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+#lang racket
+(require "../lib.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]))