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## Copyright (c) Eduardo Julian. All rights reserved.
## This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.
## If a copy of the MPL was not distributed with this file,
## You can obtain one at http://mozilla.org/MPL/2.0/.
(;import lux
(lux (control show
eq
monad)
(data (text #open ("text:" Text/Monoid Text/Eq))
(number/int #open ("int:" Int/Eq Int/Show))
maybe
(list #refer #all #open ("list:" List/Monad)))
))
(open List/Fold)
## [Structures]
(defstruct #export Type/Show (Show Type)
(def (show type)
(case type
(#;DataT name)
($ text:++ "(^ " name ")")
(#;TupleT members)
(case members
#;Nil
"(,)"
_
($ text:++ "(, " (|> members (list:map show) (interpose " ") (foldL text:++ "")) ")"))
(#;VariantT members)
(case members
#;Nil
"(|)"
_
($ text:++ "(| " (|> members (list:map show) (interpose " ") (foldL text:++ "")) ")"))
(#;LambdaT input output)
($ text:++ "(-> " (show input) " " (show output) ")")
(#;VarT id)
($ text:++ "⌈" (int:show id) "⌋")
(#;BoundT idx)
(int:show idx)
(#;ExT id)
($ text:++ "⟨" (int:show id) "⟩")
(#;AppT fun param)
($ text:++ "(" (show fun) " " (show param) ")")
(#;UnivQ env body)
($ text:++ "(All " (show body) ")")
(#;ExQ env body)
($ text:++ "(Ex " (show body) ")")
(#;NamedT [module name] type)
($ text:++ module ";" name)
)))
(defstruct #export Type/Eq (Eq Type)
(def (= x y)
(case [x y]
[(#;DataT xname) (#;DataT yname)]
(text:= xname yname)
(\or [(#;VarT xid) (#;VarT yid)]
[(#;ExT xid) (#;ExT yid)]
[(#;BoundT xid) (#;BoundT yid)])
(int:= xid yid)
(\or [(#;LambdaT xleft xright) (#;LambdaT yleft yright)]
[(#;AppT xleft xright) (#;AppT yleft yright)])
(and (= xleft yleft)
(= xright yright))
[(#;NamedT [xmodule xname] xtype) (#;NamedT [ymodule yname] ytype)]
(and (text:= xmodule ymodule)
(text:= xname yname)
(= xtype ytype))
(\or [(#;TupleT xmembers) (#;TupleT ymembers)]
[(#;VariantT xmembers) (#;VariantT ymembers)])
(and (int:= (size xmembers) (size ymembers))
(foldL (lambda [prev [x y]]
(and prev (= x y)))
true
((zip 2) xmembers ymembers)))
(\or [(#;UnivQ xenv xbody) (#;UnivQ yenv ybody)]
[(#;ExQ xenv xbody) (#;ExQ yenv ybody)])
(and (int:= (size xenv) (size yenv))
(foldL (lambda [prev [x y]]
(and prev (= x y)))
(= xbody ybody)
((zip 2) xenv yenv)))
_
false
)))
## [Functions]
(def #export (beta-reduce env type)
(-> (List Type) Type Type)
(case type
(\template [<tag>]
[(<tag> members)
(<tag> (list:map (beta-reduce env) members))])
[[#;VariantT]
[#;TupleT]]
(\template [<tag>]
[(<tag> left right)
(<tag> (beta-reduce env left) (beta-reduce env right))])
[[#;LambdaT]
[#;AppT]]
(\template [<tag>]
[(<tag> env def)
(case env
#;Nil
(<tag> env def)
_
type)])
[[#;UnivQ]
[#;ExQ]]
(#;BoundT idx)
(? type (@ idx env))
(#;NamedT name type)
(beta-reduce env type)
_
type
))
(def #export (apply-type type-fun param)
(-> Type Type (Maybe Type))
(case type-fun
(#;UnivQ env body)
(#;Some (beta-reduce (@list& type-fun param env) body))
(#;AppT F A)
(do Maybe/Monad
[type-fn* (apply-type F A)]
(apply-type type-fn* param))
(#;NamedT name type)
(apply-type type param)
_
#;None))
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