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|
(;module: {#;doc "Algebraic effects."}
lux
(lux (control ["F" functor]
applicative
["M" monad #*])
[io #- run]
(data (coll [list "List/" Monad<List> Monoid<List>])
[number "Nat/" Codec<Text,Nat>]
text/format
[ident "Ident/" Eq<Ident>]
[text])
[macro]
(macro [code]
["s" syntax #+ syntax: Syntax]
(syntax ["cs" common]
(common ["csr" reader]
["csw" writer])))
[type]))
## [Type]
(sig: #export (Handler E M)
{#;doc "A way to interpret effects into arbitrary monads."}
(: (Monad M)
monad)
(: (All [a] (-> (E a) (M a)))
handle))
## [Values]
(type: #hidden (|@ L R)
(All [a] (| (L a) (R a))))
(def: #hidden (combine-functors left right)
(All [L R]
(-> (F;Functor L) (F;Functor R)
(F;Functor (|@ L R))))
(struct
(def: (map f l|r)
(case l|r
(+0 l) (+0 (:: left map f l))
(+1 r) (+1 (:: right map f r)))
)))
(def: #hidden (combine-handlers Monad<M> left right)
(All [L R M]
(-> (Monad M)
(Handler L M) (Handler R M)
(Handler (|@ L R) M)))
(struct
(def: monad Monad<M>)
(def: (handle l|r)
(case l|r
(#;Left l) (:: left handle l)
(#;Right r) (:: right handle r)
))))
## [Syntax]
(syntax: #export (|E [effects (s;many s;any)])
{#;doc (doc "A way to combine smaller effect into a larger effect."
(type: EffABC (|E EffA EffB EffC)))}
(wrap (list (` ($_ ;;|@ (~@ effects))))))
(syntax: #export (|F [functors (s;many s;any)])
{#;doc (doc "A way to combine smaller effect functors into a larger functor."
(def: Functor<EffABC>
(Functor EffABC)
(|F Functor<EffA> Functor<EffB> Functor<EffC>)))}
(wrap (list (` ($_ ;;combine-functors (~@ functors))))))
(syntax: #export (|H monad [handlers (s;many s;any)])
{#;doc (doc "A way to combine smaller effect handlers into a larger handler."
(def: Handler<EffABC,IO>
(Handler EffABC io;IO)
(|H io;Monad<IO>
Handler<EffA,IO> Handler<EffB,IO> Handler<EffC,IO>)))}
(do @
[g!combiner (macro;gensym "")]
(wrap (list (` (let [(~ g!combiner) (;;combine-handlers (~ monad))]
($_ (~ g!combiner) (~@ handlers))))))))
(type: Op
{#name Text
#inputs (List Code)
#output Code})
(def: op^
(Syntax Op)
(s;form (s;either ($_ s;seq
s;local-symbol
(s;tuple (s;some s;any))
s;any)
($_ s;seq
s;local-symbol
(:: s;Monad<Syntax> wrap (list))
s;any))))
(syntax: #export (effect: [exp-lvl csr;export]
[name s;local-symbol]
[ops (s;many op^)])
{#;doc (doc "Define effects by specifying which operations and constants a handler must provide."
(effect: #export EffA
(opA [Nat Text] Bool)
(fieldA Nat))
"In this case, 'opA' will be a function (-> Nat Text Bool)."
"'fieldA' will be a value provided by a handler.")}
(do @
[g!output (macro;gensym "g!output")
#let [op-types (List/map (function [op]
(let [g!tag (code;tag ["" (get@ #name op)])
g!inputs (` [(~@ (get@ #inputs op))])
g!output (` (-> (~ (get@ #output op)) (~ g!output)))]
(` ((~ g!tag) (~ g!inputs) (~ g!output)))))
ops)
type-name (code;symbol ["" name])
type-def (` (type: (~@ (csw;export exp-lvl))
((~ type-name) (~ g!output))
(~@ op-types)))
op-tags (List/map (|>. (get@ #name) [""] code;tag (list) code;tuple)
ops)
functor-def (` (struct: (~@ (csw;export exp-lvl)) (~' _) (F;Functor (~ type-name))
(def: ((~' map) (~' f) (~' fa))
(case (~' fa)
(^template [(~' <tag>)]
((~' <tag>) (~' params) (~' cont))
((~' <tag>) (~' params) (. (~' f) (~' cont))))
((~@ op-tags))))
))
function-defs (List/map (function [op]
(let [g!name (code;symbol ["" (get@ #name op)])
g!tag (code;tag ["" (get@ #name op)])
g!params (: (List Code)
(case (list;size (get@ #inputs op))
+0 (list)
s (|> (list;n.range +0 (n.dec s))
(List/map (|>. Nat/encode
(format "_")
[""]
code;symbol)))))]
(` (def: (~@ (csw;export exp-lvl)) ((~ g!name) (~@ g!params))
(-> (~@ (get@ #inputs op))
((~ type-name) (~ (get@ #output op))))
((~ g!tag) [(~@ g!params)] ;id)))))
ops)]]
(wrap (list& type-def
functor-def
function-defs))))
(type: Translation
{#effect Ident
#target-type Code
#target-monad Code})
(def: translation^
(Syntax Translation)
(s;form (do s;Monad<Syntax>
[_ (s;this (' =>))]
(s;seq s;symbol
(s;tuple (s;seq s;any
s;any))))))
(syntax: #export (handler: [exp-lvl csr;export]
[name s;local-symbol]
[[effect target-type target-monad] translation^]
[defs (s;many (csr;definition *compiler*))])
{#;doc (doc "Define effect handlers by implementing the operations and values of an effect."
(handler: _
(=> EffA [IO Monad<IO>])
(def: (opA length sample)
(:: Monad<IO> wrap (n.< length
(size sample))))
(def: fieldA (:: Monad<IO> wrap +10)))
"Since a name for the handler was not specified, 'handler:' will generate the name as Handler<EffA,IO>.")}
(do @
[(^@ effect [e-module _]) (macro;un-alias effect)
g!input (macro;gensym "g!input")
g!cont (macro;gensym "g!cont")
g!value (macro;gensym "value")
g!wrap (macro;gensym "wrap")
#let [g!cases (|> defs
(List/map (function [def]
(let [g!tag (code;tag [e-module (get@ #cs;definition-name def)])
g!args (List/map (|>. [""] code;symbol)
(get@ #cs;definition-args def))
eff-calc (case (get@ #cs;definition-type def)
#;None
(get@ #cs;definition-value def)
(#;Some type)
(` (: (~ type) (~ (get@ #cs;definition-value def)))))
invocation (case g!args
#;Nil
eff-calc
_
(` ((~ eff-calc) (~@ g!args))))]
(list (` ((~ g!tag) [(~@ g!args)] (~ g!cont)))
(` (do (~ target-monad)
[(~' #let) [(~ g!wrap) (~' wrap)]
(~ g!value) (~ invocation)]
((~ g!wrap) ((~ g!cont) (~ g!value)))))
))))
List/join)]]
(wrap (list (` (struct: (~@ (csw;export exp-lvl)) (~ (code;symbol ["" name]))
(;;Handler (~ (code;symbol effect)) (~ target-type))
(def: (~' monad) (~ target-monad))
(def: ((~' handle) (~ g!input))
(case (~ g!input)
(~@ g!cases))
)))))))
(def: #export (with-handler handler body)
{#;doc "Handles an effectful computation with the given handler to produce a monadic value."}
(All [E M a] (-> (Handler E M) (Free E a) (M a)))
(case body
(#M;Pure value)
(:: handler wrap value)
(#M;Effect effect)
(do (get@ #monad handler)
[result (:: handler handle effect)]
(with-handler handler result))
))
(def: (un-apply type-app)
(-> Type Type)
(case type-app
(#;App effect value)
effect
_
(error! (format "Wrong type format: " (%type type-app)))))
(def: (clean-effect effect)
(-> Type Type)
(case effect
(#;UnivQ env body)
(#;UnivQ (list) body)
_
(error! (format "Wrong effect format: " (%type effect)))))
(def: g!functor Code (code;symbol ["" "\t@E\t"]))
(syntax: #export (doE functor [bindings (s;tuple (s;some s;any))] body)
{#;doc (doc "An alternative to the 'do' macro for monads."
(with-handler Handler<EffABC,IO>
(doE Functor<EffABC>
[a (lift fieldA)
b (lift fieldB)
c (lift fieldC)]
(wrap ($_ n.+ a b c)))))}
(do @
[g!output (macro;gensym "")]
(wrap (list (` (let [(~ g!functor) (~ functor)]
(do (Monad<Free> (~ g!functor))
[(~@ bindings)
(~ g!output) (~ body)]
(#M;Pure (~ g!output)))))))))
(def: (flatten-effect-stack stack)
(-> Type (List Type))
(case stack
(#;Sum left right)
(List/append (flatten-effect-stack left)
(flatten-effect-stack right))
(^ (#;App branches (#;Var _)))
(flatten-effect-stack branches)
(^ (#;App (#;App (#;Named (ident-for ;;|@) _)
left)
right))
(#;Cons left (flatten-effect-stack right))
(^ (#;App (#;App (#;Named (ident-for M;Free) _)
effect)
param))
(list effect)
_
(list stack)
))
(def: (same-effect? expected actual)
(case [expected actual]
[(#;Named e-name _) (#;Named a-name _)]
(Ident/= e-name a-name)
_
false))
(def: (nest-effect idx total base)
(-> Nat Nat Code Code)
(cond (n.= +0 idx)
(` (+0 (~ base)))
(n.> +2 total)
(` (+1 (~ (nest-effect (n.dec idx) (n.dec total) base))))
## else
(` (+1 (~ base)))
))
(syntax: #export (lift [value (s;alt s;symbol
s;any)])
{#;doc (doc "A way to (automatically) lift effectful fields and operations from simple effects into the larger space of composite effects."
(with-handler Handler<EffABC,IO>
(doE Functor<EffABC>
[a (lift fieldA)
b (lift fieldB)
c (lift fieldC)]
(wrap ($_ n.+ a b c)))))}
(case value
(#;Left var)
(do @
[input (macro;find-type var)
output macro;expected-type]
(case [input output]
(^multi [(#;App eff0 _) (#;App stackT0 recT0)]
[(type;apply-type stackT0 recT0) (#;Some unfoldT0)]
[stackT0 (^ (#;App (#;Named (ident-for M;Free) _)
stackT1))]
[(type;apply-type stackT1 recT0) (#;Some unfoldT1)]
[(flatten-effect-stack unfoldT1) stack]
[(|> stack list;enumerate
(list;find (function [[idx effect]]
(same-effect? effect eff0))))
(#;Some [idx _])])
(wrap (list (` (#M;Effect (:: (~ g!functor) (~' map) (~' wrap)
(~ (nest-effect idx (list;size stack) (code;symbol var))))))))
_
(macro;fail (format "Invalid type to lift: " (%type output)))))
(#;Right node)
(do @
[g!value (macro;gensym "")]
(wrap (list (` (let [(~ g!value) (~ node)]
(;;lift (~ g!value)))))))))
|
