mirror of
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synced 2026-04-27 00:34:50 +00:00
structures: part of eval rules
This commit is contained in:
ProgramSnail
parent
ac88ca11cf
commit
adeefc1c87
1 changed files with 213 additions and 116 deletions
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@ -27,13 +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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@ -56,7 +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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@ -73,15 +88,21 @@
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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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Prod(
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@ -96,7 +117,7 @@
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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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@ -108,7 +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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@ -121,20 +142,19 @@
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== Value Model
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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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#let copy = `copy`
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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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@ -145,20 +165,20 @@
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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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// FIXME: embed mode into value for simplification ??
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Or[$rf copy LL$][reference value, contains label of the value in the memory] // `Ref`
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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 #deepvalue по #value:
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- $rf copy LL xarrowSquiggly(mu)_#[deep] rf copy mu[LL]$
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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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@ -258,7 +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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@ -271,7 +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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@ -279,7 +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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@ -289,7 +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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$x tpath p$,
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$x : t_x ttype p : [t_1, ... t_n]$,
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@ -298,34 +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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$x tpath p$,
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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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@ -334,7 +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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@ -342,7 +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],
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name: [ reference value access],
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$x tpath p$,
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$x eqmu v_x tval p eqmu rf l$,
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@ -352,7 +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],
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name: [ tuple value access],
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$x tpath p$,
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$x eqmu v_x tmode p eqmu [v_1, ... v_n]$,
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@ -365,11 +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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$x eqmu v_x tmode p arrmu l$,
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)
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))
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@ -379,7 +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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$x : sigma[x].2 ttype p : t$,
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@ -388,15 +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(
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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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$x : sigma[x].2 tmode p -> mode$,
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$sigma temode p -> mode$,
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$x : sigma[x].2 tmode p -> cr r space w cl$,
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$sigma temode p -> cr r space w cl$,
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)
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))
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]
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@ -405,7 +425,7 @@ $s in stmt, f in X, x in X, a in X$
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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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$x eqmu sigma[x].1 tval p eqmu v$,
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@ -418,7 +438,7 @@ $s in stmt, f in X, x in X, a in X$
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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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$x eqmu sigma[x].1 tlabel p arrmu l$,
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@ -427,34 +447,37 @@ $s in stmt, f in X, x in X, a in X$
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))
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]
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=== Mode Correctness
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=== Mode Accessors
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Функции проверки тегов, имеют тип $mode -> #[bool]$:
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#let modevar = $(i space o)$
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#let modevar = $(r space w space c space i space o)$
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$ isIn modevar = i == In $
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$ isOut modevar = o == Out $
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$ isRead modevar = r == "Read" $
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$ isAlwaysWrite modevar = w == square "Write" $
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$ isPossibleWrite modevar = w == diamond "Write" || w == square "Write" $
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$ isRef modevar = c == "Ref" $
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$ isCopy modevar = c == "Copy" $
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$ isIn modevar = i == "In" $
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$ isOut modevar = o == "Out" $
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// FIXME: move to new mode model
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// === Mode Correctness
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Требования к тегам:
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// Функции проверки тегов, имеют тип $mode -> #[bool]$:
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$ isOut mode -> isAlwaysWrite mode $
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$ isRead mode -> isIn mode $
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// #let modevar = $(r space w space c space i space o)$
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// $ isRead modevar = r == "Read" $
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// $ isAlwaysWrite modevar = w == square "Write" $
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// $ isPossibleWrite modevar = w == diamond "Write" || w == square "Write" $
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// $ isRef modevar = c == "Ref" $
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// $ isCopy modevar = c == "Copy" $
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// $ isIn modevar = i == "In" $
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// $ isOut modevar = o == "Out" $
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// Требования к тегам:
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// $ isOut mode -> isAlwaysWrite mode $
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// $ isRead mode -> isIn mode $
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// TODO: rest conditions ??
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=== Eval Rules
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// FIXME: make connected to syntax
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*TODO*
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#h(10pt)
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#let args = `args`
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#[
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@ -479,28 +502,77 @@ $ isRead mode -> isIn mode $
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// TODO: introduce spep env argument ??
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#h(10pt)
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=== Moded Type Correctness
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=== Correctness
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*TODO*
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#let tcorrect = $attach(tack.r, br: #[correct])$
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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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$ sigma in env, space mu in mem, space m in mode,
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space c in copyTag, space r, r' in readTag, space w, w' in writeTag,
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space v in value, space t, t' in type $
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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: [ is correct],
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// NOTE: moved to general mode requirements
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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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$isPossibleWrite mode and (isOut mode or not isCopy mode) -> isAlwaysWrite pathenvmode(sigma, x)$, // NOTE: may mode => should sigma(x)
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$isRead mode -> pathenvval(mu, sigma, x) != bot and pathenvval(mu, sigma, x) != X$,
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name: [ unit assignment tags correctness],
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$isCorrect_(cl sigma, mu cr) (mode, x)$,
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$r = Read => isIn m$,
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$isOut m => w = AlwaysWrite$,
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// $sigma temode x -> cr r' space w' cl$, // NOTE: not required, value passed
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$(w = AlwaysWrite or w = MaybeWrite) and (isOut m or c = Ref) => w' = AlwaysWrite$,
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// $sigma, mu teval x eqmu v$, // NOTE: not required, value passed
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$v in {0, \#, bot}$,
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$r = Read => v = 0$,
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$sigma, mu, m, c tcorrect v : r' space w' () -> r space w ()$,
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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: [ ref assignment tags correctness],
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$sigma, mu, m, c_r tcorrect v : t -> t'$,
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// TODO: FIXME: which tag translations are correct ?? <- only assignee?
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$sigma, mu, m, c tcorrect rf c_r space v : rf c' space t -> rf c_r space t'$,
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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: [ tuple assignmenttags correctness],
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$sigma, mu, m, c tcorrect v_1 : t_1 -> t'_1$,
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$...$,
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$sigma, mu, m, c tcorrect v_n : t_n -> t'_n$,
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$sigma, mu, m, c tcorrect [v_1, ... v_n] : [t_1, ..., t_n] -> [t'_1, t'_n]$,
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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: [ function pointer tags correctness],
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$sigma, mu, m, c tcorrect lambda space overline(t) space s : lambda space overline(t) -> lambda space overline(t)$,
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)
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))
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|
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@ -509,8 +581,6 @@ $ isRead mode -> isIn mode $
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=== Value Construction
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#let new = `new`
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#let Copy = `Copy`
|
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#let Ref = `Ref`
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
|
|
@ -555,7 +625,7 @@ $ isRead mode -> isIn mode $
|
|||
rule(
|
||||
name: [ new reference ref value],
|
||||
|
||||
$cl rf Ref space l, mu cr xarrowSquiggly(space)_new cl rf Ref space l, mu cr$,
|
||||
$cl rf Ref l, mu cr xarrowSquiggly(space)_new cl rf Ref l, mu cr$,
|
||||
)
|
||||
))
|
||||
|
||||
|
|
@ -568,7 +638,7 @@ $ isRead mode -> isIn mode $
|
|||
|
||||
$cl mu_v cr xarrowSquiggly(v)_#[add] cl l', mu_a cr$,
|
||||
|
||||
$cl rf Copy space l, mu cr xarrowSquiggly(space)_new cl rf copy space l', mu_a cr$,
|
||||
$cl rf Copy l, mu cr xarrowSquiggly(space)_new cl rf Copy l', mu_a cr$,
|
||||
)
|
||||
))
|
||||
|
||||
|
|
@ -585,8 +655,17 @@ $ isRead mode -> isIn mode $
|
|||
)
|
||||
))
|
||||
|
||||
=== Value Update
|
||||
|
||||
#let write = `write`
|
||||
|
||||
*TODO: write to value*
|
||||
|
||||
=== Call Finalization
|
||||
|
||||
// FIXME: make connected to syntax
|
||||
*TODO*
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
|
|
@ -658,6 +737,9 @@ $ isRead mode -> isIn mode $
|
|||
|
||||
=== Function Evaluation
|
||||
|
||||
// FIXME: make connected to syntax
|
||||
*TODO*
|
||||
|
||||
#align(center, prooftree(
|
||||
vertical-spacing: 4pt,
|
||||
rule(
|
||||
|
|
@ -707,22 +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
|
||||
$mu attach(stretch(=>)^args_sigma, tr: *) gamma$,
|
||||
|
||||
$DD(f) := d$,
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("CALL" f space overline(x))
|
||||
xarrow("CALL" f space overline(p))
|
||||
cl sigma, gamma, l cr$,
|
||||
)
|
||||
))
|
||||
|
|
@ -732,32 +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 $x$],
|
||||
|
||||
$pathenvval(mu, sigma, x) != bot$,
|
||||
$pathenvval(mu, sigma, x) != X$,
|
||||
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("READ" x)
|
||||
xarrow("READ" p)
|
||||
cl sigma, mu, l cr$,
|
||||
)
|
||||
))
|
||||
|
|
@ -769,11 +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: [ $s \; t$],
|
||||
|
||||
$cl sigma, mu cr
|
||||
stretch(->)^s
|
||||
cl sigma_s, mu_s cr$,
|
||||
|
||||
$cl sigma, mu cr
|
||||
stretch(->)^t
|
||||
cl sigma_t, mu_t cr$,
|
||||
|
||||
$cl sigma, mu, cr
|
||||
xarrow(s \; t)
|
||||
cl sigma_t, mu_t cr$,
|
||||
)
|
||||
))
|
||||
|
||||
|
|
@ -781,26 +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 ??
|
||||
$cl sigma, mu, l cr
|
||||
xarrow("CHOICE" overline(s) space overline(t))
|
||||
cl sigma, combine(mu_s, mu_t), l cr$,
|
||||
$cl sigma, mu cr
|
||||
xarrow(s | t)
|
||||
cl sigma_t, mu' cr$,
|
||||
)
|
||||
))
|
||||
|
||||
|
|
@ -808,9 +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