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#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus, with let sugar and some base types
;; (interpret Expr Table[Sym, Expr]): Value
(define (interpret expr)
(interpret-core (strip (desugar expr)) #hash()))
(define (interpret-core expr Γ)
(match expr
['sole 'sole]
[n #:when (natural? n) n]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(λ ,x ,e) `(λ ,x ,e ,Γ)]
[`(,e1 ,e2)
(match (interpret-core e1 Γ)
[`(λ ,x ,e1 ,env) (interpret-core e1 (dict-set env x (interpret-core e2 Γ)))]
[e1 `(,e1 ,(interpret-core e2 Γ))])]
[e e]))
;; (check Expr Type Table[Sym, Type]): Bool
(define (check expr with)
(check-core (desugar expr) with #hash()))
(define (check-core expr with Γ)
(match with
['sole (equal? 'Unit with)]
[n #:when (natural? n) (equal? 'Nat with)]
[x #:when (dict-has-key? Γ x)
(equal? (dict-ref Γ x) with)]
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,t2)
(and (equal? t1 t) (check-core e t2 (dict-set Γ x t1)))]
[_ #f])]
[`(,e1 ,e2)
(match (infer-core e1 Γ)
[`(,t1 → ,t2)
(and (equal? t2 with) (equal? t1 (infer-core e2 Γ)))]
[_ #f])]
[_ #f]))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr)
(infer-core (desugar expr) #hash()))
(define (infer-core expr Γ)
(match expr
['sole 'Unit]
[n #:when (natural? n) 'Nat]
[`(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))])]
[e (err (format "attempting to infer an unknown expression ~a" e))]))
(provide interpret check infer)
(require rackunit)
(check-equal? (interpret '(λ x x)) '(λ x x #hash()))
(check-equal? (interpret '((λ a a) (x y))) '(x y))
(check-equal? (interpret '((λ a (x y)) (λ z z))) '(x y))
(check-equal? (interpret '((λ a (a y)) x)) '(x y))
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