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model with structures: init from control flow model, model formal difinition draft part
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457
model_with_structures/model.typ
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457
model_with_structures/model.typ
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// #import "@preview/polylux:0.4.0": *
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#import "@preview/simplebnf:0.1.1": *
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// #import "@preview/zebraw:0.5.0": *
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// #show: zebraw
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#import "@preview/curryst:0.6.0": rule, prooftree, rule-set
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#import "@preview/xarrow:0.4.0": xarrow, xarrowDashed
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= Формальная модель используемого языка
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*TODO: проверить, что всё нужное добавлено*
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*TODO: добавить сложные структуры (типы) и работу с ними*
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*TODO: добавить тип лямбд (тип с id сигнатуры)*
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*TODO: добавить тип вызова поля структуры*
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*TODO: добавить правльную работу со вложенными тегами, path-доступ к полям переменных, корректность пути*
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Нужно будет добавить во write-flag модальности: `not write` | `may write` | `always write`
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Добавление condition-исполнения - выбор из нескольких блоков. Варианты:
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- & of | of & -вложенные блоки ?
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- добавить несколько альтернативны тел функциям. Но тогда придётся при трансляции if-блоки выносить в функции
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Лямбды - нужно тоже будет как-то находить лямбды и ля них тоже синтезировать атрибуты
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вызов лямбд будет нужен в модели?
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- lambda-аргумент - вложенные теги?, должна быть одна и та же сигнтура
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можно ввести отдельные сигнатуры-определения?
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проблема простой семантики: вызов лямбд: могут быть модифицируемые функции
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== Синтаксис
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#h(10pt)
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#let isCorrect = `isCorrect`
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#let isRead = `isRead`
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#let isAlwaysWrite = `isAlwaysWrite`
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#let isPossibleWrite = `isPossibleWrite`
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#let isRef = `isRef`
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#let isCopy = `isCopy`
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#let isIn = `isIn`
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#let isOut = `isOut`
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#let tag = `tag`
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#let value = `value`
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#let stmt = `stmt`
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#let decl = `decl`
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#let prog = `prog`
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#let path = `path`
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#let argtype = `argtype`
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#let argmem = `argmem`
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#bnf(
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Prod(`read`,
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{ Or[Read][read passed value]
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Or[Not Read][] } ),
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Prod(`write`,
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{ Or[$square$ Write][in all cases there is a write to passed variable] // always write, requre at least one write in each flow variant
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Or[$diamond$ Write][in some cases there is a write to passed variable] // possible write, no requirements (?)
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Or[$not$ Write][] } ), // no write, require n owrites in all flow variants
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Prod(`copy`,
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{ Or[Ref][pass reference to the value]
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Or[Value][pass copy of the value] } ),
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Prod(`in`,
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{ Or[In][parameter value used as input]
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Or[Not In][] } ),
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Prod(`out`,
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{ Or[Out][parametr value returned]
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Or[Not Out][] } ),
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Prod(
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`tag`,
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{
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Or[`read` #h(3pt) `write` #h(3pt) `copy` #h(3pt) `in` #h(3pt) `out`][]
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}
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),
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Prod(
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`value`,
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{
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Or[$0$][cell with some value (always)]
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Or[$X$][cell with possible value or $bot$]
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Or[$bot$][spoiled cell (always)]
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}
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),
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Prod(
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`path`,
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{
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Or[$x$][fuction argument or variable itself]
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Or[$path . n$][access $n$-th cell of the tuple]
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Or[$path : n$][access $n$-th cell of the union] // TODO: another notation ??
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}
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),
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Prod(
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`argtype`,
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{
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Or[$()$][simple type representing all primitive types] // `Unit`
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Or[\& #h(3pt) `tag` #h(3pt) `argtype`][reference to structure, contains copy / ref choice] // `Ref`
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Or[`argtype` $times$ `argtype`][pair type, allows to make tuples] // `Prod`
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// Or[`argtype` $+$ `argtype`][union type (important in some way ???)] // `Sum` // TODO ?
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Or[$F_x$][type of lambda or function pointer, defined by function declaration id] // `Fun`
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}
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),
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Prod(
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`argmem`,
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{
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Or[$[m]$][memory id for simple type variable] // `Unit`
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Or[\& #h(3pt) `tag` #h(3pt) `argmem`][reference to structure, contains copy / ref choice] // `Ref`
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Or[`argmem` $times$ `argmem`][pair type, allows specify memory for tuples] // `Prod`
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// Or[`argmem` $+$ `argmem`][union type (important in some way ???)] // `Sum` // TODO ?
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Or[$F_m$][memory for lambda or function pointer, defined by function declaration id] // `Fun` // why separated ??
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}
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),
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// Prod(
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// `arg`,
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// {
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// Or[$0$][new value, no associated variable]
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// Or[$ amp d$][value from some variable]
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// }
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// ),
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Prod(
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`stmt`,
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{
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Or[`CALL` $f space overline(path)$][call function by id]
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Or[`CALL_LAM` $path space overline(path)$][call lambda funciton (variable or funcitona argument field)]
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Or[`WRITE` $path$][write to variable]
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Or[`READ` $path$][read from variable]
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// TODO: or introduce block statement ?? // vars definiiton statment ??
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// (for example, for same named vars in nested spaces)
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Or[`CHOICE` #overline(`stmt`) #overline(`stmt`)][control flow operator, xecution of one of the blocks]
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// NOTE: var: replaced with arguments (use rvalue as init) (?)
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// Or[`VAR`][variables inside functions] // NOTE: no modifiers required, because it is in the new memory ?? // TODO: not required ??
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// NOTE: lambda: compile to call to the funciton with CHOICE between possible lambda bodies <- do this analysis inside synthesizer ?
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}
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),
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Prod(
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`decl`,
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{
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Or[$overline(stmt)$][function body]
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Or[$lambda #[`argtype`] a.$ `decl`][argument with argument pass strategy annotation]
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}
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),
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Prod(
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`prog`,
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{
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Or[`decl`][main function]
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Or[`decl` `prog`][with supplimentary funcitons]
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}
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),
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)
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== Семантика статического интерпретатора
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#h(10pt)
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$V := value$ - значения памяти
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$L := NN$ - позиции в памяти
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$X$ - можество переменных
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*TODO: специфицировать доступ*
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*TODO: формально описать accessor-ы tag*
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$sigma : X -> argmem$ - #[ позиции памяти, соответстующие переменным контекста,
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частично определённая функция ]
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$mu : NN -> V$ - память, частично определённая функция
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$l in NN$ - длина используемого фрагмента памяти
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$DD : NN -> decl$ - определения функций, частично определённая функция
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$d in decl, s in stmt, f in NN, x in X, a in NN$
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$d space @ space overline(x)$ - запись применения функции (вида #decl) к аргументам
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#let args = `args`
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#[
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#let ref = `ref`
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#let copy = `copy`
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#let read = `read`
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#let cl = $chevron.l$
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#let cr = $chevron.r$
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// #align(center, grid(
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// columns: 3,
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// gutter: 5%,
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// align(bottom, prooftree(
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// ...
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// )),
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// align(bottom, prooftree(
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// ...
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// )),
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// align(bottom, prooftree(
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// ...
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// )),
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// ))
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// TODO: introduce spep env argument ??
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// TODO: FIXME: define typeof operation
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#let typeof = `typeof`
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// TODO: FIXME: define access operation
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// TODO: two versions: write with change & read
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#let access = `access`
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// TODO: FIXME: define argtag operation
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#let argtag = `argtag`
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// TODO: FIXME: define addpaths operation: ~>
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// FIXME
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ is correct],
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$isOut tag -> isAlwaysWrite tag$, // NOTE; strong requirment should write
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$isRead tag -> isIn tag$,
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$isPossibleWrite tag and (isOut tag or not isCopy tag) -> isAlwaysWrite argtag(sigma, x)$, // NOTE: may tag => should sigma(x)
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$isRead tag -> access(mu, sigma, x) != bot and access(mu, sigma, x) != X$,
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$isCorrect_(cl sigma, mu cr) (tag, x)$,
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ spoil init],
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$mu stretch(=>)^nothing_(cl sigma, mu cr) mu$,
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ spoil step],
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$mu stretch(=>)^args_sigma gamma$,
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$isPossibleWrite tag$, // NOTE: weak requirement: may write
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$not isCopy tag$,
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$not isOut tag$,
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$isCorrect_(cl sigma, mu cr) (tag, x)$,
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// gamma - memory (as mu)
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$gamma stretch(=>)^((tag, x) : args)_sigma access(gamma, sigma, x) <- bot]$
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ fix step],
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$mu stretch(=>)^args_sigma gamma$,
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$isAlwaysWrite tag$, // NOTE: strong requirement: should write
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$isOut tag$,
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$isCorrect_(cl sigma, mu cr) (tag, x)$,
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// gamma - memory (as mu)
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$gamma stretch(=>)^((tag, x) : args)_sigma access(gamma, sigma, x) <- 0]$
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ skip step],
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$mu stretch(=>)^args_sigma gamma$,
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$not "spoil step"$,
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$not "fix step"$,
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$isCorrect_(cl sigma, mu cr) (tag, x)$,
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// mu
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$gamma stretch(=>)^((tag, x) : args)_sigma gamma$
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)
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))
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#h(10pt)
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#align(center, line())
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#h(10pt)
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// TODO: special operation to add all paths one by one ??
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ $(lambda a. d) x$],
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$cl sigma, mu, l cr
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stretch(~>)^a
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cl sigma, mu', l' cr$,
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$cl sigma', mu', l' cr
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xarrowDashed(d space @ space overline(y))
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cl sigma'', mu'', l'' cr$,
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$isRead tag$,
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$not isCopy tag$,
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// NOTE: correctness checked in CALL f
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$cl sigma, mu, l cr
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xarrowDashed((lambda a. d) space @ space x space overline(y))
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cl sigma'', mu'', l'' cr$,
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [decl body],
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$cl sigma, mu, l cr
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attach(stretch(->)^overline(s), tr: *)
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cl sigma', mu', l' cr$,
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$d = overline(s)$,
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$cl sigma, mu, l cr
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xarrowDashed(d space @)
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cl sigma', mu', l' cr$,
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)
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))
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#h(10pt)
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#align(center, line())
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ CALL $f space overline(x)$],
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$cl [], mu, l cr
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xarrowDashed(d space @ space overline(x))
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cl sigma', mu', l' cr$,
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// TODO: FIXME define args in some way
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$mu attach(stretch(=>)^args_sigma, tr: *) gamma$,
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$DD(f) := d$,
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$cl sigma, mu, l cr
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xarrow("CALL" f space overline(x))
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cl sigma, gamma, l cr$,
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ CALL_LAM $y space overline(x)$],
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$typeof(y) = F_f$,
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$cl sigma, mu, l cr
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xarrow("CALL" f space overline(x))
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cl sigma, gamma, l cr$,
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$cl sigma, mu, l cr
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xarrow("CALL_LAM" y space overline(x))
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cl sigma, gamma, l cr$,
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ READ $x$],
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$access(mu, sigma, x) != bot$,
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$access(mu, sigma, x) != X$,
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$cl sigma, mu, l cr
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xarrow("READ" x)
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cl sigma, mu, l cr$,
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ WRITE $x$],
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$isPossibleWrite sigma(x)$, // TODO: FIXME ?? always or possible ??
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$cl sigma, mu, l cr
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xarrow("WRITE" x)
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cl sigma, access(mu, sigma, x) <- 0, l cr$,
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)
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))
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#h(10pt)
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#let combine = `combine`
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ CHOICE $overline(s)$ $overline(t)$],
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$cl sigma, mu, l cr
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attach(stretch(->)^overline(s), tr: *)
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cl sigma_s, mu_s, l_s cr$,
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|
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$cl sigma, mu, l cr
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attach(stretch(->)^overline(t), tr: *)
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cl sigma_t, mu_t, l_t cr$,
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$l_t = l_s$,
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$sigma_s = sigma_t$,
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// TODO changes ?? two ways ??
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$cl sigma, mu, l cr
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xarrow("CHOICE" overline(s) space overline(t))
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cl sigma, combine(mu_s, mu_t), l cr$,
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)
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))
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#h(10pt)
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$ combine(mu_1, mu_2)[i] = combine_e (mu_1[i], mu_2[i]) $
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$ combine_e (bot, bot) = bot $
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$ combine_e (0, 0) = 0 $
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$ combine_e (\_, \_) = X $
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|
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]
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