1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
|
#lang racket
(require "lib.rkt")
(require "base.rkt")
(provide (all-defined-out))
;; The Simply-Typed Lambda Calculus with iso-recursive types
; Γ ⊢ e: [x ↦ μx.t] t
; ------------------------
; Γ ⊢ fold [μx.t] e: μx.t
; Γ ⊢ e: μx.t
; -----------------------------------
; Γ ⊢ unfold [μx.t] e: [x ↦ μx.t] t
;; (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)]
[`(fold ,e) `(fold ,(interpret-core e Γ))]
[`(unfold ,e)
(match (interpret-core e Γ)
[`(fold ,e) e]
[e `(unfold e)])]
[`(λ ,x ,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))])]
[e (err (format "interpreting an unknown expression ~a" 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 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)]))
;; (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]
[b #:when (boolean? b) 'Bool]
[x #:when (dict-has-key? Γ x)
(dict-ref Γ x)]
[`(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))])]
[e (err (format "attempting to infer an unknown expression ~a" e))]))
;; 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]))
|
