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-rw-r--r--stlc-dll.rkt1
-rw-r--r--stlc-ext.rkt56
-rw-r--r--stlc-fix.rkt18
-rw-r--r--stlc-imp.rkt57
-rw-r--r--stlc-let.rkt12
-rw-r--r--stlc-pred.rkt56
-rw-r--r--stlc-rec.rkt10
-rw-r--r--stlc-ref.rkt23
-rw-r--r--stlc.rkt10
9 files changed, 52 insertions, 191 deletions
diff --git a/stlc-dll.rkt b/stlc-dll.rkt
index 8b447c1..81bab7b 100644
--- a/stlc-dll.rkt
+++ b/stlc-dll.rkt
@@ -1,6 +1,7 @@
#lang racket
(require "lib.rkt")
(require (only-in "stlc-rec.rkt" replace))
+(require (only-in "stlc-ext.rkt" expand))
;; The Simply-Typed Lambda Calculus with higher-order *impredicative* references,
;; plus sums products booleans ascryption etc, to implement doubly-linked lists
diff --git a/stlc-ext.rkt b/stlc-ext.rkt
index b11cb58..9727068 100644
--- a/stlc-ext.rkt
+++ b/stlc-ext.rkt
@@ -77,20 +77,9 @@
(check-core (desugar expr) with #hash()))
(define (check-core expr with Γ)
(match expr
- ['sole (equal? 'Unit with)]
- [s #:when (string? s) (equal? 'Str with)]
- [n #:when (natural? n) (equal? 'Nat with)]
- [b #:when (boolean? b) (equal? 'Bool with)]
-
- [x #:when (dict-has-key? Γ x)
- (equiv? (dict-ref Γ x) with Γ Γ)]
-
[`(type ,t1 ,t2 ,in)
(check-core in with (dict-set Γ t1 t2))]
- [`(inc ,e)
- (and (equiv? 'Nat with)
- (check-core e 'Nat Γ))]
[`(if ,c ,e1 ,e2)
(and (check-core c 'Bool Γ)
(check-core e1 with Γ) (check-core e2 with Γ))]
@@ -99,22 +88,14 @@
(match with
[`(,t1 × ,t2) (and (check-core e1 t1 Γ) (check-core e2 t2 Γ))]
[_ #f])]
- [`(car ,e)
- (match (infer-core e Γ)
- [`(,t1 × ,t2) (equiv? t1 with Γ Γ)]
- [_ #f])]
- [`(cdr ,e)
- (match (infer-core e Γ)
- [`(,t1 × ,t2) (equiv? t2 with Γ Γ)]
- [_ #f])]
[`(inl ,e)
- (match (infer-core e Γ)
- [`(,t1 ⊕ ,t2) (equiv? t1 with Γ Γ)]
+ (match with
+ [`(,t1 ⊕ ,t2) (check-core e t1 Γ)]
[_ #f])]
[`(inr ,e)
- (match (infer-core e Γ)
- [`(,t1 ⊕ ,t2) (equiv? t2 with Γ Γ)]
+ (match with
+ [`(,t1 ⊕ ,t2) (check-core e t2 Γ)]
[_ #f])]
[`(case ,e (,x1 ⇒ ,e1) (,x2 ⇒ ,e2))
(match (infer-core e Γ)
@@ -122,8 +103,6 @@
(and (check-core e1 with (dict-set Γ x1 a1))
(check-core e2 with (dict-set Γ x2 a2)))]
[_ #f])]
- [`(,e : ,t)
- (and (equiv? t with Γ Γ) (check-core e t Γ))]
['nil
(match with
@@ -131,25 +110,16 @@
[_ #f])]
[`(cons ,f1 ,f2)
(match with
- [`(List ,t) (and (check-core f1 t Γ) (check-core f2 `(List ,t) Γ))]
- [_ #f])]
- [`(head ,e)
- (match (infer-core e)
- [`(List ,t) (equiv? t with Γ Γ)]
+ [`(List ,t)
+ (and (check-core f1 t Γ)
+ (check-core f2 `(List ,t) Γ))]
[_ #f])]
- [`(tail ,e)
- (equiv? (infer-core e Γ) with Γ Γ)]
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,t2)
(and (equiv? t1 t Γ Γ) (check-core e t2 (dict-set Γ x t1)))]
[_ #f])]
- [`(,e1 ,e2)
- (match (infer-core e1 Γ)
- [`(,t1 → ,t2)
- (and (equiv? t2 with Γ Γ) (equiv? t1 (infer-core e2 Γ) Γ Γ))]
- [_ #f])]
[_ (equiv? (infer-core expr Γ) with Γ Γ)]))
@@ -204,9 +174,10 @@
[`(case ,e (,x1 ⇒ ,e1) (,x2 ⇒ ,e2))
(match (infer-core e Γ)
[`(,a1 ⊕ ,a2)
- (let ([b1 (infer-core e1 (dict-set Γ x1 (expand a1 Γ)))] [b2 (infer-core e2 (dict-set Γ x2 (expand a2 Γ)))])
- (if (equiv? b1 b2 Γ Γ) b1
- (err (format "case ~a is not of consistent type!" `(case (,a1 ⊕ ,a2) b1 b2)))))]
+ (let ([b1 (infer-core e1 (dict-set Γ x1 (expand a1 Γ)))]
+ [b2 (infer-core e2 (dict-set Γ x2 (expand a2 Γ)))])
+ (if (equiv? b1 b2 Γ Γ) b1
+ (err (format "case ~a is not of consistent type!" `(case (,a1 ⊕ ,a2) b1 b2)))))]
[t (err (format "calling case on incorrect type ~a" t))])]
['nil (err (format "unable to infer type of empty list!"))]
@@ -234,8 +205,11 @@
[e (err (format "inferring an unknown expression ~a" e))]))
+;; Expands a type alias into weak-head normal form, for literal matching.
+;; (expand Type Table[Id, Expr ⊕ Type]): Type
(define (expand t Γ)
- (if (dict-has-key? Γ t) (expand (dict-ref Γ t) Γ) t))
+ (if (dict-has-key? Γ t)
+ (expand (dict-ref Γ t) Γ) t))
;; checks if two expressions are equivalent up to α-renaming and ascryption
(define (equiv? e1 e2 Γ1 Γ2)
diff --git a/stlc-fix.rkt b/stlc-fix.rkt
index 8fa96f9..ad45b90 100644
--- a/stlc-fix.rkt
+++ b/stlc-fix.rkt
@@ -35,26 +35,17 @@
(define (check-core expr with Γ)
(let ([with (if (dict-has-key? Γ with) (dict-ref Γ with) with)])
(match expr
- ['sole (equal? 'Unit with)]
- [n #:when (natural? n) (equal? 'Nat with)]
- [x #:when (dict-has-key? Γ x)
- (equal? (dict-ref Γ x) with)]
-
[`(fix ,e)
(check-core (infer-core e) `(,with → ,with) Γ)]
[`(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)))]
+ (and (equal? t1 t)
+ (check-core e t2 (dict-set Γ x t1)))]
[_ #f])]
- [_ #f])))
+ [_ (equal? (infer-core expr Γ) with)])))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr)
@@ -63,8 +54,7 @@
(match expr
['sole 'Unit]
[n #:when (natural? n) 'Nat]
- [x #:when (dict-has-key? Γ x)
- (dict-ref Γ x)]
+ [x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(fix ,e)
(match (infer-core e Γ)
diff --git a/stlc-imp.rkt b/stlc-imp.rkt
index fc34115..0c3c3c7 100644
--- a/stlc-imp.rkt
+++ b/stlc-imp.rkt
@@ -32,37 +32,19 @@
(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)]
-
[`(new ,e)
(match with
[`(Ref ,t) (check-core e t Γ)]
[_ #f])]
- [`(! ,e) (check-core e `(Ref ,with) Γ)]
- [`(set ,e1 ,e2)
- (match (infer-core e1 Γ)
- [`(Ref ,t)
- (and (equal? 'Unit with)
- (check-core e2 t Γ))]
- [_ #f])]
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,k ,t2)
(and (equal? t t1) (check-core e t2 (dict-set Γ x t))
- (> k (max-level e t1 t2 (dict-set Γ x t1))))] ; KNOB
- [_ #f])]
- [`(,e1 ,e2)
- (match (infer-core e1 Γ)
- [`(,t1 → ,k ,t2)
- (and (equal? t2 with)
- (equal? t1 (infer-core e2 Γ)))]
+ (> k (level-body e (dict-set Γ x t1))))] ; KNOB
[_ #f])]
- [_ #f]))
+ [_ (equal? (infer-core expr Γ) with)]))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr)
@@ -71,8 +53,7 @@
(match expr
['sole 'Unit]
[n #:when (natural? n) 'Nat]
- [x #:when (dict-has-key? Γ x)
- (dict-ref Γ x)]
+ [x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(new ,e) `(Ref ,(infer-core e Γ))]
[`(! ,e)
@@ -88,35 +69,28 @@
[t (err (format "attempting to update non-reference ~a: ~a" e1 t))])]
[`(λ (,x : ,t1) ,e)
- (let ([t2 (infer-core e (dict-set Γ x t1))])
- (let ([k (+ 1 (max-level e (dict-set Γ x t1) t1 t2))]) ; KNOB
- `(,t1 → ,k ,t2)))]
+ (let* ([t2 (infer-core e (dict-set Γ x t1))]
+ [k (+ 1 (level-body e (dict-set Γ x t1)))]) ; KNOB
+ `(,t1 → ,k ,t2))]
[`(,e1 ,e2)
(match (infer-core e1 Γ)
[`(,t1 → ,k ,t2)
(if (check-core e2 t1 Γ) t2
- (err (format "inferred argument type ~a does not match arg ~a of type ~a" t1 e2 (infer-core e2 Γ))))]
+ (err (format "inferred argument type ~a does not match arg ~a of type ~a"
+ t1 e2 (infer-core e2 Γ))))]
[t (err (format "expected → type on application body, got ~a" t))])]
[e (err (format "attempting to infer an unknown expression ~a" e))]))
-;; (max-level Table[Sym, Type] Expr Type Type): Natural
-(define (max-level e Γ t1 t2)
- (max
- (level-type t1)
- (level-type t2)
- (level-body e Γ)))
-
;; (level-type Type): Natural
(define (level-type t)
(match t
['Unit 0]
['Nat 0]
[`(,t1 → ,k ,t2)
- (if (or (< k (level-type t1)) (< k (level-type t2)))
+ (if (and (>= k (level-type t1)) (>= k (level-type t2))) k
(err (format "annotated level ~a is less than inferred levels of ~a and ~a!"
- k t1 t2))
- k)]
+ k t1 t2)))]
[`(Ref ,t)
(let ([k (level-type t)])
(if (zero? k) 0 (+ 1 k)))] ; KNOB
@@ -127,10 +101,7 @@
(match e
['sole 0]
[n #:when (natural? n) 0]
- [x #:when (dict-has-key? Γ x)
- (level-type (dict-ref Γ x))]
- [`(new ,e) (level-body e Γ)]
- [`(! ,e) (level-body e Γ)]
- [`(set ,e1 ,e2) (max (level-body e1 Γ) (level-body e2 Γ))]
- [`(λ (,x : ,t) ,e) (level-body e (dict-set Γ x t))] ; todo: should be 0?
- [`(,e1 ,e2) (max (level-body e1 Γ) (level-body e2 Γ))]))
+ [x #:when (dict-has-key? Γ x) (level-type (dict-ref Γ x))]
+ [(or `(new ,e) `(! ,e) `(λ (,_ : ,_) ,e)) (level-body e Γ)]
+ [(or `(set ,e1 ,e2) `(,e1 ,e2)) (max (level-body e1 Γ) (level-body e2 Γ))]
+ [x #:when (symbol? x) 0])) ; local variables, not in Γ
diff --git a/stlc-let.rkt b/stlc-let.rkt
index f906e48..089f9d0 100644
--- a/stlc-let.rkt
+++ b/stlc-let.rkt
@@ -23,21 +23,12 @@
(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]))
+ [_ (equal? (infer-core expr Γ) with)]))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr)
@@ -46,6 +37,7 @@
(match expr
['sole 'Unit]
[n #:when (natural? n) 'Nat]
+ [x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(λ (,x : ,t) ,e)
`(,t → ,(infer-core e (dict-set Γ x t)))]
[`(,e1 ,e2)
diff --git a/stlc-pred.rkt b/stlc-pred.rkt
index ee64fcb..9f3fc9c 100644
--- a/stlc-pred.rkt
+++ b/stlc-pred.rkt
@@ -29,37 +29,19 @@
(check-core (desugar expr) with #hash()))
(define (check-core expr with Γ)
(match expr
- ['sole (equal? 'Unit with)]
- [n #:when (natural? n) (equal? 'Nat with)]
- [x #:when (dict-has-key? Γ x)
- (equal? (dict-ref Γ x) with)]
-
[`(new ,e)
(match with
[`(Ref ,t) (check-core e t Γ)]
[_ #f])]
- [`(! ,e) (check-core e `(Ref ,with) Γ)]
- [`(set ,e1 ,e2)
- (match (infer-core e1 Γ)
- [`(Ref ,t)
- (and (equal? 'Unit with)
- (check-core e2 t Γ))]
- [_ #f])]
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,k ,t2)
- (and
- (equal? t t1)
- (>= k (max-level e (dict-set Γ x t1) t1 t2)) ; (KNOB)
- (check-core e t2 (dict-set Γ x t1)))])]
- [`(,e1 ,e2)
- (match (infer-core e1 Γ)
- [`(,t1 → ,k ,t2)
- (and (equal? t2 with) (equal? t1 (infer-core e2 Γ)))]
+ (and (equal? t t1) (check-core e t2 (dict-set Γ x t1))
+ (>= k (level-body e (dict-set Γ x t1))))] ; KNOB
[_ #f])]
- [_ #f]))
+ [_ (equal? (infer-core expr Γ) with)]))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr)
@@ -85,9 +67,9 @@
[t (err (format "attempting to update non-reference ~a: ~a" e1 t))])]
[`(λ (,x : ,t1) ,e)
- (let ([t2 (infer-core e (dict-set Γ x t1))])
- (let ([k (max-level e (dict-set Γ x t1) t1 t2)]) ; (KNOB)
- `(,t1 → ,k ,t2)))]
+ (let* ([t2 (infer-core e (dict-set Γ x t1))]
+ [k (level-body e (dict-set Γ x t1))]) ; KNOB
+ `(,t1 → ,k ,t2))]
[`(,e1 ,e2)
(match (infer-core e1 Γ)
[`(,t1 → ,k ,t2)
@@ -97,23 +79,14 @@
[e (err (format "attempting to infer an unknown expression ~a" e))]))
-;; (max-level Table[Sym, Type] Expr Type Type): Natural
-(define (max-level e Γ t1 t2)
- (max
- (level-type t1)
- (level-type t2)
- (level-body e Γ)))
-
;; (level-type Type): Natural
(define (level-type t)
(match t
- ['Unit 0]
- ['Nat 0]
+ [(or 'Unit 'Nat) 0]
[`(,t1 → ,k ,t2)
- (if (or (< k (level-type t1)) (< k (level-type t2)))
+ (if (and (>= k (level-type t1)) (>= k (level-type t2))) k
(err (format "annotated level ~a is less than inferred levels of ~a and ~a!"
- k t1 t2))
- k)]
+ k t1 t2)))]
[`(Ref ,t) (+ 1 (level-type t))] ; (KNOB)
[t (err (format "attempting to infer the level of unknown type ~a" t))]))
@@ -124,14 +97,9 @@
[n #:when (natural? n) 0]
[x #:when (dict-has-key? Γ x)
(level-type (dict-ref Γ x))]
-
- [`(new ,e) (level-body e Γ)]
- [`(! ,e) (level-body e Γ)]
- [`(set ,e1 ,e2) (max (level-body e1 Γ) (level-body e2 Γ))]
-
- [`(λ (,x : ,t) ,e) (level-body e (dict-set Γ x t))] ; todo: should be 0?
- [`(,e1 ,e2) (max (level-body e1 Γ) (level-body e2 Γ))]
- [e (err (format "attempting to infer the level of unknown expression ~a" e))]))
+ [(or `(new ,e) `(! ,e) `(λ (,_ : ,_) ,e)) (level-body e Γ)]
+ [(or `(set ,e1 ,e2) `(,e1 ,e2)) (max (level-body e1 Γ) (level-body e2 Γ))]
+ [x #:when (symbol? x) 0]))
; simple diverging program in STLC-ref
; https://www.youtube.com/watch?v=XNgE8kBfSz8
diff --git a/stlc-rec.rkt b/stlc-rec.rkt
index c90fdae..342f265 100644
--- a/stlc-rec.rkt
+++ b/stlc-rec.rkt
@@ -41,11 +41,6 @@
(check-core (desugar expr) with #hash()))
(define (check-core expr with Γ)
(match expr
- ['sole (equal? 'Unit with)]
- [n #:when (natural? n) (equal? 'Nat with)]
- [x #:when (dict-has-key? Γ x)
- (equal? (dict-ref Γ x) with)]
-
[`(fold (μ ,x ,t) ,e)
(match with
[`(μ ,x ,t) (check-core e t (dict-set Γ x `(μ ,x ,t)))]
@@ -56,11 +51,6 @@
[`(,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])]
[_ (equal? (infer-core expr Γ) with)]))
diff --git a/stlc-ref.rkt b/stlc-ref.rkt
index d911557..41aec59 100644
--- a/stlc-ref.rkt
+++ b/stlc-ref.rkt
@@ -42,37 +42,19 @@
(check-core (desugar expr) with #hash()))
(define (check-core expr with Γ)
(match expr
- ['sole
- (equal? 'Unit with)]
- [n #:when (natural? n)
- (equal? 'Nat with)]
- [x #:when (dict-has-key? Γ x)
- (equal? (dict-ref Γ x) with)]
-
[`(new ,e)
(match with
[`(Ref ,t) (check-core e t Γ)]
[_ #f])]
[`(! ,e) (check-core e `(Ref ,with) Γ)]
- [`(set ,e1 ,e2)
- (match (infer-core e1 Γ)
- [`(Ref ,t)
- (and (equal? 'Unit with)
- (check-core e2 t Γ))]
- [_ #f])]
[`(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]))
+ [_ (equal? (infer-core expr Γ) with)]))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr)
@@ -81,8 +63,7 @@
(match expr
['sole 'Unit]
[n #:when (natural? n) 'Nat]
- [x #:when (dict-has-key? Γ x)
- (dict-ref Γ x)]
+ [x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(new ,e) `(Ref ,(infer-core e Γ))]
[`(! ,e)
diff --git a/stlc.rkt b/stlc.rkt
index 706557d..820197b 100644
--- a/stlc.rkt
+++ b/stlc.rkt
@@ -19,23 +19,17 @@
;; (check Expr Type Table[Sym, Type]): Bool
(define (check expr with [Γ #hash()])
(match expr
- [x #:when (dict-has-key? Γ x)
- (equal? (dict-ref Γ x) with)]
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,t2)
(and (equal? t t1) (check e t2 (dict-set Γ x)))]
[_ #f])]
- [`(,e1 ,e2)
- (match (infer e1 Γ)
- [`(,t1 → ,t2)
- (and (equal? t2 with) (equal? t1 (infer e2 Γ)))]
- [_ #f])]
- [_ #f]))
+ [_ (equal? (infer with Γ) with)]))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr [Γ #hash()])
(match expr
+ [x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(λ (,x : ,t) ,e)
`(,t → ,(infer e (dict-set Γ x t)))]
[`(,e1 ,e2)