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(.module: {#.doc "Basic functionality for working with types."}
[lux #- function]
(lux (control [eq #+ Eq]
[monad #+ do Monad])
(data [text "text/" Monoid<Text> Eq<Text>]
[ident "ident/" Eq<Ident>]
[number "nat/" Codec<Text,Nat>]
[maybe]
(coll [list #+ "list/" Monad<List> Monoid<List> Fold<List>]))
(macro [code])
))
## [Utils]
(def: (beta-reduce env type)
(-> (List Type) Type Type)
(case type
(#.Primitive name params)
(#.Primitive name (list/map (beta-reduce env) params))
(^template [<tag>]
(<tag> left right)
(<tag> (beta-reduce env left) (beta-reduce env right)))
([#.Sum] [#.Product]
[#.Function] [#.Apply])
(^template [<tag>]
(<tag> old-env def)
(case old-env
#.Nil
(<tag> env def)
_
(<tag> (list/map (beta-reduce env) old-env) def)))
([#.UnivQ]
[#.ExQ])
(#.Bound idx)
(maybe.default (error! (text/compose "Unknown type var: " (nat/encode idx)))
(list.nth idx env))
_
type
))
## [Structures]
(struct: #export _ (Eq Type)
(def: (= x y)
(case [x y]
[(#.Primitive xname xparams) (#.Primitive yname yparams)]
(and (text/= xname yname)
(n/= (list.size yparams) (list.size xparams))
(list/fold (.function [[x y] prev] (and prev (= x y)))
true
(list.zip2 xparams yparams)))
(^template [<tag>]
[<tag> <tag>]
true)
([#.Void] [#.Unit])
(^template [<tag>]
[(<tag> xid) (<tag> yid)]
(n/= yid xid))
([#.Var] [#.Ex] [#.Bound])
(^or [(#.Function xleft xright) (#.Function yleft yright)]
[(#.Apply xleft xright) (#.Apply yleft yright)])
(and (= xleft yleft)
(= xright yright))
[(#.Named xname xtype) (#.Named yname ytype)]
(and (ident/= xname yname)
(= xtype ytype))
(^template [<tag>]
[(<tag> xL xR) (<tag> yL yR)]
(and (= xL yL) (= xR yR)))
([#.Sum] [#.Product])
(^or [(#.UnivQ xenv xbody) (#.UnivQ yenv ybody)]
[(#.ExQ xenv xbody) (#.ExQ yenv ybody)])
(and (n/= (list.size yenv) (list.size xenv))
(= xbody ybody)
(list/fold (.function [[x y] prev] (and prev (= x y)))
true
(list.zip2 xenv yenv)))
_
false
)))
## [Values]
(do-template [<name> <tag>]
[(def: #export (<name> type)
(-> Type [Nat Type])
(loop [num-args +0
type type]
(case type
(<tag> env sub-type)
(recur (n/inc num-args) sub-type)
_
[num-args type])))]
[flatten-univ-q #.UnivQ]
[flatten-ex-q #.ExQ]
)
(def: #export (flatten-function type)
(-> Type [(List Type) Type])
(case type
(#.Function in out')
(let [[ins out] (flatten-function out')]
[(list& in ins) out])
_
[(list) type]))
(def: #export (flatten-application type)
(-> Type [Type (List Type)])
(case type
(#.Apply arg func')
(let [[func args] (flatten-application func')]
[func (list/compose args (list arg))])
_
[type (list)]))
(do-template [<name> <tag>]
[(def: #export (<name> type)
(-> Type (List Type))
(case type
(<tag> left right)
(list& left (<name> right))
_
(list type)))]
[flatten-variant #.Sum]
[flatten-tuple #.Product]
)
(def: #export (apply params func)
(-> (List Type) Type (Maybe Type))
(case params
#.Nil
(#.Some func)
(#.Cons param params')
(case func
(^template [<tag>]
(<tag> env body)
(|> body
(beta-reduce (list& func param env))
(apply params')))
([#.UnivQ] [#.ExQ])
(#.Apply A F)
(apply (list& A params) F)
(#.Named name unnamed)
(apply params unnamed)
_
#.None)))
(def: #export (to-code type)
(-> Type Code)
(case type
(#.Primitive name params)
(` (#.Primitive (~ (code.text name))
(.list (~+ (list/map to-code params)))))
(^template [<tag>]
<tag>
(` <tag>))
([#.Void] [#.Unit])
(^template [<tag>]
(<tag> idx)
(` (<tag> (~ (code.nat idx)))))
([#.Var] [#.Ex] [#.Bound])
(^template [<tag>]
(<tag> left right)
(` (<tag> (~ (to-code left))
(~ (to-code right)))))
([#.Sum] [#.Product] [#.Function] [#.Apply])
(#.Named name sub-type)
(code.symbol name)
(^template [<tag>]
(<tag> env body)
(` (<tag> (.list (~+ (list/map to-code env)))
(~ (to-code body)))))
([#.UnivQ] [#.ExQ])
))
(def: #export (to-text type)
(-> Type Text)
(case type
(#.Primitive name params)
(case params
#.Nil
($_ text/compose "(primitive " name ")")
_
($_ text/compose "(primitive " name " " (|> params (list/map to-text) list.reverse (list.interpose " ") (list/fold text/compose "")) ")"))
#.Void
"Void"
#.Unit
"Unit"
(^template [<tag> <open> <close> <flatten>]
(<tag> _)
($_ text/compose <open>
(|> (<flatten> type)
(list/map to-text)
list.reverse
(list.interpose " ")
(list/fold text/compose ""))
<close>))
([#.Sum "(| " ")" flatten-variant]
[#.Product "[" "]" flatten-tuple])
(#.Function input output)
(let [[ins out] (flatten-function type)]
($_ text/compose "(-> "
(|> ins
(list/map to-text)
list.reverse
(list.interpose " ")
(list/fold text/compose ""))
" " (to-text out) ")"))
(#.Bound idx)
(nat/encode idx)
(#.Var id)
($_ text/compose "⌈v:" (nat/encode id) "⌋")
(#.Ex id)
($_ text/compose "⟨e:" (nat/encode id) "⟩")
(#.Apply param fun)
(let [[type-func type-args] (flatten-application type)]
($_ text/compose "(" (to-text type-func) " " (|> type-args (list/map to-text) list.reverse (list.interpose " ") (list/fold text/compose "")) ")"))
(^template [<tag> <desc>]
(<tag> env body)
($_ text/compose "(" <desc> " {" (|> env (list/map to-text) (text.join-with " ")) "} " (to-text body) ")"))
([#.UnivQ "All"]
[#.ExQ "Ex"])
(#.Named [module name] type)
($_ text/compose module "." name)
))
(def: #export (un-alias type)
(-> Type Type)
(case type
(#.Named _ (#.Named ident type'))
(un-alias (#.Named ident type'))
_
type))
(def: #export (un-name type)
(-> Type Type)
(case type
(#.Named ident type')
(un-name type')
_
type))
(do-template [<name> <base> <ctor>]
[(def: #export (<name> types)
(-> (List Type) Type)
(case types
#.Nil
<base>
(#.Cons type #.Nil)
type
(#.Cons type types')
(<ctor> type (<name> types'))))]
[variant Void #.Sum]
[tuple Unit #.Product]
)
(def: #export (function inputs output)
(-> (List Type) Type Type)
(case inputs
#.Nil
output
(#.Cons input inputs')
(#.Function input (function inputs' output))))
(def: #export (application params quant)
(-> (List Type) Type Type)
(case params
#.Nil
quant
(#.Cons param params')
(application params' (#.Apply param quant))))
(do-template [<name> <tag>]
[(def: #export (<name> size body)
(-> Nat Type Type)
(case size
+0 body
_ (<tag> (list) (<name> (n/dec size) body))))]
[univ-q #.UnivQ]
[ex-q #.ExQ]
)
(def: #export (quantified? type)
(-> Type Bool)
(case type
(#.Named [module name] _type)
(quantified? _type)
(#.Apply A F)
(maybe.default false
(do maybe.Monad<Maybe>
[applied (apply (list A) F)]
(wrap (quantified? applied))))
(^or (#.UnivQ _) (#.ExQ _))
true
_
false))
(def: #export (array level elem-type)
(-> Nat Type Type)
(case level
+0 elem-type
_ (#.Primitive "#Array" (list (array (n/dec level) elem-type)))))
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