add dep2-assist
This commit is contained in:
Stephen Chang
parent
bbb6b0a694
commit
eae7e14c44
629
turnstile/examples/dep2-assist.rkt
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629
turnstile/examples/dep2-assist.rkt
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@ -0,0 +1,629 @@
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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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; 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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;; must use free-identifier=? to work with prove/define and `?`
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[[x ≫ x- : τ_in] ... ⊢ #,(substs #'(x ...) #'(y ...) #'e free-identifier=?) ≫ 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 n P zc sc)
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#:with (_ m/d . _) (local-expand #'(#%app match/delayed 'do 'nt 'ca 're) '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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#'(match/nat n P zc sc)]
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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))]
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[⊢ e_fn ≫ _ ⇒ (~Π ([X : τ_inX] ...) τ_outX)]
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; #:do[(printf "e_fn- no: ~a\n" (stx->datum #'e_fn-))
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; (printf "args: ~a\n" (stx->datum #'(e_arg ...)))]
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;; #: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 -----------------------------------------------------------------
|
||||
(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 (n P zc sc))
|
||||
#;(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-)])
|
||||
|
||||
;; proof assistant
|
||||
|
||||
(provide prove ? refine)
|
||||
|
||||
(struct ?? ())
|
||||
(define-for-syntax ?+ (stx-cadr (local-expand #'(??) 'expression null)))
|
||||
|
||||
(define-typed-syntax ?
|
||||
[(_ ty) ≫
|
||||
#:with x (generate-temporary)
|
||||
#:do[(current-hole #'x)]
|
||||
-----
|
||||
[⊢ #,?+ ⇒ ty]]
|
||||
[_:id ⇐ ty ≫
|
||||
#:with x (generate-temporary)
|
||||
#:do[(current-hole #'x)]
|
||||
-----
|
||||
[⊢ #,?+]])
|
||||
|
||||
(begin-for-syntax
|
||||
(define current-ty (make-parameter #f))
|
||||
(define current-hole (make-parameter #f))
|
||||
(define current-expr (make-parameter #f))
|
||||
(define (update-expr e)
|
||||
(set-expr (subst e ?+ (current-expr) free-identifier=?)))
|
||||
(define (set-expr e)
|
||||
(current-expr e)
|
||||
(printf "current proof: ~a\n" (stx->datum (current-expr))))
|
||||
(define (mk-hole)
|
||||
(current-hole (generate-temporary))
|
||||
(current-hole)))
|
||||
|
||||
|
||||
(define-syntax prove
|
||||
(syntax-parser
|
||||
[(_ ty)
|
||||
#:do[(current-ty ((current-type-eval) #'ty))]
|
||||
#:when (local-expand #'(? ty) 'expression null)
|
||||
#:do[(set-expr #'?)]
|
||||
#'(void)]))
|
||||
|
||||
(define-typed-syntax refine
|
||||
[(_ e) ≫
|
||||
#:do[(printf "refining with: ~a\n" (stx->datum #'e))]
|
||||
#:with ty (current-ty)
|
||||
#:with e0 (subst #'e #'? (current-expr) free-identifier=?)
|
||||
[⊢ e0 ≫ e0- ⇐ ty]
|
||||
#:do [(displayln "ok.")
|
||||
(set-expr #'e0)
|
||||
(let ([x (generate-temporary)])
|
||||
(when ((current-type=?) #'e0 (subst #'x #'? #'e0 free-identifier=?))
|
||||
(displayln "qed.")))]
|
||||
-------
|
||||
[⊢ (void) ⇒ ty]])
|
||||
295
turnstile/examples/tests/dep2-assist-tests.rkt
Normal file
295
turnstile/examples/tests/dep2-assist-tests.rkt
Normal file
|
|
@ -0,0 +1,295 @@
|
|||
#lang s-exp "../dep2-assist.rkt"
|
||||
(require "rackunit-typechecking.rkt")
|
||||
|
||||
; Π → λ ∀ ≻ ⊢ ≫ ⇒
|
||||
|
||||
;; examples from Prabhakar's Proust paper
|
||||
|
||||
(prove (∀ (A B C) (→ (→ A B) (→ B C) (→ A C))))
|
||||
|
||||
(refine (λ (a b c) ?))
|
||||
(refine (λ (f g) ?))
|
||||
(refine (λ (x) ?))
|
||||
; (refine (f ?)) ; wrong, g first
|
||||
(refine (g ?))
|
||||
(refine (f ?))
|
||||
(refine x)
|
||||
|
||||
;; ;; the following examples to not require type-level eval
|
||||
;; (check-type (λ ([x : *]) x) : (Π ([x : *]) *))
|
||||
|
||||
;; (typecheck-fail ((λ ([x : *]) x) (λ ([x : *]) x))
|
||||
;; #:verb-msg "expected *, given (Π ([x : *]) *)")
|
||||
|
||||
;; (check-type (λ ([A : *][B : *])
|
||||
;; (λ ([x : A])
|
||||
;; (λ ([y : (→ A B)])
|
||||
;; (y x))))
|
||||
;; : (∀ (A B) (→ A (→ (→ A B) B))))
|
||||
|
||||
;; ;; check alpha equiv
|
||||
;; ;; TODO: is this correct behavior?
|
||||
;; (check-type (λ ([A : *][B : *])
|
||||
;; (λ ([x : A])
|
||||
;; (λ ([y : (→ A B)])
|
||||
;; (y x))))
|
||||
;; : (∀ (Y Z) (→ Y (→ (→ Y Z) Z))))
|
||||
;; (check-type (λ ([Y : *][Z : *])
|
||||
;; (λ ([x : Y])
|
||||
;; (λ ([y : (→ Y Z)])
|
||||
;; (y x))))
|
||||
;; : (∀ (A B) (→ A (→ (→ A B) B))))
|
||||
;; ;; check infer direction
|
||||
;; (check-type (λ (A B) (λ (x) (λ (y) (y x))))
|
||||
;; : (∀ (A B) (→ A (→ (→ A B) B))))
|
||||
;; (check-type (λ (A B) (λ (x) (λ (y) (y x))))
|
||||
;; : (∀ (X Y) (→ X (→ (→ X Y) Y))))
|
||||
|
||||
;; ;; transitivity of implication --------------------
|
||||
;; (check-type (λ ([A : *][B : *][C : *])
|
||||
;; (λ ([f : (→ B C)])
|
||||
;; (λ ([g : (→ A B)])
|
||||
;; (λ ([x : A])
|
||||
;; (f (g x))))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
|
||||
;; ;; less currying
|
||||
;; (check-type (λ ([A : *][B : *][C : *])
|
||||
;; (λ ([f : (→ B C)][g : (→ A B)])
|
||||
;; (λ ([x : A])
|
||||
;; (f (g x)))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
|
||||
;; ;; infer direction (no annotations)
|
||||
;; (check-type (λ (A B C) (λ (f) (λ (g) (λ (x) (f (g x))))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
|
||||
;; ;; less currying
|
||||
;; (check-type (λ (A B C) (λ (f g) (λ (x) (f (g x)))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
|
||||
;; (check-type (λ (A B C) (λ (f g x) (f (g x))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ A B) A C)))
|
||||
;; (check-type (λ (A B C f g x) (f (g x)))
|
||||
;; : (Π ([A : *][B : *][C : *][f : (→ B C)][g : (→ A B)][x : A]) C))
|
||||
;; (check-type (λ (A B C f g x) (f (g x)))
|
||||
;; : (Π ([X : *][Y : *][Z : *][a : (→ Y Z)][b : (→ X Y)][c : X]) Z))
|
||||
|
||||
;; ;; partial annotations - outer lam with no annotations
|
||||
;; (check-type (λ (A B C)
|
||||
;; (λ (f g)
|
||||
;; (λ ([x : A])
|
||||
;; (f (g x)))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
|
||||
;; (check-type (λ (A B C)
|
||||
;; (λ ([f : (→ B C)][g : (→ A B)])
|
||||
;; (λ ([x : A])
|
||||
;; (f (g x)))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
|
||||
;; (typecheck-fail (ann
|
||||
;; (λ (A B C)
|
||||
;; (λ (f g)
|
||||
;; (λ ([x : C])
|
||||
;; (f (g x)))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
|
||||
;; #:with-msg "expected A, given C")
|
||||
;; ;; partial annotations - inner lam with no annotations
|
||||
;; (check-type (λ ([A : *][B : *][C : *])
|
||||
;; (λ (f g)
|
||||
;; (λ (x)
|
||||
;; (f (g x)))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
|
||||
;; (check-type (λ ([A : *][B : *][C : *])
|
||||
;; (λ ([f : (→ B C)])
|
||||
;; (λ (g)
|
||||
;; (λ (x)
|
||||
;; (f (g x))))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
|
||||
;; (check-type (λ ([A : *][B : *][C : *])
|
||||
;; (λ ([f : (→ B C)])
|
||||
;; (λ (g)
|
||||
;; (λ ([x : A])
|
||||
;; (f (g x))))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
|
||||
;; (check-type (λ ([A : *][B : *][C : *])
|
||||
;; (λ ([f : (→ B C)])
|
||||
;; (λ ([g : (→ A B)])
|
||||
;; (λ (x)
|
||||
;; (f (g x))))))
|
||||
;; : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
|
||||
|
||||
;; ;; Peirce's Law (doesnt work)
|
||||
;; (typecheck-fail (ann
|
||||
;; (λ ([A : *][B : *][C : *])
|
||||
;; (λ ([f : (→ (→ A B) A)])
|
||||
;; (λ ([g : (→ A B)]) ; need concrete (→ A B) (not in type)
|
||||
;; (f g))))
|
||||
;; : (∀ (A B C) (→ (→ (→ A B) A) A)))
|
||||
;; #:verb-msg "expected (∀ (A B C) (→ (→ (→ A B) A) A)), given (Π ((A : *) (B : *) (C : *)) (Π ((f : (→ (→ A B) A))) (Π ((g : (→ A B))) A)))")
|
||||
|
||||
;; ;; booleans -------------------------------------------------------------------
|
||||
|
||||
;; ;; Bool base type
|
||||
;; ;; TODO: use define instead of define-type-alias
|
||||
;; (define-type-alias Bool (∀ (A) (→ A A A)))
|
||||
;; (check-type Bool : *)
|
||||
|
||||
;; ;; Bool terms
|
||||
;; (define T (λ ([A : *]) (λ ([x : A][y : A]) x)))
|
||||
;; (define F (λ ([A : *]) (λ ([x : A][y : A]) y)))
|
||||
;; (check-type T : Bool)
|
||||
;; (check-type F : Bool)
|
||||
;; ;; check infer case
|
||||
;; (define T2 (λ ([abool : *]) (λ ([x : abool][y : abool]) x)))
|
||||
;; (define F2 (λ ([abool : *]) (λ ([x : abool][y : abool]) y)))
|
||||
;; (check-type T2 : Bool)
|
||||
;; (check-type F2 : Bool)
|
||||
;; (define T3 : Bool (λ (abool) (λ (x y) x)))
|
||||
;; (define F3 : Bool (λ (abool) (λ (x y) y)))
|
||||
;; (check-type T3 : Bool)
|
||||
;; (check-type F3 : Bool)
|
||||
|
||||
;; ;; defining `and` requires instantiating polymorphic types
|
||||
;; (define and (λ ([x : Bool][y : Bool]) ((x Bool) y F)))
|
||||
;; (check-type and : (→ Bool Bool Bool))
|
||||
;; (define or (λ ([x : Bool][y : Bool]) ((x Bool) T y)))
|
||||
;; (check-type or : (→ Bool Bool Bool))
|
||||
;; (define not (λ ([x : Bool]) ((x Bool) F T)))
|
||||
;; (check-type not : (→ Bool Bool))
|
||||
|
||||
;; ;; `And` type constructor, ie type-level fn
|
||||
;; (define-type-alias And
|
||||
;; (λ ([P : *][Q : *])
|
||||
;; (∀ (C) (→ (→ P Q C) C))))
|
||||
;; (check-type And : (→ * * *))
|
||||
|
||||
;; ;; And type intro (logical conj)
|
||||
;; (define ∧
|
||||
;; (λ ([P : *][Q : *])
|
||||
;; (λ ([p : P][q : Q])
|
||||
;; (λ ([C : *])
|
||||
;; (λ ([f : (→ P Q C)])
|
||||
;; (f p q))))))
|
||||
;; (check-type ∧ : (∀ (P Q) (→ P Q (And P Q))))
|
||||
|
||||
;; ;; `And` type elim
|
||||
;; (define proj1
|
||||
;; (λ ([P : *][Q : *])
|
||||
;; (λ ([e : (And P Q)])
|
||||
;; ((e P) (λ ([x : P][y : Q]) x)))))
|
||||
;; (define proj2
|
||||
;; (λ ([P : *][Q : *])
|
||||
;; (λ ([e : (And P Q)])
|
||||
;; ((e Q) (λ ([x : P][y : Q]) y)))))
|
||||
;; ;; bad proj2: (e A) should be (e B)
|
||||
;; (typecheck-fail
|
||||
;; (λ ([P : *][Q : *])
|
||||
;; (λ ([e : (And P Q)])
|
||||
;; ((e P) (λ ([x : P][y : Q]) y))))
|
||||
;; #:verb-msg
|
||||
;; "expected (→ P Q C), given (Π ((x : P) (y : Q)) Q)")
|
||||
;; (check-type proj1 : (∀ (P Q) (→ (And P Q) P)))
|
||||
;; (check-type proj2 : (∀ (P Q) (→ (And P Q) Q)))
|
||||
|
||||
;; ;; proj1, no annotations
|
||||
;; (check-type (λ (P Q) (λ (e) ((e P) (λ (x y) x))))
|
||||
;; : (∀ (P Q) (→ (And P Q) P)))
|
||||
;; ;; proj2, no annotations
|
||||
;; (check-type (λ (P Q) (λ (e) ((e Q) (λ (x y) y))))
|
||||
;; : (∀ (P Q) (→ (And P Q) Q)))
|
||||
;; (typecheck-fail (ann (λ (P Q) (λ (e) ((e Q) (λ (x y) x))))
|
||||
;; : (∀ (P Q) (→ (And P Q) Q)))
|
||||
;; #:with-msg "expected C, given P") ; TODO: err msg, fix orig
|
||||
;; (typecheck-fail (ann (λ (P Q) (λ (e) ((e P) (λ (x y) y))))
|
||||
;; : (∀ (P Q) (→ (And P Q) Q)))
|
||||
;; #:with-msg "expected C, given Q") ; TODO: err msg
|
||||
|
||||
;; ;((((conj q) p) (((proj2 p) q) a)) (((proj1 p) q) a)))))
|
||||
;; (define and-commutes
|
||||
;; (λ ([A : *][B : *])
|
||||
;; (λ ([e : (And A B)])
|
||||
;; ((∧ B A) ((proj2 A B) e) ((proj1 A B) e)))))
|
||||
;; ;; bad and-commutes, dont flip A and B: (→ (And A B) (And A B))
|
||||
;; (typecheck-fail
|
||||
;; (λ ([A : *][B : *])
|
||||
;; (λ ([e : (And A B)])
|
||||
;; ((∧ A B) ((proj2 A B) e) ((proj1 A B) e))))
|
||||
;; #:verb-msg
|
||||
;; "#%app: type mismatch: expected P, given C") ; TODO: err msg
|
||||
;; (check-type and-commutes : (∀ (A B) (→ (And A B) (And B A))))
|
||||
|
||||
;; ;; nats -----------------------------------------------------------------------
|
||||
;; (define-type-alias nat (∀ (A) (→ A (→ A A) A)))
|
||||
;; (check-type nat : *)
|
||||
|
||||
;; (define-type-alias z (λ ([Ty : *]) (λ ([zero : Ty][succ : (→ Ty Ty)]) zero)))
|
||||
;; (define-type-alias s (λ ([n : nat])
|
||||
;; (λ ([Ty : *])
|
||||
;; (λ ([zero : Ty][succ : (→ Ty Ty)])
|
||||
;; (succ ((n Ty) zero succ))))))
|
||||
;; (check-type z : nat)
|
||||
;; (check-type s : (→ nat nat))
|
||||
|
||||
;; (define-type-alias one (s z))
|
||||
;; (define-type-alias two (s (s z)))
|
||||
;; (check-type one : nat)
|
||||
;; (check-type two : nat)
|
||||
|
||||
;; (define-type-alias plus
|
||||
;; (λ ([x : nat][y : nat])
|
||||
;; ((x nat) y s)))
|
||||
;; (check-type plus : (→ nat nat nat))
|
||||
;; (check-type (λ (x y) ((x nat) y s)) : (→ nat nat nat))
|
||||
|
||||
;; ;; equality -------------------------------------------------------------------
|
||||
;; (check-type (eq-refl one) : (= one one))
|
||||
;; (typecheck-fail (ann (eq-refl one) : (= two one))
|
||||
;; #:verb-msg "expected (= two one), given (= one one)")
|
||||
;; (check-type (ann (eq-refl one) : (= one one)) : (= one one))
|
||||
;; (check-type (eq-refl one) : (= (s z) one))
|
||||
;; (check-type (eq-refl two) : (= (s (s z)) two))
|
||||
;; (check-type (eq-refl two) : (= (s one) two))
|
||||
;; (check-type (eq-refl two) : (= two (s one)))
|
||||
;; (check-type (eq-refl two) : (= (s (s z)) (s one)))
|
||||
;; ;; the following example requires recursive expansion after eval/app
|
||||
;; (check-type (eq-refl two) : (= (plus one one) two))
|
||||
;; (check-not-type (eq-refl two) : (= (plus one one) one))
|
||||
|
||||
;; ;; symmetry of =
|
||||
;; (check-type (∀ (A B) (→ (= A B) (= B A))) : *)
|
||||
;; (check-type
|
||||
;; (λ ([A : *][B : *])
|
||||
;; (λ ([e : (= A B)])
|
||||
;; (eq-elim A (λ ([W : *]) (= W A)) (eq-refl A) B e)))
|
||||
;; : (∀ (A B) (→ (= A B) (= B A))))
|
||||
|
||||
;; (check-type
|
||||
;; (λ (A B)
|
||||
;; (λ (e)
|
||||
;; (eq-elim A (λ (W) (= W A)) (eq-refl A) B e)))
|
||||
;; : (∀ (A B) (→ (= A B) (= B A))))
|
||||
|
||||
;; (check-not-type
|
||||
;; (λ ([A : *][B : *])
|
||||
;; (λ ([e : (= A B)])
|
||||
;; (eq-elim A (λ ([W : *]) (= W A)) (eq-refl A) B e)))
|
||||
;; : (∀ (A B) (→ (= A B) (= A B))))
|
||||
|
||||
;; ;; transitivity of =
|
||||
;; (check-type
|
||||
;; (λ ([X : *][Y : *][Z : *])
|
||||
;; (λ ([e1 : (= X Y)][e2 : (= Y Z)])
|
||||
;; (eq-elim Y (λ ([W : *]) (= X W)) e1 Z e2)))
|
||||
;; : (∀ (A B C) (→ (= A B) (= B C) (= A C))))
|
||||
;; (check-type
|
||||
;; (λ (X Y Z)
|
||||
;; (λ (e1 e2)
|
||||
;; (eq-elim Y (λ (W) (= X W)) e1 Z e2)))
|
||||
;; : (∀ (A B C) (→ (= A B) (= B C) (= A C))))
|
||||
|
||||
;; ;; general tests that app/eval is properly applied recursively
|
||||
;; (check-type ((λ ([f : (→ * *)][x : *]) (f x))
|
||||
;; (λ ([x : *]) x)
|
||||
;; *)
|
||||
;; : *)
|
||||
|
||||
;; (check-type (((λ ([f : (→ (→ * *) * *)]) f) (λ ([g : (→ * *)][x : *]) (g x)))
|
||||
;; (λ ([y : *]) *)
|
||||
;; *)
|
||||
;; : *)
|
||||
Loading…
Reference in New Issue
Block a user