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structs model: syntax, start of the value & memory models
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ProgramSnail
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1 changed files with 151 additions and 115 deletions
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@ -11,20 +11,7 @@
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// TODO: check correctnes for path, mem & type ??
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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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== Syntax
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#h(10pt)
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@ -38,18 +25,19 @@
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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 mode = `mode`
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#let expr = `expr`
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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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#let type = `type`
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#bnf(
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Prod(`read`,
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// NOTE: not three modalities for write, because read does not change value
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// => it is not important to observe rsult, no differenc between always and maybe
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{ Or[Read][read passed value]
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Or[Not Read][] } ),
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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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@ -59,114 +47,157 @@
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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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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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{ Or[Out][parameter value returned]
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Or[$not$ Out][] } ),
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Prod(
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`tag`,
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`mode`,
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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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`path`,
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{
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// NOTE: global vars & local vars names could be used with one constructor
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// Or[$\#x$][funciton or global variable itself]
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Or[$@ X$][function argument or variable itself]
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Or[$* path$][reference insede path]
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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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`type`,
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{
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Or[$()$][simple type representing all primitive types] // `Unit`
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Or[\& #h(3pt) `mode` #h(3pt) `type`][reference to structure, contains copy / ref choice] // `Ref`
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Or[$\[type+\]$][tuple type] // `Prod`
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// Or[`type` $times$ `type`][pair type, allows to make tuples] // `Prod`
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// Or[`type` $+$ `type`][union type (important in some way ???)] // `Sum` // TODO ?
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// NOTE: do not use names in type
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// Or[$lambda_((x type)+)$][type of lambda or function pointer, defined by function declaration] // `Fun`
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Or[$lambda_(type+)$][type of lambda or function pointer, defined by function declaration] // `Fun`
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}
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),
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// FIXME: replace with expr
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Prod(
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`expr`,
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{
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Or[$()$][value of simple type] // `Unit`
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Or[$path$][value from variable] // `Path`
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Or[$\& #h(3pt) expr$][reference expr] // `Ref`
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Or[\[$expr+$\]][tuple expr] // `Prod`
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// NOTE: replaced with simple path value
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// Or[$lambda_path$][function value from variable] // `Fun`
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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` $f space expr+$][call function]
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Or[`WRITE` $path$][write to variable]
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Or[`READ` $path$][read from variable]
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Or[$stmt ; stmt$][control flow operator, xecution ]
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Or[$stmt | stmt$][control flow operator, excution of one statements]
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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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// TODO: path not allowed ??
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Or[$"var" X : type = expr$][global variable declaration]
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Or[$"fun" X ((X : type)+) = stmt$][function declaration]
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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[$decl stmt$][declarations and executet statement]
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}
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),
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)
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== Value Model
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// FIXME: check & add details
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#let value = `value`
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#bnf(
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Prod(
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`value`,
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{
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Or[$()$][value of simple type] // `Unit`
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Or[$@ X$][function pointer value] // `Fun`
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Or[$\& #h(3pt) value$][reference value] // `Ref`
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Or[\[$value+$\]][tuple value] // `Prod`
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}
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),
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)
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$value$ - значения, которые могут лежать в переменных на семантическом уровне (то, во что вычисляется $expr$)
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== Memory Model
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// FIXME: check & add details
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#let memvalue = `memvalue`
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#let argmem = `argmem`
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#bnf(
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Prod(
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`memvalue`,
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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[$* path$][reference insede path]
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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[\[#overline(`argtype`)\]][pair type, allows to make tuples] // `Prod`
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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) `argmem`][reference to structure, contains copy / ref choice] // `Ref`
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// Or[\& #h(3pt) `tag` #h(3pt) `argmem`][reference to structure, contains copy / ref choice] // `Ref`
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Or[\[#overline(`argmem`)\]][pair type, allows specify memory for tuples] // `Prod`
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// Or[\& #h(3pt) `mode` #h(3pt) `argmem`][reference to structure, contains copy / ref choice] // `Ref`
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Or[$\[argmem+\]$][pair type, allows specify memory for tuples] // `Prod`
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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[$F$][memory for lambda or function pointer, defined by function declaration id] // `Fun` // why separated ??
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Or[$lambda$][memory for lambda or function pointer, defined by function declaration id] // `Fun` // why separated ??
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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[$lambda a : argtype.$ `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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== Semantics
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// FIXME: make connected to syntax
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*TODO*
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#h(10pt)
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$V := value$ - значения памяти
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$V := memvalue$ - значения памяти
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$L := NN$ - позиции в памяти
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// FIXME: not required, remove
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// $L := NN$ - позиции в памяти
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$X$ - можество переменных
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$sigma : X -> argmem times argtype$ - #[ позиции памяти, соответстующие переменным контекста,
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$LL$ - множество меток памяти
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_пока решил использовать всё-таки $NN$ для того, чтобы работать с размером памяти
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и добавлением ячеек, может стоит поменять_
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$FF$ -множество меток функций
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$sigma : X -> argmem times type$ - #[ 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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$DD : FF -> decl$ - 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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$d in decl, s in stmt, f in FF, x in X, a in X$
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$d space @ space overline(x)$ - запись применения функции (вида #decl) к аргументам
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@ -201,9 +232,10 @@ $d space @ space overline(x)$ - запись применения функции
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=== Path
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// FIXME: types & description for functios
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#let pathtype = `pathtype`
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$ pathtype(t, @x) = t $
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$ pathtype(\& #h(3pt) tag #h(3pt) t, *p) = pathtype(t, p) $
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$ pathtype(\& #h(3pt) mode #h(3pt) t, *p) = pathtype(t, p) $
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$ pathtype([t_1, t_2, ..., t_n], p.i) = pathtype(t_i, p) $
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#let pathmem = `pathmem`
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@ -218,8 +250,8 @@ $ pathmem([m_1, m_2, ..., m_n], p.i) = pathmem(m_i, p) $
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// $ pathfun([m_1, m_2, ..., m_n], p.i) = pathfun(m_i, p) $
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#let pathtag = `pathtag`
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$ pathtag(\& #h(3pt) tag #h(3pt) t, @x) = tag $
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$ pathtag(\& #h(3pt) tag #h(3pt) t, *p) = pathtag(t, p) $
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$ pathtag(\& #h(3pt) mode #h(3pt) t, @x) = mode $
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$ pathtag(\& #h(3pt) mode #h(3pt) t, *p) = pathtag(t, p) $
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$ pathtag([t_1, t_2, ..., t_n], p.i) = pathtag(t_i, p) $
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#let pathvar = `pathvar`
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@ -248,17 +280,21 @@ $ access(sigma, mu, p) = mu[accessmem(sigma, p)] $
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=== Correctness
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// TODO: FIXME: well formatness for mode, extract
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// TODO: FIXME: check for mode, is recursion required ??
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// TODO: FIXME: check mode & access corectness in os correct
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// TODO: check all requirements
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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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$isOut mode -> isAlwaysWrite mode$, // NOTE; strong requirment should write
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$isRead mode -> isIn mode$,
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$isPossibleWrite mode and (isOut mode or not isCopy mode) -> isAlwaysWrite argtag(sigma, x)$, // NOTE: may mode => should sigma(x)
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$isRead mode -> access(mu, sigma, x) != bot and access(mu, sigma, x) != X$,
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$isCorrect_(cl sigma, mu cr) (tag, x)$,
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$isCorrect_(cl sigma, mu cr) (mode, x)$,
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)
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))
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@ -266,10 +302,10 @@ $ access(sigma, mu, p) = mu[accessmem(sigma, p)] $
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=== Call Initialization
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Отсутствующий ижний индекс ($ref$, $copy$) означает произвольный индекс.
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Отсутствующий нижний индекс ($ref$, $copy$) означает произвольный индекс.
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Считается, что выбранный индекс одинаков в рамках одного правила.
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// NOTE: no empty argtype
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// NOTE: no empty type
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// #align(center, prooftree(
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// vertical-spacing: 4pt,
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// rule(
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@ -310,9 +346,9 @@ $ access(sigma, mu, p) = mu[accessmem(sigma, p)] $
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rule(
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name: [ add paths ref],
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$cl sigma, mu, l cr xarrowSquiggly(*p : t)_ref cl sigma', mu', l' cr$,
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$isRef tag$,
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$isRef mode$,
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$cl sigma, mu, l cr xarrowSquiggly(p : \& tag t) cl sigma', mu', l' cr$,
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$cl sigma, mu, l cr xarrowSquiggly(p : \& mode t) cl sigma', mu', l' cr$,
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)
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))
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@ -323,9 +359,9 @@ $ access(sigma, mu, p) = mu[accessmem(sigma, p)] $
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rule(
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name: [ add paths ref],
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$cl sigma, mu, l cr xarrowSquiggly(*p : t)_copy cl sigma, mu, l cr$,
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$isCopy tag$,
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$isCopy mode$,
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$cl sigma, mu, l cr xarrowSquiggly(p : \& tag t) cl sigma', mu', l' cr$,
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$cl sigma, mu, l cr xarrowSquiggly(p : \& mode t) cl sigma', mu', l' cr$,
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)
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))
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@ -375,14 +411,14 @@ $ access(sigma, mu, p) = mu[accessmem(sigma, p)] $
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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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$isPossibleWrite mode$, // NOTE: weak requirement: may write
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$not isCopy mode$,
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$not isOut mode$,
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$isCorrect_(cl sigma, mu cr) (tag, x)$,
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$isCorrect_(cl sigma, mu cr) (mode, x)$,
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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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$gamma stretch(=>)^((mode, x) : args)_sigma access(gamma, sigma, x) <- bot]$
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)
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))
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@ -395,13 +431,13 @@ $ access(sigma, mu, p) = mu[accessmem(sigma, p)] $
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|
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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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$isAlwaysWrite mode$, // NOTE: strong requirement: should write
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$isOut mode$,
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$isCorrect_(cl sigma, mu cr) (tag, x)$,
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$isCorrect_(cl sigma, mu cr) (mode, x)$,
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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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$gamma stretch(=>)^((mode, x) : args)_sigma access(gamma, sigma, x) <- 0]$
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)
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))
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@ -417,10 +453,10 @@ $ access(sigma, mu, p) = mu[accessmem(sigma, p)] $
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$not "spoil step"$,
|
||||
$not "fix step"$,
|
||||
|
||||
$isCorrect_(cl sigma, mu cr) (tag, x)$,
|
||||
$isCorrect_(cl sigma, mu cr) (mode, x)$,
|
||||
|
||||
// mu
|
||||
$gamma stretch(=>)^((tag, x) : args)_sigma gamma$
|
||||
$gamma stretch(=>)^((mode, x) : args)_sigma gamma$
|
||||
)
|
||||
))
|
||||
|
||||
|
|
@ -444,8 +480,8 @@ $ access(sigma, mu, p) = mu[accessmem(sigma, p)] $
|
|||
xarrowDashed(d space @ space overline(y))
|
||||
cl sigma'', mu'', l'' cr$,
|
||||
|
||||
$isRead tag$,
|
||||
$not isCopy tag$,
|
||||
$isRead mode$,
|
||||
$not isCopy mode$,
|
||||
|
||||
// NOTE: correctness checked in CALL f
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue