| '|2|)) (∩ 1/K (U '|0| '|1| '|2|))))))
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(cons '|3| (None (list kx ky))))])))
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#;((inst g propagate-τ '|1| Number '|3| String '|7| Symbol)
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oracle '|1| 100 '|3| "bee" '|7| 'buzz)
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@ -10,10 +10,9 @@
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꩜chunk[<*>
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(provide builder-τ
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None
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Some
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Some?
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Some-f
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propagate-τ)
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propagate-τ
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oracle
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builder-f)
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(require racket/require
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(for-syntax (subtract-in racket/base subtemplate/override)
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@ -23,8 +22,7 @@
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subtemplate/override)
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(for-meta 2 racket/base))
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(struct (T) Some ([f : T]))
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(struct (T) None ([f : T]))
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(struct (T) None ([f : (Promise T)]))
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(define-type-expander BinaryTree
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(syntax-parser
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@ -32,20 +30,11 @@
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;; TODO: implement BinaryTree.
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#'(List leafⱼ …)]))
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(define-syntax (def-SomeNone* stx)
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(syntax-case stx ()
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[(_ Some n)
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(with-syntax ([(Someᵢ …) (map (λ (i) (format-id #'Some "Some~a" i))
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(range n))])
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#`(begin
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(provide Someᵢ …)
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(struct (T) Someᵢ Some ()) …))]))
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(def-SomeNone* Some 4)
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<propagate-τ>
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<oracle-τ>
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<oracle>
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<builder-τ>
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<propagate-τ>]
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<builder-f>]
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We first define the builder function's type. Since this type is rather
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complex, we define it using a macro. The type expander takes two arguments.
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@ -95,7 +84,7 @@ corresponding ꩜racket[Kⱼ] matches the leaf name, and ꩜racket[None] otherwi
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꩜chunk[|<Some or None>|
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(U |<(Some Xⱼ) if Kⱼ = NSymᵢ>|
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|<None if ∀ k ∈ Kⱼ, k ≠ NSymᵢ>|)]
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|<None if ∀ k ∈ Kⱼ , k ≠ NSymᵢ>|)]
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This type-level conditional is achieved via a trick involving intersection
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types. The ꩜racket[Kⱼ] type should be a singleton type containing exactly one
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@ -110,14 +99,14 @@ pair.
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꩜chunk[|<(Some Xⱼ) if Kⱼ = NSymᵢ>|
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(Pairof (∩ Kᵢⱼ 'NSymᵢⱼ)
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(Some Xᵢⱼ))
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Xᵢⱼ)
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…]
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where ꩜racket[Kᵢⱼ], ꩜racket[Xᵢⱼ] and ꩜racket[NSymᵢⱼ] are defined as follows:
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꩜chunk[<builder-τ-with-3>
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#:with ((Kᵢⱼ …) …) (map (const (Kⱼ …)) (Nᵢ …))
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#:with ((Xᵢⱼ …) …) (map (const (Xⱼ …)) (Nᵢ …))
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#:with ((Kᵢⱼ …) …) (map (const #'(Kⱼ …)) (Nᵢ …))
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#:with ((Xᵢⱼ …) …) (map (const #'(Xⱼ …)) (Nᵢ …))
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#:with ((NSymᵢⱼ …) …) (map λni.(map (const ni) (Xⱼ …)) (NSymᵢ …))]
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We use this fact to construct a pair above. Its first element is either
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@ -148,9 +137,8 @@ The resulting type should therefore be ꩜racket[Nothing] only if there is no
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꩜racket[Kⱼ] equal to ꩜racket[Nᵢ], and be the list of symbols
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꩜racket[(List . exceptᵢ)] otherwise.
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꩜chunk[|<None if ∀ k ∈ Kⱼ, k ≠ NSymᵢ>|
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(Pairof 'NSymᵢ
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(None (List {∩ Kᵢⱼ {U 'exceptᵢⱼ …}} …)))]
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꩜chunk[|<None if ∀ k ∈ Kⱼ , k ≠ NSymᵢ>|
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(None (List {∩ Kᵢⱼ {U 'exceptᵢⱼ …}} …))]
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This approach relies on the fact that occurrences of ꩜racket[Nothing] within
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structs and pairs containing collapse the entire struct or pair type to
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@ -192,9 +180,8 @@ instantiated.
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꩜chunk[<propagate-τ>
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(define-type propagate-τ
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(Pairof Any
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(U (None (Listof Natural))
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(Some Any))))]
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(U (Pairof Any Any)
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(None (Listof Any))))]
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꩜;Use chunkref instead of ꩜racket[|<Some or None>|] ?
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@ -209,18 +196,27 @@ an ꩜racket[oracle] function, which transforms an element with the type
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꩜racket[(∩ A B)], where ꩜racket[B] is the original type of the value to
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upgrade.
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꩜chunk[<oracle-type>
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(∀ (B) (→ (∩ B
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(Pairof Any (U (Some Any) (None (Listof Any)))))
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(∩ A B)))]
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꩜chunk[<oracle-τ>
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(define-type (oracle-τ A)
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(∀ (B) (→ (∩ B
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(U (Pairof Any Any)
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(None (Listof Any))))
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(∩ A B))))]
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The builder function type is updated as follows:
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The oracle does nothing more than return its argument unchanged:
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꩜chunk[<oracle>
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(: oracle (oracle-τ propagate-τ))
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(define (oracle v) v)]
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We update the builder function type to accept an extra argument for the
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oracle:
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꩜hlite[|<builder-function-type''>|
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{/(∀(_ _ _)(→ + _ _ / _ _ ooo _))}
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(∀ (A {?@ Kⱼ Xⱼ} …)
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(→ (code:comment "; Oracle:")
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<oracle-type>
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(oracle-τ A)
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(code:comment "; Keys and values:")
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{?@ (∩ Kⱼ (U 'NSymⱼᵢ …)) Xⱼ} …
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;; Result type:
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@ -228,3 +224,30 @@ The builder function type is updated as follows:
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꩜chunk[<builder-f>
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(define-syntax builder-f
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(syntax-parser
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[(_ name n m)
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<builder-τ-with-1>
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<builder-τ-with-2>
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<builder-τ-with-3>
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<builder-τ-with-4>
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#'(begin |<builder-function-implementation>|)]))]
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꩜chunk[<builder-τ-with-4>
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#:with ((kᵢⱼ …) …) (map (const #'(kⱼ …)) (Nᵢ …))
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#:with ((xᵢⱼ …) …) (map (const #'(xⱼ …)) (Nᵢ …))]
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꩜chunk[<builder-function-implementation>
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(: name |<builder-function-type''>| #;(builder-τ n m))
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(define (name oracle {?@ kⱼ xⱼ} …)
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(list (cond
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[((make-predicate 'NSymᵢⱼ) kᵢⱼ)
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((inst oracle (Pairof (∩ Kᵢⱼ 'NSymᵢⱼ) Xᵢⱼ)) (cons kᵢⱼ xᵢⱼ))]
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…
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[else
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((inst oracle (None (List (∩ Kᵢⱼ (U 'exceptᵢⱼ …)) …)))
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(None (delay (list kᵢⱼ …))))])
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…))]
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