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(.module:
[lux #*
[control
[monad (#+ do)]
["ex" exception (#+ exception:)]]
[data
["." maybe]
["." text
format]
[collection
["." list ("list/." functor)]]]
["." type
["." check]]
["." macro]]
["." /// ("operation/." monad)
["." extension]]
[// (#+ Tag Analysis Operation Phase)]
["." //type])
(exception: #export (variant-tag-out-of-bounds {size Nat} {tag Tag} {type Type})
(ex.report ["Tag" (%n tag)]
["Variant size" (%i (.int size))]
["Variant type" (%type type)]))
(exception: #export (cannot-infer {type Type} {args (List Code)})
(ex.report ["Type" (%type type)]
["Arguments" (|> args
list.enumerate
(list/map (function (_ [idx argC])
(format text.new-line " " (%n idx) " " (%code argC))))
(text.join-with ""))]))
(exception: #export (cannot-infer-argument {inferred Type} {argument Code})
(ex.report ["Inferred Type" (%type inferred)]
["Argument" (%code argument)]))
(exception: #export (smaller-variant-than-expected {expected Nat} {actual Nat})
(ex.report ["Expected" (%i (.int expected))]
["Actual" (%i (.int actual))]))
(do-template [<name>]
[(exception: #export (<name> {type Type})
(%type type))]
[not-a-variant-type]
[not-a-record-type]
[invalid-type-application]
)
(def: (replace parameter-idx replacement type)
(-> Nat Type Type Type)
(case type
(#.Primitive name params)
(#.Primitive name (list/map (replace parameter-idx replacement) params))
(^template [<tag>]
(<tag> left right)
(<tag> (replace parameter-idx replacement left)
(replace parameter-idx replacement right)))
([#.Sum]
[#.Product]
[#.Function]
[#.Apply])
(#.Parameter idx)
(if (n/= parameter-idx idx)
replacement
type)
(^template [<tag>]
(<tag> env quantified)
(<tag> (list/map (replace parameter-idx replacement) env)
(replace (n/+ 2 parameter-idx) replacement quantified)))
([#.UnivQ]
[#.ExQ])
_
type))
(def: (named-type cursor id)
(-> Cursor Nat Type)
(let [name (format "{New Type @ " (.cursor-description cursor) " " (%n id) "}")]
(#.Primitive name (list))))
(def: new-named-type
(Operation Type)
(do ///.monad
[cursor (extension.lift macro.cursor)
[ex-id _] (//type.with-env check.existential)]
(wrap (named-type cursor ex-id))))
## Type-inference works by applying some (potentially quantified) type
## to a sequence of values.
## Function types are used for this, although inference is not always
## done for function application (alternative uses may be records and
## tagged variants).
## But, so long as the type being used for the inference can be treated
## as a function type, this method of inference should work.
(def: #export (general analyse inferT args)
(-> Phase Type (List Code) (Operation [Type (List Analysis)]))
(case args
#.Nil
(do ///.monad
[_ (//type.infer inferT)]
(wrap [inferT (list)]))
(#.Cons argC args')
(case inferT
(#.Named name unnamedT)
(general analyse unnamedT args)
(#.UnivQ _)
(do ///.monad
[[var-id varT] (//type.with-env check.var)]
(general analyse (maybe.assume (type.apply (list varT) inferT)) args))
(#.ExQ _)
(do ///.monad
[[var-id varT] (//type.with-env check.var)
output (general analyse
(maybe.assume (type.apply (list varT) inferT))
args)
bound? (//type.with-env
(check.bound? var-id))
_ (if bound?
(wrap [])
(do @
[newT new-named-type]
(//type.with-env
(check.check varT newT))))]
(wrap output))
(#.Apply inputT transT)
(case (type.apply (list inputT) transT)
(#.Some outputT)
(general analyse outputT args)
#.None
(///.throw invalid-type-application inferT))
## Arguments are inferred back-to-front because, by convention,
## Lux functions take the most important arguments *last*, which
## means that the most information for doing proper inference is
## located in the last arguments to a function call.
## By inferring back-to-front, a lot of type-annotations can be
## avoided in Lux code, since the inference algorithm can piece
## things together more easily.
(#.Function inputT outputT)
(do ///.monad
[[outputT' args'A] (general analyse outputT args')
argA (<| (///.with-stack cannot-infer-argument [inputT argC])
(//type.with-type inputT)
(analyse argC))]
(wrap [outputT' (list& argA args'A)]))
(#.Var infer-id)
(do ///.monad
[?inferT' (//type.with-env (check.read infer-id))]
(case ?inferT'
(#.Some inferT')
(general analyse inferT' args)
_
(///.throw cannot-infer [inferT args])))
_
(///.throw cannot-infer [inferT args]))
))
## Turns a record type into the kind of function type suitable for inference.
(def: #export (record inferT)
(-> Type (Operation Type))
(case inferT
(#.Named name unnamedT)
(record unnamedT)
(^template [<tag>]
(<tag> env bodyT)
(do ///.monad
[bodyT+ (record bodyT)]
(wrap (<tag> env bodyT+))))
([#.UnivQ]
[#.ExQ])
(#.Apply inputT funcT)
(case (type.apply (list inputT) funcT)
(#.Some outputT)
(record outputT)
#.None
(///.throw invalid-type-application inferT))
(#.Product _)
(operation/wrap (type.function (type.flatten-tuple inferT) inferT))
_
(///.throw not-a-record-type inferT)))
## Turns a variant type into the kind of function type suitable for inference.
(def: #export (variant tag expected-size inferT)
(-> Nat Nat Type (Operation Type))
(loop [depth 0
currentT inferT]
(case currentT
(#.Named name unnamedT)
(do ///.monad
[unnamedT+ (recur depth unnamedT)]
(wrap unnamedT+))
(^template [<tag>]
(<tag> env bodyT)
(do ///.monad
[bodyT+ (recur (inc depth) bodyT)]
(wrap (<tag> env bodyT+))))
([#.UnivQ]
[#.ExQ])
(#.Sum _)
(let [cases (type.flatten-variant currentT)
actual-size (list.size cases)
boundary (dec expected-size)]
(cond (or (n/= expected-size actual-size)
(and (n/> expected-size actual-size)
(n/< boundary tag)))
(case (list.nth tag cases)
(#.Some caseT)
(operation/wrap (if (n/= 0 depth)
(type.function (list caseT) currentT)
(let [replace' (replace (|> depth dec (n/* 2)) inferT)]
(type.function (list (replace' caseT))
(replace' currentT)))))
#.None
(///.throw variant-tag-out-of-bounds [expected-size tag inferT]))
(n/< expected-size actual-size)
(///.throw smaller-variant-than-expected [expected-size actual-size])
(n/= boundary tag)
(let [caseT (type.variant (list.drop boundary cases))]
(operation/wrap (if (n/= 0 depth)
(type.function (list caseT) currentT)
(let [replace' (replace (|> depth dec (n/* 2)) inferT)]
(type.function (list (replace' caseT))
(replace' currentT))))))
## else
(///.throw variant-tag-out-of-bounds [expected-size tag inferT])))
(#.Apply inputT funcT)
(case (type.apply (list inputT) funcT)
(#.Some outputT)
(variant tag expected-size outputT)
#.None
(///.throw invalid-type-application inferT))
_
(///.throw not-a-variant-type inferT))))
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