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structures: partial statement eval
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ProgramSnail
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1 changed files with 79 additions and 63 deletions
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@ -118,7 +118,7 @@
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Prod(
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`stmt`,
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{
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Or[`CALL` $path space expr+$][call function]
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Or[`CALL` $path expr+$][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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@ -153,7 +153,7 @@
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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[$lambda$][function pointer value] // `Fun`
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Or[$lambda overline(x) space stmt$][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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}
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@ -164,7 +164,7 @@
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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[$lambda$][function pointer value] // `Fun`
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Or[$lambda overline(x) space stmt$][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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Or[$[value+]$][tuple value] // `Prod`
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}
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@ -204,17 +204,12 @@ $v in value$ - произвольное значение
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== Semantics
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// TODO: FIXME: add vars & funcs from global context in the beginnning
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// $V := memelem$ - значения памяти
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$X$ - можество переменных
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// FIXME: TMP
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#let valuemem = `valuemem`
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#let memelem = `memelem`
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#let pathenvmode = `pathenvmode`
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#let pathenvval = `pathenvval`
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#let pathenvmem = `pathenvmem`
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#let pathenvtype = `pathenvtype`
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#let vals = $Sigma$
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#let types = $Gamma$
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@ -734,7 +729,7 @@ $ vals in envv, types in envt, space mu in mem, space m in mode,
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rule(
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name: [ combine tuple values],
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$mu'_0 = nothing$,
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$mu'_0 = []$,
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// NOTE: same labels required
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$mu_1 = {l_1 -> v^1_1, ... l_n -> v^1_n}$,
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$mu_2 = {l_1 -> v^2_1, ... l_n -> v^2_n}$,
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@ -754,16 +749,6 @@ $ vals in envv, types in envt, space mu in mem, space m in mode,
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// FIXME: make connected to syntax
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*TODO*
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ spoil init],
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$mu stretch(=>)^nothing_(cl sigma, mu cr) mu$,
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)
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))
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#h(10pt)
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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@ -778,7 +763,7 @@ $ vals in envv, types in envt, space mu in mem, space m in mode,
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$isCorrect_(cl sigma, mu cr) (mode, x)$,
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// gamma - memory (as mu)
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$gamma stretch(=>)^((mode, x) : args)_sigma pathenvval(gamma, sigma, x) <- bot]$
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$gamma stretch(=>)^((mode, x) : args)_sigma "pathenvval"(gamma, sigma, x) <- bot]$
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)
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))
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@ -794,10 +779,12 @@ $ vals in envv, types in envt, space mu in mem, space m in mode,
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$isAlwaysWrite mode$, // NOTE: strong requirement: should write
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$mode = (\_, not Out)$,
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// NOTE: correctness looks like this
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// $types, vals, mu, m, c tcorrect v : cl r', w' cr -> cl r, w cr$,
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$isCorrect_(cl sigma, mu cr) (mode, x)$,
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// gamma - memory (as mu)
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$gamma stretch(=>)^((mode, x) : args)_sigma pathenvval(gamma, sigma, x) <- 0]$
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$gamma stretch(=>)^((mode, x) : args)_sigma "pathenvval"(gamma, sigma, x) <- 0]$
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)
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))
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@ -823,52 +810,55 @@ $ vals in envv, types in envt, space mu in mem, space m in mode,
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#h(10pt)
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=== Expression Evaluation
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*TODO*
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=== Expresion Typing
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*TODO*
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=== Function Evaluation
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// FIXME: make connected to syntax
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*TODO*
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ $(lambda a : t. d) m$],
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// #align(center, prooftree(
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// vertical-spacing: 4pt,
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// rule(
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// name: [ $(lambda a : t. d) m$],
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// TODO: verify that type of m is t ??
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// // TODO: verify that type of m is t ??
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$cl sigma [a <- (m, t)], mu, l cr
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xarrowSquiggly(t)
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cl sigma', mu', l' cr$,
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// $cl sigma [a <- (m, t)], mu, l cr
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// xarrowSquiggly(t)
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// cl sigma', mu', l' cr$,
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$cl sigma', mu', l' cr
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xarrowDashed(d space @ space overline(y))
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cl sigma'', mu'', l'' cr$,
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// $cl sigma', mu', l' cr
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// xarrowDashed(d space @ space overline(y))
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// cl sigma'', mu'', l'' cr$,
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$isRead mode$,
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$not isCopy mode$,
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// $isRead mode$,
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// $not isCopy mode$,
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// NOTE: correctness checked in CALL f
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// // NOTE: correctness checked in CALL f
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$cl sigma, mu, l cr
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xarrowDashed((lambda a. d) space @ space x space overline(y))
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cl sigma'', mu'', l'' cr$,
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)
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))
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// $cl sigma, mu, l cr
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// xarrowDashed()
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// cl sigma'', mu'', l'' cr$,
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// )
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// ))
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#h(10pt)
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// TODO: FIXME: arrow to eval expr to value ??
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// TODO: fixme
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [decl body],
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name: [ add argument],
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$cl sigma, mu, l cr
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attach(stretch(->)^overline(s), tr: *)
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cl sigma', mu', l' cr$,
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$d = overline(s)$,
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$cl sigma, mu, l cr
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xarrowDashed(d space @)
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xarrowDashed(x space m space t space p)
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cl sigma', mu', l' cr$,
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)
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))
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@ -877,23 +867,48 @@ $ vals in envv, types in envt, space mu in mem, space m in mode,
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=== Statement Evaluation
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// FIXME: make connected to syntax
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*TODO: check type of lambda?, args from type?*
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ CALL $f space overline(p)$],
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$cl [], mu, l cr
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xarrowDashed(f space @ space overline(p))
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cl sigma', mu', l' cr$,
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// TODO: FIXME: take corresponding statement & var names
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// use eval ??
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[*TODO: statement (from value?) + x'es \<\- expr eval ? *],
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// TODO: FIXME define args in some way
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$mu attach(stretch(=>)^args_sigma, tr: *) gamma$,
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$types ttype f : lambda args $,
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$args = [m_1 t_1, ... m_n t_n]$,
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$overline(p) = [p_1, ... p_n]$,
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$overline(x) = [x_1, ... x_n]$,
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$cl sigma, mu, l cr
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// TODO: add args before statement eval
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$types_0 = []$,
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$vals_0 = []$,
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$mu_0 = mu$,
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// NOTE: dashed arrow to fill context
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$cl types_0, vals_0, mu_0, l cr
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xarrowDashed(x_1 space m_1 space t_1 space p_1)
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cl types', vals_1, mu_1, l' cr$,
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$...$,
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$cl types_(n - 1), vals_(n - 1), mu_(n - 1), l cr
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xarrowDashed(x_n space m_n space t_n space p_n)
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cl types', vals_n, mu_n, l' cr$,
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$cl types_n, vals_n, mu_n, l cr
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xarrow(s)
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cl types', vals', mu', l' cr$,
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// NOTE: thick arrow to "spoil" context
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$gamma_0 = mu$,
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$gamma_0 stretch(=>)^(x_1 space m_1 space t_1)_(cl vals, types cr) gamma_1$,
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$...$,
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$gamma_(n - 1) stretch(=>)^(x_n space m_n space t_n)_(cl vals, types cr) gamma_n$,
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$cl vals, types, mu, l cr
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xarrow("CALL" f space overline(p))
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cl sigma, gamma, l cr$,
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cl vals, types, gamma_n, l cr$,
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)
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))
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@ -917,16 +932,17 @@ $ vals in envv, types in envt, space mu in mem, space m in mode,
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#align(center, prooftree(
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vertical-spacing: 4pt,
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rule(
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name: [ WRITE $x$],
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name: [ WRITE $p$],
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$types ttype p : cl r, w cr$,
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$w = MaybeWrite or w = AlwaysWrite$,
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$p arrpath x$,
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$mu[x] xarrowSquiggly(p)_modify v'$,
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$l = vals(x)$,
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$mu[l] xarrowSquiggly(cl p \, 0 cr)_modify v'$,
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$cl types, vals, mu cr
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xarrow("WRITE" p)
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cl types, vals, mu[x <- v'] cr$,
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cl types, vals, mu[l <- v'] cr$,
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)
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))
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