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(.module: {#.doc "Basic functionality for working with types."}
[lux (#- function)
[abstract
[equivalence (#+ Equivalence)]
[monad (#+ Monad do)]]
[control
["." function]
["." exception (#+ exception:)]
["p" parser
["s" code (#+ Parser)]]]
[data
["." text ("#@." monoid equivalence)]
["." name ("#@." equivalence codec)]
[number
["n" nat ("#@." decimal)]]
["." maybe]
[collection
["." array]
["." list ("#@." functor monoid fold)]]]
["." macro
["." code]
[syntax (#+ syntax:)]]])
(template [<name> <tag>]
[(def: #export (<name> type)
(-> Type [Nat Type])
(loop [num-args 0
type type]
(case type
(<tag> env sub-type)
(recur (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)]))
(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 (to-text type)
(-> Type Text)
(case type
(#.Primitive name params)
($_ text@compose
"(primitive "
(text.enclose' text.double-quote name)
(|> params
(list@map (|>> to-text (text@compose " ")))
(list@fold (function.flip text@compose) ""))
")")
(^template [<tag> <open> <close> <flatten>]
(<tag> _)
($_ 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)]
($_ text@compose "(-> "
(|> ins
(list@map to-text)
list.reverse
(list.interpose " ")
(list@fold text@compose ""))
" " (to-text out) ")"))
(#.Parameter idx)
(n@encode idx)
(#.Var id)
($_ text@compose "⌈v:" (n@encode id) "⌋")
(#.Ex id)
($_ text@compose "⟨e:" (n@encode id) "⟩")
(#.Apply param fun)
(let [[type-func type-args] (flatten-application type)]
($_ 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: (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])
(#.Parameter idx)
(maybe.default (error! ($_ text@compose
"Unknown type parameter" text.new-line
" Index: " (n@encode idx) text.new-line
"Environment: " (|> env
list.enumerate
(list@map (.function (_ [index type])
($_ text@compose
(n@encode index)
" " (..to-text type))))
(text.join-with (text@compose text.new-line " ")))))
(list.nth idx env))
_
type
))
(structure: #export equivalence (Equivalence Type)
(def: (= x y)
(or (is? 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)))
#1
(list.zip2 xparams yparams)))
(^template [<tag>]
[(<tag> xid) (<tag> yid)]
(n.= yid xid))
([#.Var] [#.Ex] [#.Parameter])
(^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 (name@= 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)))
#1
(list.zip2 xenv yenv)))
_
#0
))))
(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> idx)
(` (<tag> (~ (code.nat idx)))))
([#.Var] [#.Ex] [#.Parameter])
(^template [<tag>]
(<tag> left right)
(` (<tag> (~ (to-code left))
(~ (to-code right)))))
([#.Sum] [#.Product] [#.Function] [#.Apply])
(#.Named name sub-type)
(code.identifier name)
(^template [<tag>]
(<tag> env body)
(` (<tag> (.list (~+ (list@map to-code env)))
(~ (to-code body)))))
([#.UnivQ] [#.ExQ])
))
(def: #export (un-alias type)
(-> Type Type)
(case type
(#.Named _ (#.Named name type'))
(un-alias (#.Named name type'))
_
type))
(def: #export (un-name type)
(-> Type Type)
(case type
(#.Named name type')
(un-name type')
_
type))
(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 Nothing #.Sum]
[tuple Any #.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))))
(template [<name> <tag>]
[(def: #export (<name> size body)
(-> Nat Type Type)
(case size
0 body
_ (|> body (<name> (dec size)) (<tag> (list)))))]
[univ-q #.UnivQ]
[ex-q #.ExQ]
)
(def: #export (quantified? type)
(-> Type Bit)
(case type
(#.Named [module name] _type)
(quantified? _type)
(#.Apply A F)
(maybe.default #0
(do maybe.monad
[applied (apply (list A) F)]
(wrap (quantified? applied))))
(^or (#.UnivQ _) (#.ExQ _))
#1
_
#0))
(def: #export (array depth elem-type)
(-> Nat Type Type)
(case depth
0 elem-type
_ (|> elem-type (array (dec depth)) (list) (#.Primitive array.type-name))))
(syntax: #export (:log! {input (p.or s.identifier
s.any)})
(case input
(#.Left valueN)
(do macro.monad
[cursor macro.cursor
valueT (macro.find-type valueN)
#let [_ (log! ($_ text@compose
(name@encode (name-of ..:log!)) " @ " (.cursor-description cursor) text.new-line
"Value: " (name@encode valueN) text.new-line
" Type: " (..to-text valueT) text.new-line))]]
(wrap (list (code.identifier valueN))))
(#.Right valueC)
(macro.with-gensyms [g!value]
(wrap (list (` (.let [(~ g!value) (~ valueC)]
(..:log! (~ g!value)))))))))
(def: type-parameters
(Parser (List Text))
(s.tuple (p.some s.local-identifier)))
(syntax: #export (:cast {type-vars type-parameters}
input
output
{value (p.maybe s.any)})
(let [casterC (` (: (All [(~+ (list@map code.local-identifier type-vars))]
(-> (~ input) (~ output)))
(|>> :assume)))]
(case value
#.None
(wrap (list casterC))
(#.Some value)
(wrap (list (` ((~ casterC) (~ value))))))))
(type: Typed
{#type Code
#expression Code})
(def: typed
(Parser Typed)
(s.record (p.and s.any s.any)))
## TODO: Make sure the generated code always gets optimized away.
(syntax: #export (:share {type-vars type-parameters}
{exemplar typed}
{computation typed})
(macro.with-gensyms [g!_]
(let [shareC (` (: (All [(~+ (list@map code.local-identifier type-vars))]
(-> (~ (get@ #type exemplar))
(~ (get@ #type computation))))
(.function ((~ g!_) (~ g!_))
(~ (get@ #expression computation)))))]
(wrap (list (` ((~ shareC) (~ (get@ #expression exemplar)))))))))
(syntax: #export (:by-example {type-vars type-parameters}
{exemplar typed}
{extraction s.any})
(wrap (list (` (:of ((~! :share)
[(~+ (list@map code.local-identifier type-vars))]
{(~ (get@ #type exemplar))
(~ (get@ #expression exemplar))}
{(~ extraction)
(:assume [])}))))))
(exception: #export (hole-type {location Cursor} {type Type})
(exception.report
["Location" (.cursor-description location)]
["Type" (..to-text type)]))
(syntax: #export (:hole)
(do macro.monad
[cursor macro.cursor
expectedT macro.expected-type]
(macro.fail (exception.construct ..hole-type [cursor expectedT]))))
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