add dep-ind example with define-datatype
This commit is contained in:
Stephen Chang
parent
7fc8bd8c15
commit
804c82bf24
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@ -1,7 +1,7 @@
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#lang turnstile/lang
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; second attempt at a basic dependently-typed calculus
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; initially copied from dep.rkt
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; a basic dependently-typed calculus
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; extends dep.rkt
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; Π λ ≻ ⊢ ≫ → ∧ (bidir ⇒ ⇐) τ⊑
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695
turnstile/examples/dep-ind.rkt
Normal file
695
turnstile/examples/dep-ind.rkt
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@ -0,0 +1,695 @@
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#lang turnstile/lang
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; a basic dependently-typed calculus
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; - with inductive datatypes
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; Π λ ≻ ⊢ ≫ → ∧ (bidir ⇒ ⇐) τ⊑
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(provide (rename-out [#%type *])
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Π → ∀
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= eq-refl eq-elim
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; Nat (rename-out [Zero Z][Succ S]) nat-ind #;nat-rec
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λ (rename-out [app #%app]) ann
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define define-type-alias
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)
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;; TODO:
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;; - map #%datum to S and Z
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;; - rename define-type-alias to define
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;; - add "assistant" part
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;; - provide match and match/lambda so nat-ind can be fn
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;; - eg see https://gist.github.com/AndrasKovacs/6769513
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;; - add dependent existential
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;; - remove debugging code?
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;; #;(begin-for-syntax
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;; (define old-ty= (current-type=?))
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;; (current-type=?
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;; (λ (t1 t2)
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;; (displayln (stx->datum t1))
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;; (displayln (stx->datum t2))
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;; (old-ty= t1 t2)))
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;; (current-typecheck-relation (current-type=?)))
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;(define-syntax-category : kind) ; defines #%kind for #%type
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;; set Type : Type
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;; alternatively, could define new base type Type,
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;; and make #%type typecheck with Type
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(begin-for-syntax
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(define debug? #f)
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(define type-eq-debug? #f)
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(define debug-match? #f)
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;; TODO: fix `type` stx class
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;; (define old-type? (current-type?))
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;; (current-type?
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;; (lambda (t) (or (#%type? t) (old-type? t))))
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(define old-relation (current-typecheck-relation))
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(current-typecheck-relation
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(lambda (t1 t2)
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(when type-eq-debug?
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(pretty-print (stx->datum t1))
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(pretty-print (stx->datum t2)))
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;; assumed #f can only come from (typeof #%type)
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;; (so this wont work when interacting with untyped code)
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(or (and (false? (syntax-e t1)) (#%type? t2)) ; assign Type : Type
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(old-relation t1 t2)))))
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(define-for-syntax Type ((current-type-eval) #'#%type))
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(define-internal-type-constructor →) ; equiv to Π with no uses on rhs
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(define-internal-binding-type ∀) ; equiv to Π with #%type for all params
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;; Π expands into combination of internal →- and ∀-
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;; uses "let*" syntax where X_i is in scope for τ_i+1 ...
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;; TODO: add tests to check this
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(define-typed-syntax (Π ([X:id : τ_in] ...) τ_out) ≫
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;; TODO: check that τ_in and τ_out have #%type?
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[[X ≫ X- : τ_in] ... ⊢ [τ_out ≫ τ_out- ⇐ #%type] [τ_in ≫ τ_in- ⇐ #%type] ...]
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-------
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[⊢ (∀- (X- ...) (→- τ_in- ... τ_out-)) ⇒ #%type])
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;; abbrevs for Π
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;; (→ τ_in τ_out) == (Π (unused : τ_in) τ_out)
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(define-simple-macro (→ τ_in ... τ_out)
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#:with (X ...) (generate-temporaries #'(τ_in ...))
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(Π ([X : τ_in] ...) τ_out))
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;; (∀ (X) τ) == (∀ ([X : #%type]) τ)
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(define-simple-macro (∀ (X ...) τ)
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(Π ([X : #%type] ...) τ))
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;; pattern expanders
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(begin-for-syntax
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(define-syntax ~Π
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(pattern-expander
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(syntax-parser
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[(_ ([x:id : τ_in] ... (~and (~literal ...) ooo)) τ_out)
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#'(~∀ (x ... ooo) (~→ τ_in ... ooo τ_out))]
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[(_ ([x:id : τ_in] ...) τ_out)
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#'(~∀ (x ...) (~→ τ_in ... τ_out))]))))
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;; equality -------------------------------------------------------------------
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(define-internal-type-constructor =)
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(define-typed-syntax (= t1 t2) ≫
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[⊢ t1 ≫ t1- ⇒ ty]
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[⊢ t2 ≫ t2- ⇐ ty]
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;; #:do [(printf "t1: ~a\n" (stx->datum #'t1-))
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;; (printf "t2: ~a\n" (stx->datum #'t2-))]
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; [t1- τ= t2-]
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---------------------
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[⊢ (=- t1- t2-) ⇒ #%type])
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;; Q: what is the operational meaning of eq-refl?
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(define-typed-syntax (eq-refl e) ≫
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[⊢ e ≫ e- ⇒ _]
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----------
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[⊢ (#%app- void-) ⇒ (= e- e-)])
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;; eq-elim: t : T
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;; P : (T -> Type)
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;; pt : (P t)
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;; w : T
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;; peq : (= t w)
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;; -> (P w)
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(define-typed-syntax (eq-elim t P pt w peq) ≫
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[⊢ t ≫ t- ⇒ ty]
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[⊢ P ≫ P- ⇐ (→ ty #%type)]
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[⊢ pt ≫ pt- ⇐ (app P- t-)]
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[⊢ w ≫ w- ⇐ ty]
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[⊢ peq ≫ peq- ⇐ (= t- w-)]
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--------------
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[⊢ pt- ⇒ (app P- w-)])
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;; lambda and #%app -----------------------------------------------------------
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;; TODO: fix `type` stx class
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(define-typed-syntax λ
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;; expected ty only
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[(_ (y:id ...) e) ⇐ (~Π ([x:id : τ_in] ... ) τ_out) ≫
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[[x ≫ x- : τ_in] ... ⊢ #,(substs #'(x ...) #'(y ...) #'e) ≫ e- ⇐ τ_out]
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---------
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[⊢ (λ- (x- ...) e-)]]
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;; both expected ty and annotations
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[(_ ([y:id : τ_in*] ...) e) ⇐ (~Π ([x:id : τ_in] ...) τ_out) ≫
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; [(_ ([y:id : τy_in:type] ...) e) ⇐ (~Π ([x:id : τ_in] ...) τ_out) ≫
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#:fail-unless (stx-length=? #'(y ...) #'(x ...))
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"function's arity does not match expected type"
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[⊢ τ_in* ≫ τ_in** ⇐ #%type] ...
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; #:when (typechecks? (stx-map (current-type-eval) #'(τ_in* ...))
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#:when (typechecks? #'(τ_in** ...) #'(τ_in ...))
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; #:when (typechecks? #'(τy_in.norm ...) #'(τ_in ...))
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; [τy_in τ= τ_in] ...
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[[x ≫ x- : τ_in] ... ⊢ #,(substs #'(x ...) #'(y ...) #'e) ≫ e- ⇐ τ_out]
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-------
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[⊢ (λ- (x- ...) e-)]]
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;; annotations only
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[(_ ([x:id : τ_in] ...) e) ≫
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[[x ≫ x- : τ_in] ... ⊢ [e ≫ e- ⇒ τ_out] [τ_in ≫ τ_in- ⇒ _] ...]
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-------
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[⊢ (λ- (x- ...) e-) ⇒ (Π ([x- : τ_in-] ...) τ_out)]])
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;; ;; classes for matching number literals
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;; (begin-for-syntax
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;; (define-syntax-class nat
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;; (pattern (~or n:exact-nonnegative-integer (_ n:exact-nonnegative-integer))
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;; #:attr val
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;; #'n))
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;; (define-syntax-class nats
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;; (pattern (n:nat ...) #:attr vals #'(n.val ...)))
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;; ; extract list of quoted numbers
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;; (define stx->nat (syntax-parser [n:nat (stx-e #'n.val)]))
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;; (define (stx->nats stx) (stx-map stx->nat stx))
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;; (define (stx+ ns) (apply + (stx->nats ns)))
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;; (define (delta op-stx args)
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;; (syntax-parse op-stx
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;; [(~literal +-) (stx+ args)]
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;; [(~literal zero?-) (apply zero? (stx->nats args))])))
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;; TODO: fix orig after subst, for err msgs
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;; app/eval should not try to ty check anymore
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(define-syntax app/eval
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(syntax-parser
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#;[(_ f . args) #:do[(printf "app/evaling ")
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(printf "f: ~a\n" (stx->datum #'f))
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(printf "args: ~a\n" (stx->datum #'args))]
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#:when #f #'void]
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[(_ f:id (_ matcher) (_ _ . args))
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#:with (_ m/d . _) (local-expand #'(#%app match/delayed 'dont 'care) 'expression null)
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#:when (free-identifier=? #'m/d #'f)
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;; TODO: need to attach type?
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#'(matcher . args)]
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;; TODO: apply to only lambda args or all args?
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[(_ (~and f ((~literal #%plain-lambda) (x ...) e)) e_arg ...)
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#:do[(when debug?
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(printf "apping: ~a\n" (stx->datum #'f))
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(printf "args\n")
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(pretty-print (stx->datum #'(e_arg ...)))
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(printf "expected type\n")
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(pretty-print (stx->datum (typeof this-syntax))))]
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; #:with (~Π ([X : _] ...) τ_out) (typeof #'f) ; must re-subst in type
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;; TODO: need to replace all #%app- in this result with app/eval again
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;; and then re-expand
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; #:with ((~literal #%plain-app) newf . newargs) #'e
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; #:do[(displayln #'newf)(displayln #'newargs)(displayln (stx-car #'e+))]
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#:with r-app (datum->syntax (if (identifier? #'e) #'e (stx-car #'e)) '#%app)
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;; TODO: is this assign-type needed only for tests?
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;; eg, see id tests in dep2-peano.rkt
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#:with ty (typeof this-syntax)
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#:with e-inst (substs #'(app/eval e_arg ...) #'(r-app x ...) #'e free-identifier=?)
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;; some apps may not have type (eg in internal reps)
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#:with e+ (if (syntax-e #'ty) (assign-type #'e-inst #'ty) #'e-inst)
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#:do[(when debug?
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(displayln "res:--------------------")
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(pretty-print (stx->datum #'e+))
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;; (displayln "actual type:")
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;; (pretty-print (stx->datum (typeof #'e+)))
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;; (displayln "new type:")
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;; (pretty-print (stx->datum (substs #'(e_arg ...) #'(X ...) (typeof #'e+))))
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;; (displayln "res expanded:------------------------")
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;; (pretty-print
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;; (stx->datum (local-expand (substs #'(e_arg ...) #'(x ...) #'e) 'expression null)))
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(displayln "res app/eval re-expanding-----------------------"))]
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#:with ((~literal let-values) () ((~literal let-values) () e++))
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(local-expand
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#'(let-syntax (#;[app (make-rename-transformer #'app/eval)]
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#;[x (make-variable-like-transformer #'e_arg)]) e+)
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'expression null)
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#:do[(when debug?
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(pretty-print (stx->datum #'e++))
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; (pretty-print (stx->datum (typeof #'e++)))
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#;(local-expand
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#'(let-syntax ([app (make-rename-transformer #'app/eval)]
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#;[x (make-variable-like-transformer #'e_arg)]) e+)
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'expression null))]
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#'e++ #;(substs #'(e_arg ...) #'(x ...) #'e)]
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[(_ f . args)
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#:do[(when debug?
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(printf "not apping\n")
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(pretty-print (stx->datum #'f))
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(displayln "args")
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(pretty-print (stx->datum #'args)))]
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#:with f+ (expand/df #'f)
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#:with args+ (stx-map expand/df #'args)
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;; TODO: need to attach type?
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; #:with ty (typeof this-syntax)
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(syntax-parse #'f+
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[((~literal #%plain-lambda) . _)
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#'(app/eval f+ . args+)]
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[_
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#'(#%app- f+ . args+)])]))
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;; TODO: fix orig after subst
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(define-typed-syntax app
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;; matching, ; TODO: where to put this?
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#;[(_ f:id . args) ≫
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#:with (_ m/d . _) (local-expand #'(match/delayed 1 2 3 4) 'expression null)
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#:when (free-identifier=? #'m/d #'f)
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------------
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[≻ (match/nat . args)]]
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[(_ e_fn e_arg ...) ≫
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#:do[(when debug?
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(displayln "TYPECHECKING")
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(pretty-print (stx->datum this-syntax)))]
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; #:do[(printf "applying (1) ~a\n" (stx->datum #'e_fn))]
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; [⊢ e_fn ≫ (~and e_fn- (_ (x:id ...) e ~!)) ⇒ (~Π ([X : τ_inX] ...) τ_outX)]
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[⊢ e_fn ≫ e_fn- ⇒ (~Π ([X : τ_in] ...) τ_out)]
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; #:do[(printf "applying (1) ~a\n" (stx->datum #'e_fn-))]
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#:fail-unless (stx-length=? #'[τ_in ...] #'[e_arg ...])
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(num-args-fail-msg #'e_fn #'[τ_in ...] #'[e_arg ...])
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[⊢ e_arg ≫ e_arg- ⇐ τ_in] ... ; typechecking args
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-----------------------------
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[⊢ (app/eval e_fn- e_arg- ...) ⇒ #,(substs #'(e_arg- ...) #'(X ...) #'τ_out)]])
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#;(define-typed-syntax #%app
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[(_ e_fn e_arg ...) ≫ ; apply lambda
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#:do[(printf "applying (1) ~a\n" (stx->datum #'e_fn))]
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[⊢ e_fn ≫ (~and e_fn- (_ (x:id ...) e ~!)) ⇒ (~Π ([X : τ_inX] ...) τ_outX)]
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#:do[(printf "e_fn-: ~a\n" (stx->datum #'e_fn-))
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(printf "args: ~a\n" (stx->datum #'(e_arg ...)))]
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#:fail-unless (stx-length=? #'[τ_inX ...] #'[e_arg ...])
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(num-args-fail-msg #'e_fn #'[τ_inX ...] #'[e_arg ...])
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[⊢ e_arg ≫ e_argX- ⇒ ty-argX] ... ; typechecking args must be fold; do in 2 steps
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#:do[(define (ev e)
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(syntax-parse e
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; [_ #:do[(printf "eval: ~a\n" (stx->datum e))] #:when #f #'(void)]
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[(~or _:id
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; ((~literal #%plain-lambda) . _)
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(~= _ _)
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~Nat
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((~literal quote) _))
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e]
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;; handle nums
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[((~literal #%plain-app)
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(~and op (~or (~literal +-) (~literal zero?-)))
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. args:nats)
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#`#,(delta #'op #'args.vals)]
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[((~literal #%plain-app) (~and f ((~literal #%plain-lambda) . b)) . rst)
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(expand/df #`(#%app f . #,(stx-map ev #'rst)))]
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[(x ...)
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;; #:do[(printf "t before: ~a\n" (typeof e))
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;; (printf "t after: ~a\n" (typeof #`#,(stx-map ev #'(x ...))))]
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(syntax-property #`#,(stx-map ev #'(x ...)) ': (typeof e))]
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[_ e] ; other literals
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#;[es (stx-map L #'es)]))]
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#:with (ty-arg ...)
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(stx-map
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(λ (t) (ev (substs #'(e_argX- ...) #'(X ...) t)))
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#'(ty-argX ...))
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#:with (e_arg- ...) (stx-map (λ (e t) (assign-type e t)) #'(e_argX- ...) #'(ty-arg ...))
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#:with (τ_in ... τ_out)
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(stx-map
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(λ (t) (ev (substs #'(e_arg- ...) #'(X ...) t)))
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#'(τ_inX ... τ_outX))
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; #:do[(printf "vars: ~a\n" #'(X ...))]
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; #:when (stx-andmap (λ (t1 t2)(displayln (stx->datum t1)) (displayln (stx->datum t2)) (displayln (typecheck? t1 t2)) #;(typecheck? t1 t2)) #'(ty-arg ...) #'(τ_in ...))
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;; #:do[(stx-map
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;; (λ (tx t) (printf "ty_in inst: \n~a\n~a\n" (stx->datum tx) (stx->datum t)))
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;; #'(τ_inX ...) #'(τ_in ...))]
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; [⊢ e_arg- ≫ _ ⇐ τ_in] ...
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#:do[(printf "res e =\n~a\n" (stx->datum (substs #'(e_arg- ...) #'(x ...) #'e)))
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(printf "res t = ~a\n" (stx->datum (substs #'(e_arg- ...) #'(X ...) #'τ_out)))]
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#:with res-e (let L ([e (substs #'(e_arg- ...) #'(x ...) #'e)]) ; eval
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(syntax-parse e
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[(~or _:id
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((~literal #%plain-lambda) . _)
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(~Π ([_ : _] ...) _)
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(~= _ _)
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~Nat)
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e]
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;; handle nums
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[((~literal #%plain-app)
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(~and op (~or (~literal +-) (~literal zero?-)))
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. args:nats)
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#`#,(delta #'op #'args.vals)]
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[((~literal #%plain-app) . rst)
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(expand/df #`(#%app . #,(stx-map L #'rst)))]
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[_ e] ; other literals
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#;[es (stx-map L #'es)]))
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;; #:with res-ty (syntax-parse (substs #'(e_arg- ...) #'(X ...) #'τ_out)
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;; [((~literal #%plain-app) . rst) (expand/df #'(#%app . rst))]
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;; [other-ty #'other-ty])
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--------
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[⊢ res-e #;#,(substs #'(e_arg- ...) #'(x ...) #'e) ⇒ τ_out
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#;#,(substs #'(e_arg- ...) #'(X ...) #'τ_out)]]
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[(_ e_fn e_arg ... ~!) ≫ ; apply var
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; #:do[(printf "applying (2) ~a\n" (stx->datum #'e_fn))]
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[⊢ e_fn ≫ e_fn- ⇒ ty-fn]
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; #:do[(printf "e_fn- ty: ~a\n" (stx->datum #'ty-fn))]
|
||||
[⊢ e_fn ≫ _ ⇒ (~Π ([X : τ_inX] ...) τ_outX)]
|
||||
; #:do[(printf "e_fn- no: ~a\n" (stx->datum #'e_fn-))
|
||||
; (printf "args: ~a\n" (stx->datum #'(e_arg ...)))]
|
||||
;; #:with e_fn- (syntax-parse #'e_fn*
|
||||
;; [((~literal #%plain-app) . rst) (expand/df #'(#%app . rst))]
|
||||
;; [other #'other])
|
||||
#:fail-unless (stx-length=? #'[τ_inX ...] #'[e_arg ...])
|
||||
(num-args-fail-msg #'e_fn #'[τ_inX ...] #'[e_arg ...])
|
||||
[⊢ e_arg ≫ e_argX- ⇒ ty-argX] ... ; typechecking args must be fold; do in 2 steps
|
||||
#:do[(define (ev e)
|
||||
(syntax-parse e
|
||||
; [_ #:do[(printf "eval: ~a\n" (stx->datum e))] #:when #f #'(void)]
|
||||
[(~or _:id
|
||||
; ((~literal #%plain-lambda) . _)
|
||||
(~= _ _)
|
||||
~Nat
|
||||
((~literal quote) _))
|
||||
e]
|
||||
;; handle nums
|
||||
[((~literal #%plain-app)
|
||||
(~and op (~or (~literal +-) (~literal zero?-)))
|
||||
. args:nats)
|
||||
#`#,(delta #'op #'args.vals)]
|
||||
[((~literal #%plain-app) (~and f ((~literal #%plain-lambda) . b)) . rst)
|
||||
(expand/df #`(#%app f . #,(stx-map ev #'rst)))]
|
||||
[(x ...)
|
||||
;; #:do[(printf "t before: ~a\n" (typeof e))
|
||||
;; (printf "t after: ~a\n" (typeof #`#,(stx-map ev #'(x ...))))]
|
||||
(syntax-property #`#,(stx-map ev #'(x ...)) ': (typeof e))]
|
||||
[_ e] ; other literals
|
||||
#;[es (stx-map L #'es)]))]
|
||||
#:with (ty-arg ...)
|
||||
(stx-map
|
||||
(λ (t) (ev (substs #'(e_argX- ...) #'(X ...) t)))
|
||||
#'(ty-argX ...))
|
||||
#:with (e_arg- ...) (stx-map (λ (e t) (assign-type e t)) #'(e_argX- ...) #'(ty-arg ...))
|
||||
#:with (τ_in ... τ_out)
|
||||
(stx-map
|
||||
(λ (t) (ev (substs #'(e_arg- ...) #'(X ...) t)))
|
||||
#'(τ_inX ... τ_outX))
|
||||
;; #:do[(printf "vars: ~a\n" #'(X ...))]
|
||||
; #:when (stx-andmap (λ (e t1 t2)(displayln (stx->datum e))(displayln (stx->datum t1)) (displayln (stx->datum t2)) (displayln (typecheck? t1 t2)) #;(typecheck? t1 t2)) #'(e_arg ...)#'(ty-arg ...) #'(τ_in ...))
|
||||
;; #:do[(stx-map
|
||||
;; (λ (tx t) (printf "ty_in inst: \n~a\n~a\n" (stx->datum tx) (stx->datum t)))
|
||||
;; #'(τ_inX ...) #'(τ_in ...))]
|
||||
; [⊢ e_arg ≫ _ ⇐ τ_in] ...
|
||||
; #:do[(printf "res e2 =\n~a\n" (stx->datum #'(#%app- e_fn- e_arg- ...)))
|
||||
; (printf "res t2 = ~a\n" (stx->datum (substs #'(e_arg- ...) #'(X ...) #'τ_out)))]
|
||||
;; #:with res-e (syntax-parse #'e_fn-
|
||||
;; [((~literal #%plain-lambda) . _) (expand/df #'(#%app e_fn- e_arg- ...))]
|
||||
;; [other #'(#%app- e_fn- e_arg- ...)])
|
||||
--------
|
||||
[⊢ (#%app- e_fn- e_arg- ...) ⇒ τ_out
|
||||
#;#,(expand/df (substs #'(e_arg- ...) #'(X ...) #'τ_out))]])
|
||||
|
||||
(define-typed-syntax (ann e (~datum :) τ) ≫
|
||||
[⊢ e ≫ e- ⇐ τ]
|
||||
--------
|
||||
[⊢ e- ⇒ τ])
|
||||
|
||||
;; (define-typed-syntax (if e1 e2 e3) ≫
|
||||
;; [⊢ e1 ≫ e1- ⇒ _]
|
||||
;; [⊢ e2 ≫ e2- ⇒ ty]
|
||||
;; [⊢ e3 ≫ e3- ⇒ _]
|
||||
;; #:do[(displayln #'(e1 e2 e3))]
|
||||
;; --------------
|
||||
;; [⊢ (#%app- void-) ⇒ ty])
|
||||
|
||||
;; top-level ------------------------------------------------------------------
|
||||
;; TODO: shouldnt need define-type-alias, should be same as define
|
||||
(define-syntax define-type-alias
|
||||
(syntax-parser
|
||||
[(_ alias:id τ);τ:any-type)
|
||||
#'(define-syntax- alias
|
||||
(make-variable-like-transformer #'τ))]
|
||||
#;[(_ (f:id x:id ...) ty)
|
||||
#'(define-syntax- (f stx)
|
||||
(syntax-parse stx
|
||||
[(_ x ...)
|
||||
#:with τ:any-type #'ty
|
||||
#'τ.norm]))]))
|
||||
|
||||
(define-typed-syntax define
|
||||
[(_ x:id (~datum :) τ e:expr) ≫
|
||||
[⊢ e ≫ e- ⇐ τ]
|
||||
#:with y (generate-temporary #'x)
|
||||
#:with y+props (transfer-props #'e- #'y #:except '(origin))
|
||||
--------
|
||||
[≻ (begin-
|
||||
(define-syntax x (make-rename-transformer #'y+props))
|
||||
(define- y e-))]]
|
||||
[(_ x:id e) ≫
|
||||
;This won't work with mutually recursive definitions
|
||||
[⊢ e ≫ e- ⇒ _]
|
||||
#:with y (generate-temporary #'x)
|
||||
#:with y+props (transfer-props #'e- #'y #:except '(origin))
|
||||
--------
|
||||
[≻ (begin-
|
||||
(define-syntax x (make-rename-transformer #'y+props))
|
||||
(define- y e-))]]
|
||||
#;[(_ (f [x (~datum :) ty] ... (~or (~datum →) (~datum ->)) ty_out) e ...+) ≫
|
||||
#:with f- (add-orig (generate-temporary #'f) #'f)
|
||||
--------
|
||||
[≻ (begin-
|
||||
(define-syntax- f
|
||||
(make-rename-transformer (⊢ f- : (→ ty ... ty_out))))
|
||||
(define- f-
|
||||
(stlc+lit:λ ([x : ty] ...)
|
||||
(stlc+lit:ann (begin e ...) : ty_out))))]])
|
||||
|
||||
|
||||
;; peano nums -----------------------------------------------------------------
|
||||
(provide define-datatype)
|
||||
(struct TmpTy ())
|
||||
(struct TmpTy2 ())
|
||||
(define-typed-syntax define-datatype
|
||||
[(_ Name (~datum :) kind [C:id (~datum :) TY #;(~and TY (ar tyin ... tyout))] ...) ≫
|
||||
; need to expand `TY` but `Name` is still unbound so use tmp id
|
||||
#:with (TY* ...) (subst #'TmpTy #'Name #'(TY ...))
|
||||
[⊢ TY* ≫ TY- ⇐ #%type] ...
|
||||
#:with (_ TmpTy+) (local-expand #'(TmpTy) 'expression null)
|
||||
;; TODO: ignoring X ... for now
|
||||
;; TODO: replace TmpTy in origs of τ_in ... τ_out
|
||||
#:with ((~Π ([X : τ_in] ...) τ_out) ...)
|
||||
(subst #'Name #'TmpTy+ #'(TY- ...) free-id=?)
|
||||
#:with (C* ...) (generate-temporaries #'(C ...))
|
||||
#:with (C** ...) (generate-temporaries #'(C ...))
|
||||
#:with (Ccase ...) (generate-temporaries #'(C ...))
|
||||
#:with (C- ...) (generate-temporaries #'(C ...))
|
||||
;; Can I just use X instead of fld?
|
||||
#:with ((fld ...) ...) (stx-map generate-temporaries #'((τ_in ...) ...))
|
||||
#:with ((fld- ...) ...) (stx-map generate-temporaries #'((τ_in ...) ...))
|
||||
#:with elim-Name (format-id #'Name "elim-~a" #'Name)
|
||||
#:with match-Name (format-id #'Name "match-~a" #'Name)
|
||||
#:with match-Name/delayed (format-id #'Name "match-~a/delayed" #'Name)
|
||||
--------
|
||||
[≻ (begin-
|
||||
(define-base-type Name)
|
||||
(struct C* (fld ...) #:transparent) ...
|
||||
(define-typed-syntax C
|
||||
[:id ≫ --- [⊢ C* ⇒ TY]]
|
||||
[(_ fld ...) ≫
|
||||
[⊢ fld ≫ fld- ⇐ τ_in] ...
|
||||
--------
|
||||
[⊢ (C* fld- ...) ⇒ τ_out]]) ...
|
||||
(define-typed-syntax (elim-Name x P C* ...) ≫
|
||||
[⊢ x ≫ x- ⇐ Name]
|
||||
[⊢ P ≫ P- ⇐ (→ Name #%type)] ; prop / motive
|
||||
; [⊢ z ≫ z- ⇐ (app P- Zero)] ; zero
|
||||
; [⊢ C ≫ C- ⇐ (Π ([k : Nat]) (→ (app P- k) (app P- (Succ k))))] ; succ
|
||||
;; TODO: the (app P- fld) ... is wrong, should only include recur args
|
||||
;; for now, each case consumes the number of args for each C,
|
||||
;; and then an IH for each arg
|
||||
[⊢ C* ≫ C- ⇐ (Π ([fld : τ_in] ...) (→ (app P- fld) ... (app P- (C fld ...))))] ...
|
||||
-----------
|
||||
[⊢ (match-Name x- P- C- ...) ⇒ (app P- x-)])
|
||||
(struct match-Name/delayed (m))
|
||||
(define-syntax match-Name
|
||||
(syntax-parser
|
||||
#;[(_ . args)
|
||||
#:do[(printf "trying to match:\n~a\n" (stx->datum #'args))]
|
||||
#:when #f #'(void)]
|
||||
[(_ n P Ccase ...)
|
||||
(syntax-parse #'n
|
||||
[((~literal #%plain-app) C-:id fld ...)
|
||||
;; TODO: check C- matches actual C
|
||||
;; for now, it's just an arity match
|
||||
#'(app/eval (app/eval Ccase fld ...) (match-Name fld P Ccase ...) ...)] ...
|
||||
[_ #'(#%app match/delayed 'match-Name (void n P Ccase ...))])]))
|
||||
)]])
|
||||
;; ;; #:with res (if (typecheck? #'n- (expand/df #'Z))
|
||||
;; ;; #'z-
|
||||
;; ;; #'(s- (nat-ind P- z- s- (sub1 n-))))
|
||||
;; ----------------
|
||||
;; [⊢ (match/nat n-
|
||||
;; P-
|
||||
;; z-
|
||||
;; s-
|
||||
;; #;(λ ([n-1 : Nat][rec : (app P- n-)])
|
||||
;; (app s- n-1 rec #;(nat-ind P- z- s- n-1))))
|
||||
;; ⇒ (app P- n-)])
|
||||
; [≻ (P- d-)])
|
||||
;; (define-syntax match/nat
|
||||
;; (syntax-parser
|
||||
;; [(_ n P zc sc)
|
||||
;; #:do[(when debug-match?
|
||||
;; (printf "match/nating: ~a\n" (stx->datum #'(n P zc sc)))
|
||||
;; #;(printf "zc ty: ~a\n" (stx->datum (typeof #'zc)))
|
||||
;; #;(printf "sc ty: ~a\n" (stx->datum (typeof #'sc))))]
|
||||
;; #:when #f #'(void)]
|
||||
;; [(_ (~and n ((~literal #%plain-app) z0:id)) P zc sc)
|
||||
;; #:with (_ z1) (local-expand #'(#%app Z) 'expression null)
|
||||
;; #:when (free-identifier=? #'z0 #'z1)
|
||||
;; #:do [(when debug-match? (displayln 'zc))]
|
||||
;; ;; #:when (printf "match eval res zero ety: ~a\n" (stx->datum (typeof this-syntax)))
|
||||
;; ;; #:when (printf "match eval res zero ty: ~a\n" (stx->datum (typeof #'zc)))
|
||||
;; (assign-type #'zc #'(app/eval P n))]
|
||||
;; [(_ (~and n ((~literal #%plain-app) s0:id m)) P zc sc)
|
||||
;; #:with (_ s1 . _) (local-expand #'(#%app S 'dont-care) 'expression null)
|
||||
;; #:when (free-identifier=? #'s0 #'s1)
|
||||
;; #:with (~Π ([_ : _] ...) τ_out) (typeof #'sc)
|
||||
;; #:do[(when debug-match? (displayln 'sc))]
|
||||
;; ;; #:when (printf "match eval res succ ety: ~a\n" (stx->datum (typeof this-syntax)))
|
||||
;; ;; #:when (printf "match eval res succ ty: ~a\n" (stx->datum (typeof #'sc)))
|
||||
;; ;; #:when (printf "match eval res succ ty: ~a\n" (stx->datum (typeof #'(app/eval (app/eval sc m) (match/nat m P zc sc)))))
|
||||
;; ; #`(app sc m (nat-rec #,(typeof #'zc) zc sc m))]
|
||||
;; ; #:with ty (typeof this-syntax)
|
||||
;; (assign-type
|
||||
;; #`(app/eval #,(assign-type #'(app/eval sc m) #'τ_out) (match/nat m P zc sc))
|
||||
;; #'(app/eval P n))
|
||||
;; ; #'res
|
||||
;; ; (if (syntax-e #'ty) (assign-type #'res #'ty) #'res)
|
||||
;; #;(assign-type #`(app/eval #,(assign-type #'(app/eval sc m) #'τ_out) (match/nat m P zc sc)) (typeof this-syntax))]
|
||||
;; [(_ n P zc sc)
|
||||
;; #:do[(when debug-match? (displayln "delay match"))]
|
||||
;; (assign-type #'(#%app match/delayed n P zc sc) #'(app/eval P n))]))
|
||||
;; #;(define-typed-syntax (nat-rec ty zc sc n) ≫
|
||||
;; [⊢ ty ≫ ty- ⇐ #%type]
|
||||
;; [⊢ zc ≫ zc- ⇐ ty-] ; zero case
|
||||
;; [⊢ sc ≫ sc- ⇐ (→ ty- ty-)] ; succ case
|
||||
;; [⊢ n ≫ n- ⇐ Nat]
|
||||
;; ;; #:with res
|
||||
;; ;; (syntax-parse #'n-
|
||||
;; ;; [aaa #:do[(printf "matching: ~a\n" (stx->datum #'aaa))] #:when #f #'(void)]
|
||||
;; ;; [((~literal #%plain-app) (~literal Z)) #'zc-]
|
||||
;; ;; [((~literal #%plain-app) (~literal S) m) #'(app sc- (nat-rec zc- sc- m))])
|
||||
;; --------------------
|
||||
;; ; [⊢ (match/eval n- zc- sc-) ⇒ ty-])
|
||||
;; [⊢ (match/nat n-
|
||||
;; zc-
|
||||
;; (λ ([n-1 : Nat][rec : ty-])
|
||||
;; (sc- rec)))
|
||||
;; ⇒ ty-])
|
||||
; )]])
|
||||
;; (define-base-type Nat)
|
||||
|
||||
;; (struct Z () #:transparent)
|
||||
;; (struct S (n) #:transparent)
|
||||
|
||||
;; (define-typed-syntax Zero
|
||||
;; [_:id ≫ --- [⊢ (Z) ⇒ Nat]])
|
||||
|
||||
;; (define-typed-syntax (Succ n) ≫
|
||||
;; [⊢ n ≫ n- ⇐ Nat]
|
||||
;; -----------
|
||||
;; [⊢ (S n-) ⇒ Nat])
|
||||
;; #;(define-typed-syntax (sub1 n) ≫
|
||||
;; [⊢ n ≫ n- ⇐ Nat]
|
||||
;; #:do[(displayln #'n-)]
|
||||
;; -----------
|
||||
;; [⊢ (#%app- -- n- 1) ⇒ Nat])
|
||||
|
||||
;; ;; generalized recursor over natural nums
|
||||
;; ;; (cases dispatched in #%app)
|
||||
;; ;; (define- (nat-ind- P z s n) (#%app- void))
|
||||
;; ;; (define-syntax nat-ind
|
||||
;; ;; (make-variable-like-transformer
|
||||
;; ;; (assign-type
|
||||
;; ;; #'nat-ind-
|
||||
;; ;; #'(Π ([P : (→ Nat #%type)]
|
||||
;; ;; [z : (app P Zero)]
|
||||
;; ;; [s : (Π ([k : Nat]) (→ (app P k) (app P (Succ k))))]
|
||||
;; ;; [n : Nat])
|
||||
;; ;; (app P n)))))
|
||||
|
||||
;; #;(define-type-alias nat-ind
|
||||
;; (λ ([P : (→ Nat #%type)]
|
||||
;; [z : (P Z)]
|
||||
;; [s : (Π ([k : Nat]) (→ (P k) (P (S k))))]
|
||||
;; [n : Nat])
|
||||
;; #'(#%app- nat-ind- P z s n)))
|
||||
(struct match/delayed (name args))
|
||||
;; #;(define-syntax match/eval
|
||||
;; (syntax-parser
|
||||
;; [(_ n zc sc) #:do[(printf "matching: ~a\n" (stx->datum #'n))] #:when #f #'(void)]
|
||||
;; [(_ ((~literal #%plain-app) z0:id) zc sc)
|
||||
;; #:with (_ z1) (local-expand #'(Z) 'expression null)
|
||||
;; #:when (free-identifier=? #'z0 #'z1)
|
||||
;; #'zc]
|
||||
;; [(_ ((~literal #%plain-app) s0:id m) zc sc)
|
||||
;; #:with (_ s1 . _) (local-expand #'(S 'dont-care) 'expression null)
|
||||
;; #:when (free-identifier=? #'s0 #'s1)
|
||||
;; #:when (displayln 2)
|
||||
;; #`(app sc (nat-rec #,(typeof #'zc) zc sc m))]
|
||||
;; [(_ n zc sc) #'(match/delayed n zc sc)]))
|
||||
|
||||
;; ;; this is an "eval" form; should not do any more type checking
|
||||
;; ;; otherwise, will get type errs some some subexprs may still have uninst tys
|
||||
;; ;; eg, zc and sc were typechecked with paramaterized P instead of inst'ed P
|
||||
;; (define-syntax match/nat
|
||||
;; (syntax-parser
|
||||
;; [(_ n P zc sc)
|
||||
;; #:do[(when debug-match?
|
||||
;; (printf "match/nating: ~a\n" (stx->datum #'(n P zc sc)))
|
||||
;; #;(printf "zc ty: ~a\n" (stx->datum (typeof #'zc)))
|
||||
;; #;(printf "sc ty: ~a\n" (stx->datum (typeof #'sc))))]
|
||||
;; #:when #f #'(void)]
|
||||
;; [(_ (~and n ((~literal #%plain-app) z0:id)) P zc sc)
|
||||
;; #:with (_ z1) (local-expand #'(#%app Z) 'expression null)
|
||||
;; #:when (free-identifier=? #'z0 #'z1)
|
||||
;; #:do [(when debug-match? (displayln 'zc))]
|
||||
;; ;; #:when (printf "match eval res zero ety: ~a\n" (stx->datum (typeof this-syntax)))
|
||||
;; ;; #:when (printf "match eval res zero ty: ~a\n" (stx->datum (typeof #'zc)))
|
||||
;; (assign-type #'zc #'(app/eval P n))]
|
||||
;; [(_ (~and n ((~literal #%plain-app) s0:id m)) P zc sc)
|
||||
;; #:with (_ s1 . _) (local-expand #'(#%app S 'dont-care) 'expression null)
|
||||
;; #:when (free-identifier=? #'s0 #'s1)
|
||||
;; #:with (~Π ([_ : _] ...) τ_out) (typeof #'sc)
|
||||
;; #:do[(when debug-match? (displayln 'sc))]
|
||||
;; ;; #:when (printf "match eval res succ ety: ~a\n" (stx->datum (typeof this-syntax)))
|
||||
;; ;; #:when (printf "match eval res succ ty: ~a\n" (stx->datum (typeof #'sc)))
|
||||
;; ;; #:when (printf "match eval res succ ty: ~a\n" (stx->datum (typeof #'(app/eval (app/eval sc m) (match/nat m P zc sc)))))
|
||||
;; ; #`(app sc m (nat-rec #,(typeof #'zc) zc sc m))]
|
||||
;; ; #:with ty (typeof this-syntax)
|
||||
;; (assign-type
|
||||
;; #`(app/eval #,(assign-type #'(app/eval sc m) #'τ_out) (match/nat m P zc sc))
|
||||
;; #'(app/eval P n))
|
||||
;; ; #'res
|
||||
;; ; (if (syntax-e #'ty) (assign-type #'res #'ty) #'res)
|
||||
;; #;(assign-type #`(app/eval #,(assign-type #'(app/eval sc m) #'τ_out) (match/nat m P zc sc)) (typeof this-syntax))]
|
||||
;; [(_ n P zc sc)
|
||||
;; #:do[(when debug-match? (displayln "delay match"))]
|
||||
;; (assign-type #'(#%app match/delayed n P zc sc) #'(app/eval P n))]))
|
||||
;; #;(define-typed-syntax (nat-rec ty zc sc n) ≫
|
||||
;; [⊢ ty ≫ ty- ⇐ #%type]
|
||||
;; [⊢ zc ≫ zc- ⇐ ty-] ; zero case
|
||||
;; [⊢ sc ≫ sc- ⇐ (→ ty- ty-)] ; succ case
|
||||
;; [⊢ n ≫ n- ⇐ Nat]
|
||||
;; ;; #:with res
|
||||
;; ;; (syntax-parse #'n-
|
||||
;; ;; [aaa #:do[(printf "matching: ~a\n" (stx->datum #'aaa))] #:when #f #'(void)]
|
||||
;; ;; [((~literal #%plain-app) (~literal Z)) #'zc-]
|
||||
;; ;; [((~literal #%plain-app) (~literal S) m) #'(app sc- (nat-rec zc- sc- m))])
|
||||
;; --------------------
|
||||
;; ; [⊢ (match/eval n- zc- sc-) ⇒ ty-])
|
||||
;; [⊢ (match/nat n-
|
||||
;; zc-
|
||||
;; (λ ([n-1 : Nat][rec : ty-])
|
||||
;; (sc- rec)))
|
||||
;; ⇒ ty-])
|
||||
|
||||
;; (define-typed-syntax (nat-ind P z s n) ≫
|
||||
;; [⊢ P ≫ P- ⇐ (→ Nat #%type)]
|
||||
;; [⊢ z ≫ z- ⇐ (app P- Zero)] ; zero
|
||||
;; [⊢ s ≫ s- ⇐ (Π ([k : Nat]) (→ (app P- k) (app P- (Succ k))))] ; succ
|
||||
;; [⊢ n ≫ n- ⇐ Nat]
|
||||
;; ;; #:with res (if (typecheck? #'n- (expand/df #'Z))
|
||||
;; ;; #'z-
|
||||
;; ;; #'(s- (nat-ind P- z- s- (sub1 n-))))
|
||||
;; ----------------
|
||||
;; [⊢ (match/nat n-
|
||||
;; P-
|
||||
;; z-
|
||||
;; s-
|
||||
;; #;(λ ([n-1 : Nat][rec : (app P- n-)])
|
||||
;; (app s- n-1 rec #;(nat-ind P- z- s- n-1))))
|
||||
;; ⇒ (app P- n-)])
|
||||
;; ; [≻ (P- d-)])
|
||||
137
turnstile/examples/tests/dep-ind-tests.rkt
Normal file
137
turnstile/examples/tests/dep-ind-tests.rkt
Normal file
|
|
@ -0,0 +1,137 @@
|
|||
#lang s-exp "../dep-ind.rkt"
|
||||
(require "rackunit-typechecking.rkt")
|
||||
|
||||
; Π → λ ∀ ≻ ⊢ ≫ ⇒
|
||||
|
||||
;; examples from Prabhakar's Proust paper
|
||||
|
||||
;; this file is like dep-peano-tests.rkt except it uses
|
||||
;; define-datatype from #lang dep-ind.rkt to define Nat,
|
||||
;; instead of using the builtin Nat from #lang dep.rkt
|
||||
|
||||
;; the examples in this file are mostly identical to dep-peano-tests.rkt,
|
||||
;; except Z is replaced with (Z)
|
||||
|
||||
;; Peano nums -----------------------------------------------------------------
|
||||
|
||||
(define-datatype Nat : *
|
||||
[Z : (→ Nat)]
|
||||
[S : (→ Nat Nat)])
|
||||
|
||||
; TODO: special case 0-arity constructor using id macro
|
||||
(check-type Z : (→ Nat))
|
||||
(check-type S : (→ Nat Nat))
|
||||
;(check-type Z : Nat -> Z)
|
||||
(check-type (Z) : Nat -> (Z))
|
||||
(check-type (S (Z)) : Nat -> (S (Z)))
|
||||
(check-type (S (S (Z))) : Nat -> (S (S (Z))))
|
||||
|
||||
(define-type-alias nat-rec
|
||||
(λ ([C : *])
|
||||
(λ ([zc : (→ C)][sc : (→ C C)])
|
||||
(λ ([n : Nat])
|
||||
(elim-Nat n
|
||||
(λ ([x : Nat]) C)
|
||||
(λ () zc)
|
||||
(λ ([x : Nat]) sc))))))
|
||||
(check-type nat-rec : (∀ (C) (→ (→ C) (→ C C) (→ Nat C))))
|
||||
|
||||
;; nat-rec with no annotations
|
||||
(check-type
|
||||
(λ (C)
|
||||
(λ (zc sc)
|
||||
(λ (n)
|
||||
(elim-Nat n
|
||||
(λ (x) C)
|
||||
(λ () zc)
|
||||
(λ (x) sc)))))
|
||||
: (∀ (C) (→ (→ C) (→ C C) (→ Nat C))))
|
||||
|
||||
(check-type (nat-rec Nat) : (→ (→ Nat) (→ Nat Nat) (→ Nat Nat)))
|
||||
(check-type ((nat-rec Nat) Z (λ ([n : Nat]) (S n))) : (→ Nat Nat))
|
||||
|
||||
;; basic identity example, to test eval
|
||||
(define-type-alias id ((nat-rec Nat) Z (λ ([n : Nat]) (S n))))
|
||||
|
||||
(check-type (id (Z)) : Nat -> (Z))
|
||||
;; this example will err if eval tries to tycheck again
|
||||
(check-type (id (S (Z))) : Nat)
|
||||
(check-type (id (S (Z))) : Nat -> (S (Z)))
|
||||
|
||||
(define-type-alias plus
|
||||
(λ ([n : Nat])
|
||||
(((nat-rec (→ Nat Nat))
|
||||
(λ () (λ ([m : Nat]) m))
|
||||
(λ ([pm : (→ Nat Nat)])
|
||||
(λ ([x : Nat])
|
||||
(S (pm x)))))
|
||||
n)))
|
||||
|
||||
(check-type plus : (→ Nat (→ Nat Nat)))
|
||||
|
||||
;; infer, and dont curry
|
||||
(check-type
|
||||
(λ (n1 n2)
|
||||
((((nat-rec (→ Nat Nat))
|
||||
(λ () (λ (m) m))
|
||||
(λ (pm) (λ (x) (S (pm x)))))
|
||||
n1)
|
||||
n2))
|
||||
: (→ Nat Nat Nat))
|
||||
|
||||
;(check-type ((plus Z) Z) : Nat -> 0)
|
||||
;(check-type ((plus (S Z)) (S Z)) : Nat -> 2)
|
||||
;(check-type ((plus (S Z)) Z) : Nat -> 1)
|
||||
;(check-type ((plus (S Z)) Z) : Nat -> 1)
|
||||
(check-type (plus (Z)) : (→ Nat Nat))
|
||||
(check-type ((plus (Z)) (Z)) : Nat -> (Z))
|
||||
(check-type ((plus (Z)) (S (Z))) : Nat -> (S (Z)))
|
||||
(check-type ((plus (S (Z))) (Z)) : Nat -> (S (Z)))
|
||||
(check-type ((plus (S (Z))) (S (Z))) : Nat -> (S (S (Z))))
|
||||
(check-type ((plus (S (S (Z)))) (S (Z))) : Nat -> (S (S (S (Z)))))
|
||||
(check-type ((plus (S (Z))) (S (S (Z)))) : Nat -> (S (S (S (Z)))))
|
||||
|
||||
;; plus zero (left)
|
||||
(check-type (λ ([n : Nat]) (eq-refl n))
|
||||
: (Π ([n : Nat]) (= ((plus (Z)) n) n)))
|
||||
|
||||
;; plus zero (right)
|
||||
(check-type
|
||||
(λ ([n : Nat])
|
||||
(elim-Nat n
|
||||
(λ ([m : Nat]) (= ((plus m) (Z)) m))
|
||||
(λ () (λ () (eq-refl (Z))))
|
||||
(λ ([k : Nat])
|
||||
(λ ([p : (= ((plus k) (Z)) k)])
|
||||
(eq-elim ((plus k) (Z))
|
||||
(λ ([W : Nat]) (= (S ((plus k) (Z))) (S W)))
|
||||
(eq-refl (S ((plus k) (Z))))
|
||||
k
|
||||
p)))))
|
||||
: (Π ([n : Nat]) (= ((plus n) (Z)) n)))
|
||||
|
||||
;; plus zero identity, no annotations
|
||||
;; left:
|
||||
(check-type (λ (n) (eq-refl n))
|
||||
: (Π ([n : Nat]) (= ((plus (Z)) n) n)))
|
||||
;; right:
|
||||
(check-type
|
||||
(λ (n)
|
||||
(elim-Nat n
|
||||
(λ (m) (= ((plus m) (Z)) m))
|
||||
(λ () (λ () (eq-refl (Z))))
|
||||
(λ (k) (λ (p)
|
||||
(eq-elim ((plus k) (Z))
|
||||
(λ (W) (= (S ((plus k) (Z))) (S W)))
|
||||
(eq-refl (S ((plus k) (Z))))
|
||||
k
|
||||
p)))))
|
||||
: (Π ([n : Nat]) (= ((plus n) (Z)) n)))
|
||||
|
||||
;; nat-ind as a function ; TODO: need matching form or matching lambda
|
||||
#;(define-typed-alias nat-ind2
|
||||
(λ ([P : (→ Nat *)]
|
||||
[Zcase : (P Z)]
|
||||
[Scase : (Π ([k : Nat]) (→ (P k) (P (S k))))]
|
||||
[n : Nat])
|
||||
(match/nat n ZCase (SCase n (nat-ind2 P ZCase SCase n-1)))))
|
||||
Loading…
Reference in New Issue
Block a user