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#lang racket
(require "lib.rkt")
(require "base.rkt")
(provide (all-defined-out))
;; The Simply-Typed Lambda Calculus with iso-recursive types
;; Checks an expression for syntactic well-formedness.
(define (stlc-rec/expr? expr)
(match expr
[x #:when (symbol? x) #t]
[(or `(fold ,e) `(unfold ,e)) (stlc-rec/expr? e)]
[`(,e1 ,e2) (and (stlc-rec/expr? e1) (stlc-rec/expr? e2))]
[`(λ (,x : ,t) ,e) (and (symbol? x) (stlc-rec/type? t) (stlc-rec/expr? e))]
[_ #f]))
;; Checks a type for syntactic well-formedness.
(define (stlc-rec/type? type)
(match type
[t #:when (symbol? t) #t]
[`(,t1 → ,t2) (and (stlc-rec/type? t1) (stlc-rec/type? t2))]
[_ #f]))
;; Checks a value for syntactic well-formedness.
(define (stlc-rec/value? value)
(match value
[x #:when (symbol? x) #t]
[`(,v1 ,v2) (and (stlc-rec/value? v1) (stlc-rec/value? v2))]
[`(λ ,x ,e ,env) (and (symbol? x) (stlc-rec/expr? e) (dict? env))]
[_ #f]))
;; Interprets an expression down to a value, in a given context.
(define (interpret expr)
(interpret/core (desugar expr) #hash()))
(define/contract (interpret/core expr Γ)
(-> stlc-rec/expr? dict? stlc-rec/value?)
(match expr
['sole 'sole]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[n #:when (natural? n) n]
[f #:when (symbol? f) f]
[`(fold ,e) `(fold ,(interpret/core e Γ))]
[`(unfold ,e)
(match (interpret/core e Γ)
[`(fold ,e) e]
[e `(unfold e)])]
[`(λ (,x : ,t) ,e) `(λ ,x ,e ,Γ)]
[`(,e1 ,e2)
(match (interpret/core e1 Γ)
[`(λ ,x ,e ,env)
(interpret/core e (dict-set env x (interpret/core e2 Γ)))]
[e (err (format "applying arg ~a to unknown expression ~a" e2 e))])]))
;; Checks an expression against some type, in a given context.
(define (check expr with)
(check/core (desugar expr) with #hash()))
(define/contract (check/core expr with Γ)
(-> stlc-rec/expr? stlc-rec/type? dict? boolean?)
(match expr
[`(fold (μ ,x ,t) ,e)
(match with
[`(μ ,x ,t) (check/core e t (dict-set Γ x `(μ ,x ,t)))]
[_ #f])]
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,t2)
(and (equal? t1 t) (check/core e t2 (dict-set Γ x t1)))]
[_ #f])]
[_ (equal? (infer/core expr Γ) with)]))
;; Infers a type from some expression, in a given context.
(define (infer expr)
(infer/core (desugar expr) #hash()))
(define/contract (infer/core expr Γ)
(-> stlc-rec/expr? dict? stlc-rec/type?)
(match expr
['sole 'Unit]
[x #:when (dict-has-key? Γ x)
(dict-ref Γ x)]
[b #:when (boolean? b) 'Bool]
[n #:when (natural? n) 'Nat]
[f #:when (symbol? f)
(err (format "attempting to infer type of free variable ~a" f))]
[`(fold (μ ,x ,t) ,e)
(if (check/core e t (dict-set Γ x `(μ ,x ,t))) `(μ ,x ,t)
(err (format "expected ~a to be of type ~a, got ~a"
e t (infer e (dict-set Γ x `(μ ,x ,t))))))]
[`(unfold (μ ,x ,t) ,e)
(if (check/core e `(μ ,x ,t)) (replace t x `(μ ,x ,t))
(err (format "expected ~a to be of type ~a, got ~a"
e `(μ ,x ,t) (infer/core e Γ))))]
[`(λ (,x : ,t) ,e)
`(,t → ,(infer/core e (dict-set Γ x t)))]
[`(,e1 ,e2)
(match (infer/core e1 Γ)
[`(,t1 → ,t2)
(if (check/core e2 t1 Γ) t2
(err (format "inferred argument type ~a does not match arg ~a" t1 e2)))]
[t (err (format "expected → type on application body, got ~a" t))])]))
;; Replace all references to an expression with a value.
(define (replace expr key value)
(match expr
; do not accidentally replace shadowed bindings
[(or `(λ (,x : ,_) ,_) `(λ ,x ,_) `(μ ,x ,_)
`(type ,x ,_ ,_)) #:when (equal? x key) expr]
[`(,e ...) `(,@(map (λ (x) (replace x key value)) e))]
[x #:when (equal? x key) value]
[v v]))
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