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adeefc1c87
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|---|---|---|---|
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adeefc1c87 | ||
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ac88ca11cf |
1 changed files with 259 additions and 174 deletions
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@ -15,6 +15,8 @@
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#h(10pt)
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#let rf = $\& #h(3pt)$
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#let isCorrect = `isCorrect`
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#let isRead = `isRead`
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@ -25,13 +27,28 @@
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#let isIn = `isIn`
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#let isOut = `isOut`
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#let readTag = `read`
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#let writeTag = `write`
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#let copyTag = `copy`
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#let inTag = `in`
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#let outTag = `out`
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#let mode = `mode`
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#let Copy = `Copy`
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#let Ref = `Ref`
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#let MaybeWrite = [$diamond$ `Write`]
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#let AlwaysWrite = [$square$ `Write`]
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#let Read = `Read`
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#let In = `In`
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#let Out = `Out`
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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 type = `type`
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#let modedType = `modedtype`
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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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@ -54,7 +71,7 @@
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Prod(
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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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Or[$inTag space outTag$][]
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}
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),
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Prod(
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@ -71,33 +88,36 @@
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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[$readTag writeTag ()$][simple type representing all primitive types] // `Unit`
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Or[$rf copyTag space type$][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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Or[$lambda (modedType)+$][type of lambda or function pointer, defined by function declaration] // `Fun`
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}
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),
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Prod(
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`modedtype`,
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{
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Or[$mode type$][type woth in and out modifiers]
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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[$rf expr$][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[`CALL` $path space expr+$][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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@ -109,7 +129,7 @@
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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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Or[$"fun" X ((X : modedType)+) = stmt$][function declaration]
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}
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),
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Prod(
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@ -122,21 +142,19 @@
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== Value Model
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#let rf = $\& #h(3pt)$
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// FIXME: check & add details
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#let deepvalue = `deepvalue`
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#let deepValue = `deepvalue`
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#let value = `value`
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#bnf(
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Prod(
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$deepvalue$,
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$deepValue$,
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{
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Or[$0$][valid value of simple type] // `Unit`
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Or[$\#$][valid or spoiled value of simple type] // `Unit`
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Or[$bot$][spoiled value of simple type] // `Unit`
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Or[$lambda type+ stmt$][function pointer value] // `Fun`
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Or[$rf deepvalue$][reference value, contains label of the value in the memory] // `Ref`
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Or[$[deepvalue+]$][tuple value] // `Prod`
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Or[$rf deepValue$][reference value, contains label of the value in the memory] // `Ref`
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Or[$[deepValue+]$][tuple value] // `Prod`
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}
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),
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Prod(
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@ -146,22 +164,23 @@
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Or[$\#$][valid or spoiled value of simple type] // `Unit`
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Or[$bot$][spoiled value of simple type] // `Unit`
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Or[$lambda type+ stmt$][function pointer value] // `Fun`
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Or[$rf LL$][reference value, contains label of the value in the memory] // `Ref`
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// FIXME: embed mode into value for simplification ??
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Or[$rf copyTag LL$][reference value, contains label of the value in the memory] // `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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#deepvalue - полное значение, #value - слой значения, привязан к конкретной памяти $mu$
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#deepValue - полное значение, #value - слой значения, привязан к конкретной памяти $mu$
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Значения, могут лежать в переменных и передаваться как аргументы функций (то, во что вычисляется $expr$)
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$v in value$ - произвольное значение
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Получение #value по #deepvalue:
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- $rf LL xarrowSquiggly(mu)_#[deep] rf mu[LL]$
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Получение #deepValue по #value:
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- $rf c l xarrowSquiggly(mu)_#[deep] rf c mu[l]$
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- $* xarrowSquiggly(mu)_#[deep] *$
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где $*$ - произвольный конструктор значения кроме $rf$
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где $*$ - произвольный конструктор значения, кроме $rf$
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== Memory Model
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@ -173,17 +192,16 @@ $v in value$ - произвольное значение
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- $LL$ - множество меток памяти
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- $mem := LL -> value, space mu : mem$ - память, частично определённая функция
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- $l in LL$ - новый тег памяти (ранее не использованный)
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- `next` - получение следующей неиспользованной метки
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- `next` - получение следующей неиспользованной метки в памяти
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ add value to memory],
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$l' = #[next] (l)$,
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$l = #[next] (mu)$,
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// TODO: check that access is what required ??
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$cl mu, l cr xarrowSquiggly(v)_#[add] cl mu [l <- v], l' cr$,
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$cl mu cr xarrowSquiggly(v)_#[add] cl l, mu [l <- v] cr$,
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)
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))
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@ -260,7 +278,7 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ access path],
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name: [ tuple access path],
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$x tpath p$,
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@ -273,7 +291,7 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ variable typing],
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name: [ variable type access],
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$x : t_x ttype @x : t_x$,
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)
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@ -281,7 +299,7 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ reference typing],
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name: [ reference type access],
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$x tpath p$,
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$x : t_x ttype p : rf mode t_p$,
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|
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@ -291,7 +309,7 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
|
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name: [ access typing],
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name: [ tuple type access],
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|
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$x tpath p$,
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$x : t_x ttype p : [t_1, ... t_n]$,
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|
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@ -300,34 +318,34 @@ $s in stmt, f in X, x in X, a in X$
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))
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]
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- #[ Получение тега поля
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- #[ Получение read-write тега поля
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ variable typing],
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name: [ variable rw tag access],
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$t_x = rf mode t$,
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$x : t_x tmode @x -> mode$,
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$t_x = r w ()$,
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$x : t_x tmode @x -> cr r w cl$,
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)
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))
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ reference typing],
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name: [ reference rw tag access],
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$x tpath p$,
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$x : t_x tmode p : rf mode t_p$,
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$x : t_x tmode *p : t_p$,
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$x : t_x tmode p -> cr r w cl$,
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$x : t_x tmode *p -> cr r w cl$,
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)
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))
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
|
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name: [ access typing],
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name: [ tuple rw tag access],
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|
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$x tpath p$,
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$x : t_x tmode p : [t_1, ... t_n]$,
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$x : t_x tmode p.i : t_i$,
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$x : t_x tmode p -> cr r w cl$,
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$x : t_x tmode p.i -> cr r w cl$,
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)
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))
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]
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|
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@ -336,7 +354,7 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ variable typing],
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name: [ variable value access],
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$x eqmu v_x tval @x eqmu v_x$,
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)
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|
|
@ -344,7 +362,7 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
|
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name: [ reference typing],
|
||||
name: [ reference value access],
|
||||
|
||||
$x tpath p$,
|
||||
$x eqmu v_x tval p eqmu rf l$,
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|
|
@ -354,7 +372,7 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
|
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vertical-spacing: 4pt,
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rule(
|
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name: [ access typing],
|
||||
name: [ tuple value access],
|
||||
|
||||
$x tpath p$,
|
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$x eqmu v_x tmode p eqmu [v_1, ... v_n]$,
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|
|
@ -367,11 +385,11 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
|
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vertical-spacing: 4pt,
|
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rule(
|
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name: [ variable typing],
|
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name: [ access],
|
||||
|
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$v_x = rf l$,
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$x eqmu v_x tval p eqmu rf l$,
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|
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$x eqmu v_x tmode p arrmu l$,
|
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)
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))
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|
|
@ -381,7 +399,7 @@ $s in stmt, f in X, x in X, a in X$
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#align(center, prooftree(
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vertical-spacing: 4pt,
|
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rule(
|
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name: [ access typing],
|
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name: [ access],
|
||||
|
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$x tpath p$,
|
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$x : sigma[x].2 ttype p : t$,
|
||||
|
|
@ -390,15 +408,15 @@ $s in stmt, f in X, x in X, a in X$
|
|||
))
|
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]
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|
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- #[ Получение тега поля по окружению
|
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- #[ Получение read-write тега поля по окружению
|
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#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ access typing],
|
||||
name: [ access],
|
||||
|
||||
$x tpath p$,
|
||||
$x : sigma[x].2 tmode p -> mode$,
|
||||
$sigma temode p -> mode$,
|
||||
$x : sigma[x].2 tmode p -> cr r space w cl$,
|
||||
$sigma temode p -> cr r space w cl$,
|
||||
)
|
||||
))
|
||||
]
|
||||
|
|
@ -407,7 +425,7 @@ $s in stmt, f in X, x in X, a in X$
|
|||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ access typing],
|
||||
name: [ access],
|
||||
|
||||
$x tpath p$,
|
||||
$x eqmu sigma[x].1 tval p eqmu v$,
|
||||
|
|
@ -420,7 +438,7 @@ $s in stmt, f in X, x in X, a in X$
|
|||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ access typing],
|
||||
name: [ access],
|
||||
|
||||
$x tpath p$,
|
||||
$x eqmu sigma[x].1 tlabel p arrmu l$,
|
||||
|
|
@ -429,34 +447,37 @@ $s in stmt, f in X, x in X, a in X$
|
|||
))
|
||||
]
|
||||
|
||||
=== Mode Correctness
|
||||
=== Mode Accessors
|
||||
|
||||
Функции проверки тегов, имеют тип $mode -> #[bool]$:
|
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#let modevar = $(i space o)$
|
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|
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#let modevar = $(r space w space c space i space o)$
|
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$ isIn modevar = i == In $
|
||||
$ isOut modevar = o == Out $
|
||||
|
||||
$ isRead modevar = r == "Read" $
|
||||
$ isAlwaysWrite modevar = w == square "Write" $
|
||||
$ isPossibleWrite modevar = w == diamond "Write" || w == square "Write" $
|
||||
$ isRef modevar = c == "Ref" $
|
||||
$ isCopy modevar = c == "Copy" $
|
||||
$ isIn modevar = i == "In" $
|
||||
$ isOut modevar = o == "Out" $
|
||||
// FIXME: move to new mode model
|
||||
// === Mode Correctness
|
||||
|
||||
Требования к тегам:
|
||||
// Функции проверки тегов, имеют тип $mode -> #[bool]$:
|
||||
|
||||
$ isOut mode -> isAlwaysWrite mode $
|
||||
$ isRead mode -> isIn mode $
|
||||
// #let modevar = $(r space w space c space i space o)$
|
||||
|
||||
// $ isRead modevar = r == "Read" $
|
||||
// $ isAlwaysWrite modevar = w == square "Write" $
|
||||
// $ isPossibleWrite modevar = w == diamond "Write" || w == square "Write" $
|
||||
// $ isRef modevar = c == "Ref" $
|
||||
// $ isCopy modevar = c == "Copy" $
|
||||
// $ isIn modevar = i == "In" $
|
||||
// $ isOut modevar = o == "Out" $
|
||||
|
||||
// Требования к тегам:
|
||||
|
||||
// $ isOut mode -> isAlwaysWrite mode $
|
||||
// $ isRead mode -> isIn mode $
|
||||
|
||||
// TODO: rest conditions ??
|
||||
|
||||
=== Eval Rules
|
||||
|
||||
// FIXME: make connected to syntax
|
||||
*TODO*
|
||||
|
||||
#h(10pt)
|
||||
|
||||
#let args = `args`
|
||||
|
||||
#[
|
||||
|
|
@ -481,124 +502,170 @@ $ isRead mode -> isIn mode $
|
|||
|
||||
// TODO: introduce spep env argument ??
|
||||
|
||||
#h(10pt)
|
||||
=== Moded Type Correctness
|
||||
|
||||
=== Correctness
|
||||
#let tcorrect = $attach(tack.r, br: #[correct])$
|
||||
|
||||
// TODO: FIXME: well formatness for mode, extract
|
||||
// TODO: FIXME: check for mode, is recursion required ??
|
||||
// TODO: FIXME: check mode & access corectness in os correct
|
||||
|
||||
// TODO: check all requirements
|
||||
$ sigma in env, space mu in mem, space m in mode,
|
||||
space c in copyTag, space r, r' in readTag, space w, w' in writeTag,
|
||||
space v in value, space t, t' in type $
|
||||
|
||||
#h(10pt)
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ is correct],
|
||||
$isOut mode -> isAlwaysWrite mode$, // NOTE; strong requirment should write
|
||||
$isRead mode -> isIn mode$,
|
||||
$isPossibleWrite mode and (isOut mode or not isCopy mode) -> isAlwaysWrite pathenvmode(sigma, x)$, // NOTE: may mode => should sigma(x)
|
||||
$isRead mode -> pathenvval(mu, sigma, x) != bot and pathenvval(mu, sigma, x) != X$,
|
||||
name: [ unit assignment tags correctness],
|
||||
|
||||
$isCorrect_(cl sigma, mu cr) (mode, x)$,
|
||||
$r = Read => isIn m$,
|
||||
$isOut m => w = AlwaysWrite$,
|
||||
// $sigma temode x -> cr r' space w' cl$, // NOTE: not required, value passed
|
||||
$(w = AlwaysWrite or w = MaybeWrite) and (isOut m or c = Ref) => w' = AlwaysWrite$,
|
||||
|
||||
// $sigma, mu teval x eqmu v$, // NOTE: not required, value passed
|
||||
$v in {0, \#, bot}$,
|
||||
$r = Read => v = 0$,
|
||||
|
||||
$sigma, mu, m, c tcorrect v : r' space w' () -> r space w ()$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
=== Call Initialization
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ ref assignment tags correctness],
|
||||
|
||||
Отсутствующий нижний индекс ($ref$, $copy$) означает произвольный индекс.
|
||||
Считается, что выбранный индекс одинаков в рамках одного правила.
|
||||
$sigma, mu, m, c_r tcorrect v : t -> t'$,
|
||||
|
||||
// NOTE: no empty type
|
||||
// #align(center, prooftree(
|
||||
// vertical-spacing: 4pt,
|
||||
// rule(
|
||||
// name: [ add paths init],
|
||||
// TODO: FIXME: which tag translations are correct ?? <- only assignee?
|
||||
$sigma, mu, m, c tcorrect rf c_r space v : rf c' space t -> rf c_r space t'$,
|
||||
)
|
||||
))
|
||||
|
||||
// $cl sigma, mu, l cr stretch(~>)^nothing cl sigma, mu, l cr$,
|
||||
// )
|
||||
// ))
|
||||
|
||||
// #h(10pt)
|
||||
#h(10pt)
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ add paths field by copy],
|
||||
name: [ tuple assignmenttags correctness],
|
||||
|
||||
$sigma, mu, m, c tcorrect v_1 : t_1 -> t'_1$,
|
||||
|
||||
$...$,
|
||||
|
||||
$sigma, mu, m, c tcorrect v_n : t_n -> t'_n$,
|
||||
|
||||
$sigma, mu, m, c tcorrect [v_1, ... v_n] : [t_1, ..., t_n] -> [t'_1, t'_n]$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ function pointer tags correctness],
|
||||
|
||||
$sigma, mu, m, c tcorrect lambda space overline(t) space s : lambda space overline(t) -> lambda space overline(t)$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
=== Value Construction
|
||||
|
||||
#let new = `new`
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ new $0$ value],
|
||||
|
||||
// TODO: check that access is what required ??
|
||||
$cl sigma, mu, l cr xarrowSquiggly(p : ())_copy cl pathenvmem(sigma, p) <- l, mu [l <- 0], l + 1 cr$,
|
||||
$cl 0, mu cr xarrowSquiggly(space)_new cl 0, mu cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
// NOTE: do nothing, ref init by default
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ add paths field by reference],
|
||||
|
||||
$cl sigma, mu, l cr xarrowSquiggly(p : ())_ref cl sigma, mu, l cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ add paths ref],
|
||||
$cl sigma, mu, l cr xarrowSquiggly(*p : t)_ref cl sigma', mu', l' cr$,
|
||||
$isRef mode$,
|
||||
name: [ new $\#$ value],
|
||||
|
||||
$cl sigma, mu, l cr xarrowSquiggly(p : \& mode t) cl sigma', mu', l' cr$,
|
||||
// TODO: check that access is what required ??
|
||||
$cl \#, mu cr xarrowSquiggly(space)_new cl \#, mu cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ add paths ref],
|
||||
$cl sigma, mu, l cr xarrowSquiggly(*p : t)_copy cl sigma, mu, l cr$,
|
||||
$isCopy mode$,
|
||||
name: [ new $bot$ value],
|
||||
|
||||
$cl sigma, mu, l cr xarrowSquiggly(p : \& mode t) cl sigma', mu', l' cr$,
|
||||
$cl bot, mu cr xarrowSquiggly(space)_new cl bot, mu cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ add paths tuple],
|
||||
$cl sigma, mu, l cr xarrowSquiggly(p.1 : t_1) cl sigma_1, mu_1, l_1 cr$,
|
||||
name: [ new funciton pointer value],
|
||||
|
||||
$cl lambda overline(t) s, mu cr xarrowSquiggly(space)_new cl lambda overline(t) s, mu cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ new reference ref value],
|
||||
|
||||
$cl rf Ref l, mu cr xarrowSquiggly(space)_new cl rf Ref l, mu cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ new reference copy value],
|
||||
|
||||
$cl mu[l], mu cr xarrowSquiggly(space)_new cl v, mu_v cr$,
|
||||
|
||||
$cl mu_v cr xarrowSquiggly(v)_#[add] cl l', mu_a cr$,
|
||||
|
||||
$cl rf Copy l, mu cr xarrowSquiggly(space)_new cl rf Copy l', mu_a cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ new tuple value],
|
||||
|
||||
$cl v_1, mu_0 cr xarrowSquiggly(space)_new cl lambda v'_1, mu_1 cr$,
|
||||
$...$,
|
||||
$cl sigma_(n - 1), mu_(n - 1), l_(n - 1) cr xarrowSquiggly(p.n : t_n) cl sigma_n, mu_n, l_n cr$,
|
||||
$cl v_n, mu_(n - 1) cr xarrowSquiggly(space)_new cl lambda v'_n, mu_n cr$,
|
||||
|
||||
$cl sigma, mu, l cr xarrowSquiggly(p : [t_1, ... t_n]) cl sigma_n, mu_n, l_n cr$,
|
||||
$cl [v_1, ... v_n], mu_0 cr xarrowSquiggly(space)_new cl [v'_1, ... v'_n], mu_n cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
=== Value Update
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ add paths funciton pointer],
|
||||
#let write = `write`
|
||||
|
||||
$cl sigma, mu, l cr xarrowSquiggly(F_x) cl sigma, mu, l cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
*TODO: write to value*
|
||||
|
||||
=== Call Finalization
|
||||
|
||||
// FIXME: make connected to syntax
|
||||
*TODO*
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
|
|
@ -670,6 +737,9 @@ $ isRead mode -> isIn mode $
|
|||
|
||||
=== Function Evaluation
|
||||
|
||||
// FIXME: make connected to syntax
|
||||
*TODO*
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
|
|
@ -719,22 +789,22 @@ $ isRead mode -> isIn mode $
|
|||
|
||||
=== Statement Evaluation
|
||||
|
||||
// FIXME: make connected to syntax
|
||||
*TODO: check type of lambda?, args from type?*
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ CALL $f space overline(x)$],
|
||||
name: [ CALL $f space overline(p)$],
|
||||
|
||||
$cl [], mu, l cr
|
||||
xarrowDashed(d space @ space overline(x))
|
||||
xarrowDashed(f space @ space overline(p))
|
||||
cl sigma', mu', l' cr$,
|
||||
|
||||
// TODO: FIXME define args in some way
|
||||
$mu attach(stretch(=>)^args_sigma, tr: *) gamma$,
|
||||
|
||||
$DD(f) := d$,
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("CALL" f space overline(x))
|
||||
xarrow("CALL" f space overline(p))
|
||||
cl sigma, gamma, l cr$,
|
||||
)
|
||||
))
|
||||
|
|
@ -744,32 +814,12 @@ $ isRead mode -> isIn mode $
|
|||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ CALL_LAM $y space overline(x)$],
|
||||
name: [ READ $p$],
|
||||
|
||||
$pathenvtype(sigma, y) = F_f$,
|
||||
$mu, sigma teval p eqmu 0$,
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("CALL" f space overline(x))
|
||||
cl sigma, gamma, l cr$,
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("CALL_LAM" y space overline(x))
|
||||
cl sigma, gamma, l cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ READ $x$],
|
||||
|
||||
$pathenvval(mu, sigma, x) != bot$,
|
||||
$pathenvval(mu, sigma, x) != X$,
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("READ" x)
|
||||
xarrow("READ" p)
|
||||
cl sigma, mu, l cr$,
|
||||
)
|
||||
))
|
||||
|
|
@ -781,11 +831,38 @@ $ isRead mode -> isIn mode $
|
|||
rule(
|
||||
name: [ WRITE $x$],
|
||||
|
||||
$isPossibleWrite sigma(x)$,
|
||||
$sigma temode p -> cr r space w cl$,
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("WRITE" x)
|
||||
cl sigma, pathenvval(mu, sigma, x) <- 0, l cr$,
|
||||
$w == MaybeWrite or w == AlwaysWrite$,
|
||||
|
||||
$x tpath p$,
|
||||
|
||||
$mu[x] xarrowSquiggly(p)_write v$,
|
||||
|
||||
$cl sigma, mu cr
|
||||
xarrow("WRITE" p)
|
||||
cl sigma, mu[x <- v] cr$,
|
||||
)
|
||||
))
|
||||
|
||||
#h(10pt)
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ $s \; t$],
|
||||
|
||||
$cl sigma, mu cr
|
||||
stretch(->)^s
|
||||
cl sigma_s, mu_s cr$,
|
||||
|
||||
$cl sigma, mu cr
|
||||
stretch(->)^t
|
||||
cl sigma_t, mu_t cr$,
|
||||
|
||||
$cl sigma, mu, cr
|
||||
xarrow(s \; t)
|
||||
cl sigma_t, mu_t cr$,
|
||||
)
|
||||
))
|
||||
|
||||
|
|
@ -793,26 +870,27 @@ $ isRead mode -> isIn mode $
|
|||
|
||||
#let combine = `combine`
|
||||
|
||||
*TODO: combine replacement* // FIXME
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
name: [ CHOICE $overline(s)$ $overline(t)$],
|
||||
name: [ $s | t$],
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
attach(stretch(->)^overline(s), tr: *)
|
||||
stretch(->)^s
|
||||
cl sigma_s, mu_s, l_s cr$,
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
attach(stretch(->)^overline(t), tr: *)
|
||||
stretch(->)^t
|
||||
cl sigma_t, mu_t, l_t cr$,
|
||||
|
||||
$l_t = l_s$,
|
||||
$sigma_s = sigma_t$,
|
||||
$mu' = combine(mu_s, mu_t)$,
|
||||
|
||||
// TODO changes ?? two ways ??
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("CHOICE" overline(s) space overline(t))
|
||||
cl sigma, combine(mu_s, mu_t), l cr$,
|
||||
$cl sigma, mu cr
|
||||
xarrow(s | t)
|
||||
cl sigma_t, mu' cr$,
|
||||
)
|
||||
))
|
||||
|
||||
|
|
@ -820,9 +898,16 @@ $ isRead mode -> isIn mode $
|
|||
|
||||
=== Combination
|
||||
|
||||
*TODO: rewrite as rules, fix* // FIXME
|
||||
|
||||
$ combine(mu_1, mu_2)[i] = combine_e (mu_1[i], mu_2[i]) $
|
||||
$ combine_e (bot, bot) = bot $
|
||||
$ combine_e (0, 0) = 0 $
|
||||
$ combine_e (\_, \_) = X $
|
||||
$ combine_e (\_, \_) = \# $
|
||||
// FIXME: ref to combined memory
|
||||
$ combine_e (rf c l_1, rf c' l_2) | c == c' = rf c combine_e(mu_1[l_1], mu_2[l_2])$
|
||||
$ combine_e (v^1_1, ... v^1_n, v^2_1 ... v^2_n) = [combine_e(v^1_1, v^2_1), ..., combine_e(v^1_n, v^2_n)]$
|
||||
$ combine_e (lambda space overline(t_1) space s_1, lambda space overline(t_2) space s_2) | overline(t_1) == overline(t_2) = lambda space overline(t_1) space s_1 $
|
||||
// TODO: FIXME: statemient in lambda is not important ??
|
||||
|
||||
]
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue