add provides to guide examples
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Stephen Chang
parent
691ba9c51c
commit
299051e902
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@ -2,7 +2,7 @@
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@(require scribble/example racket/sandbox
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(for-label racket/base
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(except-in turnstile/turnstile ⊢))
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(except-in turnstile/turnstile ⊢ mk-~ mk-?))
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"doc-utils.rkt" "common.rkt")
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@title{The Turnstile Guide}
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@ -24,7 +24,7 @@ expansion) and type checking. These type judgements rely on two core
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reads: "In context Γ, @racket[e] expands to @racket[e-] and must
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have type τ."
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The key difference is that τ is an output in the first relation, and
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The key difference is that τ is an output in the first relation, ande
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an input in the second relation.
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These input and output positions conveniently correspond to
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@ -286,62 +286,63 @@ here is whatever is in scope. By default it is Racket's @racket[+].
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@section{A Complete Language}
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We can now write well-typed programs! Here is the complete
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language implementation:
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language implementation, with some examples:
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@label-code["STLC"
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@#reader scribble/comment-reader
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(racketblock0
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#,(lang turnstile)
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@; using `racketmod` because `examples` doesnt work with provide
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@(racketmod0 #:file "STLC"
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turnstile
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(provide → Int λ #%app #%datum + ann)
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(define-type-constructor → #:arity > 0)
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(define-base-type Int)
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(define-primop + : (→ Int Int Int))
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;; [APP]
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(define-typed-syntax (#%app e_fn e_arg ...) ≫
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[⊢ e_fn ≫ e_fn- ⇒ (~→ τ_in ... τ_out)]
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#:fail-unless (stx-length=? #'[τ_in ...] #'[e_arg ...])
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(format "arity mismatch, expected ~a args, given ~a"
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(stx-length #'[τ_in ...]) #'[e_arg ...])
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[⊢ e_arg ≫ e_arg- ⇐ τ_in] ...
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--------
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[⊢ (#%app- e_fn- e_arg- ...) ⇒ τ_out])
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(define-base-type Int)
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(define-type-constructor → #:arity > 0)
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;; [LAM]
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(define-typed-syntax λ #:datum-literals (:)
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[(_ ([x:id : τ_in:type] ...) e) ≫
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[[x ≫ x- : τ_in.norm] ... ⊢ e ≫ e- ⇒ τ_out]
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-------
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[⊢ (λ- (x- ...) e-) ⇒ (→ τ_in.norm ... τ_out)]]
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[(_ (x:id ...) e) ⇐ (~→ τ_in ... τ_out) ≫
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[[x ≫ x- : τ_in] ... ⊢ e ≫ e- ⇐ τ_out]
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---------
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[⊢ (λ- (x- ...) e-)]])
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(define-primop + : (→ Int Int Int))
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;; [ANN]
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(define-typed-syntax (ann e (~datum :) τ:type) ≫
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[⊢ e ≫ e- ⇐ τ.norm]
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(code:comment "[APP]")
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(define-typed-syntax (#%app e_fn e_arg ...) ≫
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[⊢ e_fn ≫ e_fn- ⇒ (~→ τ_in ... τ_out)]
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#:fail-unless (stx-length=? #'[τ_in ...] #'[e_arg ...])
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(format "arity mismatch, expected ~a args, given ~a"
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(stx-length #'[τ_in ...]) #'[e_arg ...])
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[⊢ e_arg ≫ e_arg- ⇐ τ_in] ...
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--------
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[⊢ (#%app- e_fn- e_arg- ...) ⇒ τ_out])
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(code:comment "[LAM]")
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(define-typed-syntax λ #:datum-literals (:)
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[(_ ([x:id : τ_in:type] ...) e) ≫
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[[x ≫ x- : τ_in.norm] ... ⊢ e ≫ e- ⇒ τ_out]
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-------
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[⊢ (λ- (x- ...) e-) ⇒ (→ τ_in.norm ... τ_out)]]
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[(_ (x:id ...) e) ⇐ (~→ τ_in ... τ_out) ≫
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[[x ≫ x- : τ_in] ... ⊢ e ≫ e- ⇐ τ_out]
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---------
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[⊢ (λ- (x- ...) e-)]])
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(code:comment "[ANN]")
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(define-typed-syntax (ann e (~datum :) τ:type) ≫
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[⊢ e ≫ e- ⇐ τ.norm]
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--------
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[⊢ e- ⇒ τ.norm])
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(code:comment "[DATUM]")
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(define-typed-syntax #%datum
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[(_ . n:integer) ≫
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--------
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[⊢ e- ⇒ τ.norm])
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;; [DATUM]
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(define-typed-syntax #%datum
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[(_ . n:integer) ≫
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--------
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[⊢ (#%datum- . n) ⇒ Int]]
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[(_ . x) ≫
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--------
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[_ #:error (type-error #:src #'x
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#:msg "Unsupported literal: ~v" #'x)]]))]
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[⊢ (#%datum- . n) ⇒ Int]]
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[(_ . x) ≫
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--------
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[_ #:error (type-error #:src #'x
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#:msg "Unsupported literal: ~v" #'x)]]))
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@;TODO: how to run examples with the typeset code?
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@(define stlc-eval
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(parameterize ([sandbox-output 'string]
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[sandbox-error-output 'string]
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[sandbox-eval-limits #f])
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(make-base-eval #:lang 'turnstile/examples/stlc+lit )))
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(make-base-eval #:lang 'turnstile/examples/stlc+lit)))
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@examples[#:eval stlc-eval
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@examples[#:eval stlc-eval #:label "STLC Examples:" #:no-inset
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1
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(eval:error "1")
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(+ 1 2)
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@ -364,11 +365,12 @@ Since @tt{STLC} consists of just a series of macros, like any other Racket
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in other languages. Let's see how we can reuse the above implementation to
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implement a subtyping language.
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@label-code["A language with subtyping that reuses STLC"
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@(racketblock0 #:escape esc
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(esc(lang turnstile))
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@(racketmod0 #:file "STLC+SUB" #:escape UNSYNTAX
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turnstile
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(extends STLC #:except #%datum +)
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(provide Top Num Nat + add1 #%datum if)
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(define-base-types Top Num Nat)
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(define-primop + : (→ Num Num Num))
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@ -415,13 +417,13 @@ implement a subtyping language.
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[else #'Top]))
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(define current-join (make-parameter join)))
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@code:comment{[IF]}
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(code:comment "[IF]")
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(define-typed-syntax (if e_tst e1 e2) ≫
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[⊢ e_tst ≫ e_tst- ⇒ _] @code:comment{a non-false value is truthy}
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[⊢ e_tst ≫ e_tst- ⇒ _] (code:comment "a non-false value is truthy")
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[⊢ e1 ≫ e1- ⇒ τ1]
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[⊢ e2 ≫ e2- ⇒ τ2]
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--------
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[⊢ (if- e_tst- e1- e2-) ⇒ @#,((current-join) #'τ1 #'τ2)]))]
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[⊢ (if- e_tst- e1- e2-) ⇒ #,((current-join) #'τ1 #'τ2)]))
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This language uses subtyping instead of type equality as its "typecheck
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relation". Specifically, the language defines a @racket[sub?] subtyping relation
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@ -453,7 +455,7 @@ positions in Turnstile are @racket[quasisyntax]es.
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[sandbox-eval-limits #f])
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(make-base-eval #:lang 'turnstile/examples/stlc+sub)))
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@examples[#:eval stlc+sub-eval
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@examples[#:eval stlc+sub-eval #:label "STLC+SUB Examples:" #:no-inset
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((λ ([x : Top]) x) -1)
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((λ ([x : Num]) x) -1)
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((λ ([x : Int]) x) -1)
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