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(.module: {#.doc "Type-checking functionality."}
lux
(lux (control [functor #+ Functor]
[apply #+ Apply]
[monad #+ do Monad]
["ex" exception #+ exception:])
(data [text "text/" Monoid<Text> Eq<Text>]
[number "nat/" Codec<Text,Nat>]
[maybe]
[product]
(coll [list]
(set ["set" unordered #+ Set]))
["e" error])
(lang [type "type/" Eq<Type>])
))
(exception: #export (unknown-type-var {id Nat})
(nat/encode id))
(exception: #export (unbound-type-var {id Nat})
(nat/encode id))
(exception: #export (invalid-type-application {funcT Type} {argT Type})
(type.to-text (#.Apply argT funcT)))
(exception: #export (cannot-rebind-var {id Nat} {type Type} {bound Type})
($_ text/compose
" Var: " (nat/encode id) "\n"
" Wanted Type: " (type.to-text type) "\n"
"Current Type: " (type.to-text bound)))
(exception: #export (type-check-failed {expected Type} {actual Type})
($_ text/compose
"Expected: " (type.to-text expected) "\n\n"
" Actual: " (type.to-text actual)))
(type: #export Var Nat)
(type: #export Assumption
{#subsumption [Type Type]
#verdict Bool})
(type: #export (Check a)
(-> Type-Context (e.Error [Type-Context a])))
(type: #export Type-Vars
(List [Var (Maybe Type)]))
(struct: #export _ (Functor Check)
(def: (map f fa)
(function (_ context)
(case (fa context)
(#e.Error error)
(#e.Error error)
(#e.Success [context' output])
(#e.Success [context' (f output)])
))))
(struct: #export _ (Apply Check)
(def: functor Functor<Check>)
(def: (apply ff fa)
(function (_ context)
(case (ff context)
(#e.Success [context' f])
(case (fa context')
(#e.Success [context'' a])
(#e.Success [context'' (f a)])
(#e.Error error)
(#e.Error error))
(#e.Error error)
(#e.Error error)
)))
)
(struct: #export _ (Monad Check)
(def: functor Functor<Check>)
(def: (wrap x)
(function (_ context)
(#e.Success [context x])))
(def: (join ffa)
(function (_ context)
(case (ffa context)
(#e.Success [context' fa])
(case (fa context')
(#e.Success [context'' a])
(#e.Success [context'' a])
(#e.Error error)
(#e.Error error))
(#e.Error error)
(#e.Error error)
)))
)
(open Monad<Check> "check/")
(def: (var::get id plist)
(-> Var Type-Vars (Maybe (Maybe Type)))
(case plist
#.Nil
#.None
(#.Cons [var-id var-type]
plist')
(if (n/= id var-id)
(#.Some var-type)
(var::get id plist'))
))
(def: (var::new id plist)
(-> Var Type-Vars Type-Vars)
(#.Cons [id #.None] plist))
(def: (var::put id value plist)
(-> Var (Maybe Type) Type-Vars Type-Vars)
(case plist
#.Nil
(list [id value])
(#.Cons [var-id var-type]
plist')
(if (n/= id var-id)
(#.Cons [var-id value]
plist')
(#.Cons [var-id var-type]
(var::put id value plist')))
))
(def: (var::remove id plist)
(-> Var Type-Vars Type-Vars)
(case plist
#.Nil
#.Nil
(#.Cons [var-id var-type]
plist')
(if (n/= id var-id)
plist'
(#.Cons [var-id var-type]
(var::remove id plist')))
))
## [[Logic]]
(def: #export (run context proc)
(All [a] (-> Type-Context (Check a) (e.Error a)))
(case (proc context)
(#e.Error error)
(#e.Error error)
(#e.Success [context' output])
(#e.Success output)))
(def: #export (throw exception message)
(All [e a] (-> (ex.Exception e) e (Check a)))
(function (_ context)
(ex.throw exception message)))
(def: #export existential
{#.doc "A producer of existential types."}
(Check [Nat Type])
(function (_ context)
(let [id (get@ #.ex-counter context)]
(#e.Success [(update@ #.ex-counter inc context)
[id (#.Ex id)]]))))
(do-template [<name> <outputT> <fail> <succeed>]
[(def: #export (<name> id)
(-> Var (Check <outputT>))
(function (_ context)
(case (|> context (get@ #.var-bindings) (var::get id))
(^or (#.Some (#.Some (#.Var _)))
(#.Some #.None))
(#e.Success [context <fail>])
(#.Some (#.Some bound))
(#e.Success [context <succeed>])
#.None
(ex.throw unknown-type-var id))))]
[bound? Bool false true]
[read (Maybe Type) #.None (#.Some bound)]
)
(def: (peek id)
(-> Var (Check Type))
(function (_ context)
(case (|> context (get@ #.var-bindings) (var::get id))
(#.Some (#.Some bound))
(#e.Success [context bound])
(#.Some #.None)
(ex.throw unbound-type-var id)
#.None
(ex.throw unknown-type-var id))))
(def: #export (write type id)
(-> Type Var (Check Top))
(function (_ context)
(case (|> context (get@ #.var-bindings) (var::get id))
(#.Some (#.Some bound))
(ex.throw cannot-rebind-var [id type bound])
(#.Some #.None)
(#e.Success [(update@ #.var-bindings (var::put id (#.Some type)) context)
[]])
#.None
(ex.throw unknown-type-var id))))
(def: (update type id)
(-> Type Var (Check Top))
(function (_ context)
(case (|> context (get@ #.var-bindings) (var::get id))
(#.Some _)
(#e.Success [(update@ #.var-bindings (var::put id (#.Some type)) context)
[]])
#.None
(ex.throw unknown-type-var id))))
(def: #export var
(Check [Var Type])
(function (_ context)
(let [id (get@ #.var-counter context)]
(#e.Success [(|> context
(update@ #.var-counter inc)
(update@ #.var-bindings (var::new id)))
[id (#.Var id)]]))))
(def: get-bindings
(Check (List [Var (Maybe Type)]))
(function (_ context)
(#e.Success [context
(get@ #.var-bindings context)])))
(def: (set-bindings value)
(-> (List [Var (Maybe Type)]) (Check Top))
(function (_ context)
(#e.Success [(set@ #.var-bindings value context)
[]])))
(def: (apply-type! funcT argT)
(-> Type Type (Check Type))
(case funcT
(#.Var func-id)
(do Monad<Check>
[?funcT' (read func-id)]
(case ?funcT'
#.None
(throw invalid-type-application [funcT argT])
(#.Some funcT')
(apply-type! funcT' argT)))
_
(function (_ context)
(case (type.apply (list argT) funcT)
#.None
(ex.throw invalid-type-application [funcT argT])
(#.Some output)
(#e.Success [context output])))))
(type: #export Ring (Set Var))
(def: empty-ring Ring (set.new number.Hash<Nat>))
(def: #export (ring id)
(-> Var (Check Ring))
(function (_ context)
(loop [current id
output (set.add id empty-ring)]
(case (|> context (get@ #.var-bindings) (var::get current))
(#.Some (#.Some type))
(case type
(#.Var post)
(if (n/= id post)
(#e.Success [context output])
(recur post (set.add post output)))
_
(#e.Success [context empty-ring]))
(#.Some #.None)
(#e.Success [context output])
#.None
(ex.throw unknown-type-var current)))))
(def: #export fresh-context
Type-Context
{#.var-counter +0
#.ex-counter +0
#.var-bindings (list)
})
(def: (attempt op)
(All [a] (-> (Check a) (Check (Maybe a))))
(function (_ context)
(case (op context)
(#e.Success [context' output])
(#e.Success [context' (#.Some output)])
(#e.Error _)
(#e.Success [context #.None]))))
(def: #export (fail message)
(All [a] (-> Text (Check a)))
(function (_ context)
(#e.Error message)))
(def: #export (assert message test)
(-> Text Bool (Check Top))
(function (_ context)
(if test
(#e.Success [context []])
(#e.Error message))))
(def: (either left right)
(All [a] (-> (Check a) (Check a) (Check a)))
(function (_ context)
(case (left context)
(#e.Success [context' output])
(#e.Success [context' output])
(#e.Error _)
(right context))))
(def: (assumed? [e a] assumptions)
(-> [Type Type] (List Assumption) (Maybe Bool))
(:: maybe.Monad<Maybe> map product.right
(list.find (function (_ [[fe fa] status])
(and (type/= e fe)
(type/= a fa)))
assumptions)))
(def: (assume! ea status assumptions)
(-> [Type Type] Bool (List Assumption) (List Assumption))
(#.Cons [ea status] assumptions))
(def: (on id type then else)
(All [a]
(-> Var Type (Check a) (-> Type (Check a))
(Check a)))
($_ either
(do Monad<Check>
[_ (write type id)]
then)
(do Monad<Check>
[ring (ring id)
_ (assert "" (n/> +1 (set.size ring)))
_ (monad.map @ (update type) (set.to-list ring))]
then)
(do Monad<Check>
[?bound (read id)]
(else (maybe.default (#.Var id) ?bound)))))
(def: (link-2 left right)
(-> Var Var (Check Top))
(do Monad<Check>
[_ (write (#.Var right) left)]
(write (#.Var left) right)))
(def: (link-3 interpose to from)
(-> Var Var Var (Check Top))
(do Monad<Check>
[_ (update (#.Var interpose) from)]
(update (#.Var to) interpose)))
(def: (check-vars check' assumptions idE idA)
(-> (-> Type Type (List Assumption) (Check (List Assumption)))
(List Assumption)
Var Var
(Check (List Assumption)))
(if (n/= idE idA)
(check/wrap assumptions)
(do Monad<Check>
[ebound (attempt (peek idE))
abound (attempt (peek idA))]
(case [ebound abound]
## Link the 2 variables circularily
[#.None #.None]
(do @
[_ (link-2 idE idA)]
(wrap assumptions))
## Interpose new variable between 2 existing links
[(#.Some etype) #.None]
(case etype
(#.Var targetE)
(do @
[_ (link-3 idA targetE idE)]
(wrap assumptions))
_
(check' etype (#.Var idA) assumptions))
## Interpose new variable between 2 existing links
[#.None (#.Some atype)]
(case atype
(#.Var targetA)
(do @
[_ (link-3 idE targetA idA)]
(wrap assumptions))
_
(check' (#.Var idE) atype assumptions))
[(#.Some etype) (#.Some atype)]
(case [etype atype]
[(#.Var targetE) (#.Var targetA)]
(do @
[ringE (ring idE)
ringA (ring idA)]
(if (:: set.Eq<Set> = ringE ringA)
(wrap assumptions)
## Fuse 2 rings
(do @
[_ (monad.fold @ (function (_ interpose to)
(do @
[_ (link-3 interpose to idE)]
(wrap interpose)))
targetE
(set.to-list ringA))]
(wrap assumptions))))
[(#.Var targetE) _]
(do @
[ring (ring idE)
_ (monad.map @ (update atype) (set.to-list ring))]
(wrap assumptions))
[_ (#.Var targetA)]
(do @
[ring (ring idA)
_ (monad.map @ (update etype) (set.to-list ring))]
(wrap assumptions))
_
(check' etype atype assumptions))))))
(def: (with-error-stack on-error check)
(All [a] (-> (-> Top Text) (Check a) (Check a)))
(function (_ context)
(case (check context)
(#e.Error error)
(#e.Error (case error
""
(on-error [])
_
($_ text/compose
(on-error [])
"\n\n-----------------------------------------\n\n"
error)))
output
output)))
(def: (check-apply check' assumptions [eAT eFT] [aAT aFT])
(-> (-> Type Type (List Assumption) (Check (List Assumption))) (List Assumption)
[Type Type] [Type Type]
(Check (List Assumption)))
(case [eFT aFT]
(^or [(#.UnivQ _ _) (#.Ex _)] [(#.UnivQ _ _) (#.Var _)])
(do Monad<Check>
[eFT' (apply-type! eFT eAT)]
(check' eFT' (#.Apply aAT aFT) assumptions))
(^or [(#.Ex _) (#.UnivQ _ _)] [(#.Var _) (#.UnivQ _ _)])
(do Monad<Check>
[aFT' (apply-type! aFT aAT)]
(check' (#.Apply eAT eFT) aFT' assumptions))
(^or [(#.Ex _) _] [_ (#.Ex _)])
(do Monad<Check>
[assumptions (check' eFT aFT assumptions)]
(check' eAT aAT assumptions))
[(#.Var id) _]
(do Monad<Check>
[?rFT (read id)]
(case ?rFT
(#.Some rFT)
(check' (#.Apply eAT rFT) (#.Apply aAT aFT) assumptions)
_
(do Monad<Check>
[assumptions (check' eFT aFT assumptions)
e' (apply-type! aFT eAT)
a' (apply-type! aFT aAT)]
(check' e' a' assumptions))))
[_ (#.Var id)]
(do Monad<Check>
[?rFT (read id)]
(case ?rFT
(#.Some rFT)
(check' (#.Apply eAT eFT) (#.Apply aAT rFT) assumptions)
_
(do Monad<Check>
[assumptions (check' eFT aFT assumptions)
e' (apply-type! eFT eAT)
a' (apply-type! eFT aAT)]
(check' e' a' assumptions))))
_
(fail "")))
(def: #export (check' expected actual assumptions)
{#.doc "Type-check to ensure that the 'expected' type subsumes the 'actual' type."}
(-> Type Type (List Assumption) (Check (List Assumption)))
(if (is? expected actual)
(check/wrap assumptions)
(with-error-stack
(function (_ _) (ex.construct type-check-failed [expected actual]))
(case [expected actual]
[(#.Var idE) (#.Var idA)]
(check-vars check' assumptions idE idA)
[(#.Var id) _]
(on id actual
(check/wrap assumptions)
(function (_ bound)
(check' bound actual assumptions)))
[_ (#.Var id)]
(on id expected
(check/wrap assumptions)
(function (_ bound)
(check' expected bound assumptions)))
(^template [<fe> <fa>]
[(#.Apply A1 <fe>) (#.Apply A2 <fa>)]
(check-apply check' assumptions [A1 <fe>] [A2 <fa>]))
([F1 (#.Ex ex)]
[(#.Ex ex) F2]
[F1 (#.Var id)]
[(#.Var id) F2])
[(#.Apply A F) _]
(let [fx-pair [expected actual]]
(case (assumed? fx-pair assumptions)
(#.Some ?)
(if ?
(check/wrap assumptions)
(fail ""))
#.None
(do Monad<Check>
[expected' (apply-type! F A)]
(check' expected' actual (assume! fx-pair true assumptions)))))
[_ (#.Apply A F)]
(do Monad<Check>
[actual' (apply-type! F A)]
(check' expected actual' assumptions))
(^template [<tag> <instancer>]
[(<tag> _) _]
(do Monad<Check>
[[_ paramT] <instancer>
expected' (apply-type! expected paramT)]
(check' expected' actual assumptions)))
([#.UnivQ ..existential]
[#.ExQ ..var])
(^template [<tag> <instancer>]
[_ (<tag> _)]
(do Monad<Check>
[[_ paramT] <instancer>
actual' (apply-type! actual paramT)]
(check' expected actual' assumptions)))
([#.UnivQ ..var]
[#.ExQ ..existential])
[(#.Primitive e-name e-params) (#.Primitive a-name a-params)]
(if (and (text/= e-name a-name)
(n/= (list.size e-params)
(list.size a-params)))
(do Monad<Check>
[assumptions (monad.fold Monad<Check>
(function (_ [e a] assumptions) (check' e a assumptions))
assumptions
(list.zip2 e-params a-params))]
(check/wrap assumptions))
(fail ""))
(^template [<compose>]
[(<compose> eL eR) (<compose> aL aR)]
(do Monad<Check>
[assumptions (check' eL aL assumptions)]
(check' eR aR assumptions)))
([#.Sum]
[#.Product])
[(#.Function eI eO) (#.Function aI aO)]
(do Monad<Check>
[assumptions (check' aI eI assumptions)]
(check' eO aO assumptions))
[(#.Ex e!id) (#.Ex a!id)]
(if (n/= e!id a!id)
(check/wrap assumptions)
(fail ""))
[(#.Named _ ?etype) _]
(check' ?etype actual assumptions)
[_ (#.Named _ ?atype)]
(check' expected ?atype assumptions)
_
(fail "")))))
(def: #export (check expected actual)
{#.doc "Type-check to ensure that the 'expected' type subsumes the 'actual' type."}
(-> Type Type (Check Top))
(do Monad<Check>
[assumptions (check' expected actual (list))]
(wrap [])))
(def: #export (checks? expected actual)
{#.doc "A simple type-checking function that just returns a yes/no answer."}
(-> Type Type Bool)
(case (run fresh-context (check expected actual))
(#e.Error error)
false
(#e.Success _)
true))
(def: #export get-context
(Check Type-Context)
(function (_ context)
(#e.Success [context context])))
(def: #export (clean inputT)
(-> Type (Check Type))
(case inputT
(#.Primitive name paramsT+)
(do Monad<Check>
[paramsT+' (monad.map @ clean paramsT+)]
(wrap (#.Primitive name paramsT+')))
(^or (#.Bound _) (#.Ex _) (#.Named _))
(:: Monad<Check> wrap inputT)
(^template [<tag>]
(<tag> leftT rightT)
(do Monad<Check>
[leftT' (clean leftT)
rightT' (clean rightT)]
(wrap (<tag> leftT' rightT'))))
([#.Sum] [#.Product] [#.Function] [#.Apply])
(#.Var id)
(do Monad<Check>
[?actualT (read id)]
(case ?actualT
(#.Some actualT)
(clean actualT)
_
(wrap inputT)))
(^template [<tag>]
(<tag> envT+ unquantifiedT)
(do Monad<Check>
[envT+' (monad.map @ clean envT+)]
(wrap (<tag> envT+' unquantifiedT))))
([#.UnivQ] [#.ExQ])
))
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