72 lines
2.6 KiB
Racket
72 lines
2.6 KiB
Racket
#lang s-exp macrotypes/typecheck
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(extends "stlc+reco+var.rkt")
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;; existential types
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;; Types:
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;; - types from stlc+reco+var.rkt
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;; - ∃
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;; Terms:
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;; - terms from stlc+reco+var.rkt
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;; - pack and open
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(provide ∃ pack open)
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(define-binding-type ∃ #:bvs = 1)
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(define-typed-syntax pack
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[(_ (τ:type e) as ∃τ:type)
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#:with (~∃ (τ_abstract) τ_body) #'∃τ.norm
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#:with [e- τ_e] (infer+erase #'e)
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#:when (typecheck? #'τ_e (subst #'τ.norm #'τ_abstract #'τ_body))
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(⊢ e- : ∃τ.norm)])
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(define-typed-syntax open #:datum-literals (<=)
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[(_ [x:id <= e_packed with X:id] e)
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;; The subst below appears to be a hack, but it's not really.
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;; It's the (TaPL) type rule itself that is fast and loose.
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;; Leveraging the macro system's management of binding reveals this.
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;;
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;; Specifically, here is the TaPL Unpack type rule, fig24-1, p366:
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;; Γ ⊢ e_packed : {∃X,τ_body}
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;; Γ,X,x:τ_body ⊢ e : τ_e
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;; ------------------------------
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;; Γ ⊢ (open [x <= e_packed with X] e) : τ_e
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;;
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;; There's *two* separate binders, the ∃ and the let,
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;; which the rule conflates.
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;;
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;; Here's the rule rewritten to distinguish the two binding positions:
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;; Γ ⊢ e_packed : {∃X_1,τ_body}
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;; Γ,X_???,x:τ_body ⊢ e : τ_e
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;; ------------------------------
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;; Γ ⊢ (open [x <= e_packed with X_2] e) : τ_e
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;;
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;; The X_1 binds references to X in T_12.
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;; The X_2 binds references to X in t_2.
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;; What should the X_??? be?
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;;
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;; A first guess might be to replace X_??? with both X_1 and X_2,
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;; so all the potentially referenced type vars are bound.
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;; Γ ⊢ e_packed : {∃X_1,τ_body}
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;; Γ,X_1,X_2,x:τ_body ⊢ e : τ_e
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;; ------------------------------
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;; Γ ⊢ (open [x <= e_packed with X_2] e) : τ_e
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;;
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;; But this example demonstrates that the rule above doesnt work:
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;; (open [x <= (pack (Int 0) as (∃ (X_1) X_1)) with X_2]
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;; ((λ ([y : X_2]) y) x)
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;; Here, x has type X_1, y has type X_2, but they should be the same thing,
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;; so we need to replace all X_1's with X_2
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;;
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;; Here's the fixed rule, which is implemented here
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;;
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;; Γ ⊢ e_packed : {∃X_1,τ_body}
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;; Γ,X_2:#%type,x:[X_2/X_1]τ_body ⊢ e : τ_e
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;; ------------------------------
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;; Γ ⊢ (open [x <= e_packed with X_2] e) : τ_e
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;;
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#:with [e_packed- (~∃ (Y) τ_body)] (infer+erase #'e_packed)
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#:with τ_x (subst #'X #'Y #'τ_body)
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#:with [(_ x-) e- τ_e] (infer/ctx+erase #'(X [x : τ_x]) #'e)
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(⊢ (let- ([x- e_packed-]) e-) : τ_e)])
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