macrotypes/tapl/variance-constraints.rkt

390 lines
17 KiB
Racket

#lang racket/base
(provide solve-variance-constraints
variance-mapping
variance=
variance-var
variance-join/expr
variance-compose/expr
variance-mapping-ref
)
(require racket/bool
racket/list
racket/match
racket/set
(only-in (for-template "typecheck.rkt")
variance?
irrelevant
covariant
contravariant
invariant
variance-irrelevant?
variance-covariant?
variance-contravariant?
variance-invariant?
variance-join
variance-compose
))
(module+ test
(require rackunit))
;; variance<=? : Variance Variance -> Boolean
;; irrelevant < covariant
;; irrelevant < contravariant
;; covariant < invariant
;; contravariant < invariant
(define (variance<=? v1 v2)
(and (implies (variance-covariant? v2)
(variance-covariant? v1))
(implies (variance-contravariant? v2)
(variance-contravariant? v1))))
;; A Variance-Constraint is a (variance= Variance-Expr Variance-Expr)
(struct variance= (v1 v2) #:prefab)
;; variance<= : Variance-Expr Variance-Expr -> Variance-Constraint
(define (variance<= v1 v2)
(variance= (variance-expr-join v1 v2) v2))
;; A Variance-Expr is one of:
;; - Variance-Var
;; - Variance
;; - (variance-expr-join Variance-Expr Variance-Expr)
;; - (variance-expr-compose Variance-Expr Variance-Expr)
(struct variance-expr-join (v1 v2) #:prefab)
(struct variance-expr-compose (v1 v2) #:prefab)
;; A Variance-Var is a Symbol
(define (variance-var sym) sym)
(define (variance-var? v) (symbol? v))
(define (variance-var=? v1 v2) (symbol=? v1 v2))
;; A Variance-Mapping is a (Hashof Variance-Var Variance-Expr)
;; variance-mapping : -> Variance-Mapping
(define (variance-mapping) (hash))
;; variance-mapping-has? : Variance-Mapping Variance-Var -> Boolean
(define (variance-mapping-has? mapping var)
(hash-has-key? mapping var))
;; variance-mapping-ref : Variance-Mapping Variance-Var -> Variance-Expr
(define (variance-mapping-ref mapping var)
(hash-ref mapping var))
;; variance-mapping-set : Variance-Mapping Variance-Var Variance-Expr -> Variance-Mapping
(define (variance-mapping-set mapping var variance)
(hash-set mapping var variance))
;; An Unfinished-Mapping is a (Hashof Variance-Var Variance)
;; If a var is mapped to something in an Unfinished-Mapping, that
;; means that the var is at least as restrictive as the variance it's
;; mapped to.
(define (unfinished-mapping-ref mapping var)
(hash-ref mapping var irrelevant))
(define (unfinished-mapping-set mapping var value)
(hash-update mapping var (λ (v) (variance-join v value)) irrelevant))
;; solve-variance-constraints :
;; (Listof Variance-Var) (Listof Variance-Constraint) Variance-Mapping
;; -> (U False Variance-Mapping)
(define (solve-variance-constraints vars constraints mapping)
(match constraints
[(list)
(variance-mapping-interp-exprs vars mapping)]
[(cons constraint rest-cs)
(match constraint
[(variance= (? variance? v1) (? variance? v2))
(and
(equal? v1 v2)
(solve-variance-constraints vars rest-cs mapping))]
[constraint
(define free-vars (variance-constraint-variables #false constraint '()))
(cond
[(empty? free-vars)
(match-define (variance= v1 v2) constraint)
(solve-variance-constraints
vars
(cons (variance= (variance-expr-interp free-vars v1 mapping)
(variance-expr-interp free-vars v2 mapping))
rest-cs)
mapping)]
[else
(define valss
(for/list ([var (in-list free-vars)])
(list irrelevant covariant contravariant invariant)))
(for/or ([vals (in-list (apply cartesian-product valss))])
(define-values [constraints* mapping*]
(for/fold ([constraints constraints] [mapping mapping])
([var (in-list free-vars)]
[val (in-list vals)])
(values (variance-constraints-substitute constraints var val)
(variance-mapping-set/substitute mapping var val))))
(solve-variance-constraints vars constraints* mapping*))])])]))
;; variance-expr-substitute : Variance-Expr Variance-Var Variance-Expr -> Variance-Expr
(define (variance-expr-substitute expr var value)
(match expr
[(? variance-var? v) (if (variance-var=? v var) value v)]
[(? variance? v) v]
[(variance-expr-join v1 v2)
(variance-expr-join (variance-expr-substitute v1 var value)
(variance-expr-substitute v2 var value))]
[(variance-expr-compose v1 v2)
(variance-expr-compose (variance-expr-substitute v1 var value)
(variance-expr-substitute v2 var value))]))
;; variance-constraint-substitute :
;; Variance-Constraint Variance-Var Variance-Expr -> Variance-Constraint
(define (variance-constraint-substitute constraint var value)
(match constraint
[(variance= v1 v2)
(variance= (variance-expr-substitute v1 var value)
(variance-expr-substitute v2 var value))]))
;; variance-constraints-substitute :
;; (Listof Variance-Constraint) Variance-Var Variance-Expr -> (Listof Variance-Constraint)
(define (variance-constraints-substitute constraints var value)
(for/list ([constraint (in-list constraints)])
(variance-constraint-substitute constraint var value)))
;; variance-mapping-set/substitute : Variance-Mapping Variance-Var Variance-Expr -> Variance-Mapping
(define (variance-mapping-set/substitute mapping var value)
(variance-mapping-set
(for/hash ([(k v) (in-hash mapping)])
(values k (variance-expr-substitute v var value)))
var value))
;; variance-constraint-variables : (Listof Variance-Var) Variance-Constraint [(Setof Variance-Var)] -> (Setof Variance-Var)
(define (variance-constraint-variables vars constraint [acc (seteq)])
(match constraint
[(variance= v1 v2)
(variance-expr-variables vars v2 (variance-expr-variables vars v1 acc))]))
;; variance-expr-variables :
;; (Listof Variance-Var) Variance-Expr [(Setof Variance-Var)] -> (Setof Variance-Var)
(define (variance-expr-variables vars expr [acc (seteq)])
(match expr
[(? variance-var? v)
(if (implies vars (member v vars)) (set-add acc v) acc)]
[(? variance? v)
acc]
[(variance-expr-join v1 v2)
(variance-expr-variables vars v2 (variance-expr-variables vars v1 acc))]
[(variance-expr-compose v1 v2)
(variance-expr-variables vars v2 (variance-expr-variables vars v1 acc))]))
;; variance-mapping-interp-exprs : (Listof Variance-Var) Variance-Mapping -> Variance-Mapping
(define (variance-mapping-interp-exprs vars mapping)
(for/fold ([mapping mapping])
([(k v) (in-hash mapping)])
(variance-mapping-set mapping k (variance-expr-interp vars v mapping))))
;; variance-expr-interp : (Listof Variance-Var) Variance-Expr Variance-Mapping -> Variance-Expr
(define (variance-expr-interp vars expr mapping)
(match expr
[(? variance? v) v]
[(? variance-var? v)
(cond
[(variance-mapping-has? mapping v)
(define expr (variance-mapping-ref mapping v))
(cond [(member v (variance-expr-variables #f expr '()))
(error 'variance-expr-interp "bad stufs is happening right now:\n~v = ~v" v expr)
v]
[else
(variance-expr-interp vars expr mapping)])]
[else v])]
[(variance-expr-join v1 v2)
(variance-join/expr (variance-expr-interp vars v1 mapping)
(variance-expr-interp vars v2 mapping))]
[(variance-expr-compose v1 v2)
(variance-compose/expr (variance-expr-interp vars v1 mapping)
(variance-expr-interp vars v2 mapping))]))
;; variance-join/expr : Variance-Expr Variance-Expr -> Variance-Expr
(define/match (variance-join/expr v1 v2)
[[(? variance? v1) (? variance? v2)] (variance-join v1 v2)]
[[(? variance? (? variance-invariant? v1)) _] v1]
[[_ (? variance? (? variance-invariant? v2))] v2]
[[(? variance? (? variance-irrelevant? v1)) v2] v2]
[[v1 (? variance? (? variance-irrelevant? v2))] v1]
[[v1 v2] #:when (equal? v1 v2) v1]
[[v1 v2] (variance-expr-join v1 v2)])
;; variance-compose/expr : Variance-Expr Variance-Expr -> Variance-Expr
(define/match (variance-compose/expr v1 v2)
[[(? variance? v1) (? variance? v2)] (variance-compose v1 v2)]
[[(? variance? (? variance-irrelevant? v1)) _] v1]
[[_ (? variance? (? variance-irrelevant? v2))] v2]
[[(? variance? (? variance-invariant? v1)) _] v1]
[[_ (? variance? (? variance-invariant? v2))] v2]
[[(? variance? (? variance-covariant? v1)) v2] v2]
[[v1 (? variance? (? variance-covariant? v2))] v1]
[[v1 v2] (variance-expr-compose v1 v2)])
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(module+ test
(test-case "variance<=?"
(test-case "irrelevant <= everything"
(check-true (variance<=? irrelevant irrelevant))
(check-true (variance<=? irrelevant covariant))
(check-true (variance<=? irrelevant contravariant))
(check-true (variance<=? irrelevant invariant)))
(test-case "nothing else is <= irrelevant"
(check-false (variance<=? covariant irrelevant))
(check-false (variance<=? contravariant irrelevant))
(check-false (variance<=? invariant irrelevant)))
(test-case "everything <= invariant"
(check-true (variance<=? irrelevant invariant))
(check-true (variance<=? covariant invariant))
(check-true (variance<=? contravariant invariant))
(check-true (variance<=? invariant invariant)))
(test-case "invariant is not <= anything else"
(check-false (variance<=? invariant irrelevant))
(check-false (variance<=? invariant covariant))
(check-false (variance<=? invariant contravariant)))
(test-case "covariant and contravariant are not <= or >="
(check-false (variance<=? covariant contravariant))
(check-false (variance<=? contravariant covariant))))
(test-case "solve-variance-constraints"
(check-equal? (solve-variance-constraints
(list) (list) (hash))
(hash))
(check-equal? (solve-variance-constraints
(list 'a) (list (variance= 'a irrelevant)) (hash))
(hash 'a irrelevant))
(check-equal? (solve-variance-constraints
(list 'a) (list (variance= 'a covariant)) (hash))
(hash 'a covariant))
(check-equal? (solve-variance-constraints
(list 'a) (list (variance= 'a contravariant)) (hash))
(hash 'a contravariant))
(check-equal? (solve-variance-constraints
(list 'a) (list (variance= 'a invariant)) (hash))
(hash 'a invariant))
(check-equal? (solve-variance-constraints
(list 'a 'b)
(list (variance= (variance-expr-compose covariant 'a)
(variance-expr-join covariant 'b)))
(hash))
(hash 'a covariant 'b irrelevant))
(check-equal? (solve-variance-constraints
(list 'a)
(list (variance= 'a
(variance-expr-join
(variance-expr-join
covariant
(variance-expr-compose
covariant
'a))
irrelevant)))
(hash))
(hash 'a covariant))
(check-equal? (solve-variance-constraints
(list 'a)
(list (variance= 'a
(variance-expr-join
(variance-expr-compose
contravariant
covariant)
irrelevant)))
(hash))
(hash 'a contravariant))
(check-equal? (solve-variance-constraints
(list 'a)
(list (variance= 'a
(variance-expr-join
(variance-expr-compose
contravariant
'a)
irrelevant)))
(hash))
(hash 'a irrelevant))
(check-equal? (solve-variance-constraints
(list 'a)
(list (variance= 'a
(variance-expr-join
(variance-expr-compose
contravariant
'a)
covariant)))
(hash))
(hash 'a invariant))
(check-equal? (solve-variance-constraints
(list 'a)
(list (variance= 'a
(variance-expr-join
(variance-expr-compose
covariant
covariant)
(variance-expr-compose
contravariant
covariant))))
(hash))
(hash 'a invariant))
(check-equal? (solve-variance-constraints
(list 'a)
(list (variance= 'a
(variance-expr-join
(variance-expr-join
(variance-expr-compose
covariant
'a)
(variance-expr-compose
contravariant
'a))
covariant)))
(hash))
(hash 'a invariant))
(check-equal? (solve-variance-constraints
(list 'a 'b 'c 'd)
(list (variance= 'a
(variance-expr-join
(variance-expr-join
(variance-expr-join
(variance-expr-compose
contravariant
covariant)
irrelevant)
(variance-expr-compose
covariant
'c))
(variance-expr-compose
irrelevant
'd)))
(variance= 'b
(variance-expr-join
(variance-expr-join
(variance-expr-join
(variance-expr-compose
contravariant
irrelevant)
covariant)
(variance-expr-compose
covariant
'c))
(variance-expr-compose
covariant
'd)))
(variance= 'c
(variance-expr-join
(variance-expr-compose
covariant
'a)
(variance-expr-compose
covariant
'b)))
(variance= 'd
(variance-expr-join
(variance-expr-compose
irrelevant
'a)
(variance-expr-compose
irrelevant
'd))))
(hash))
(hash 'a invariant
'b invariant
'c invariant
'd irrelevant))
)
)