From 6a8b9142573c9ad00e2b31332470660d1fd69c68 Mon Sep 17 00:00:00 2001 From: Andreas Rossberg Date: Wed, 15 Mar 2017 18:40:52 +0100 Subject: [PATCH 01/15] [document] Specify validation --- document/Makefile | 1 + document/macros.rst | 26 +- document/modules/code-section.rst | 10 - document/modules/custom-section.rst | 10 - document/modules/data-section.rst | 11 - document/modules/element-section.rst | 10 - document/modules/export-section.rst | 10 - document/modules/function-section.rst | 10 - document/modules/global-section.rst | 10 - document/modules/import-section.rst | 10 - document/modules/index.rst | 23 - document/modules/instantiation.rst | 10 - document/modules/invocation.rst | 10 - document/modules/memory-section.rst | 10 - document/modules/overview.rst | 24 - document/modules/start-section.rst | 10 - document/modules/summary-execution.rst | 27 - document/modules/table-section.rst | 10 - document/modules/type-section.rst | 10 - document/syntax/conventions.rst | 2 + document/syntax/instructions.rst | 10 +- document/syntax/modules.rst | 23 +- document/syntax/types.rst | 35 +- document/syntax/values.rst | 16 +- document/validation/conventions.rst | 177 +++++++ document/validation/index.rst | 2 +- document/validation/instructions.rst | 708 +++++++++++++++++++++++++ document/validation/modules.rst | 647 ++++++++++++++++++++++ 28 files changed, 1612 insertions(+), 250 deletions(-) delete mode 100644 document/modules/code-section.rst delete mode 100644 document/modules/custom-section.rst delete mode 100644 document/modules/data-section.rst delete mode 100644 document/modules/element-section.rst delete mode 100644 document/modules/export-section.rst delete mode 100644 document/modules/function-section.rst delete mode 100644 document/modules/global-section.rst delete mode 100644 document/modules/import-section.rst delete mode 100644 document/modules/index.rst delete mode 100644 document/modules/instantiation.rst delete mode 100644 document/modules/invocation.rst delete mode 100644 document/modules/memory-section.rst delete mode 100644 document/modules/overview.rst delete mode 100644 document/modules/start-section.rst delete mode 100644 document/modules/summary-execution.rst delete mode 100644 document/modules/table-section.rst delete mode 100644 document/modules/type-section.rst create mode 100644 document/validation/conventions.rst create mode 100644 document/validation/instructions.rst create mode 100644 document/validation/modules.rst diff --git a/document/Makefile b/document/Makefile index 8a3c4d3c04..5df0df135e 100644 --- a/document/Makefile +++ b/document/Makefile @@ -94,6 +94,7 @@ html: sed s:BASEDIR:..:g <$$file >$$file.out; \ sed 's;MathJax.Hub.Config({TeX: {MAXBUFFER: 10*1024}})$$file; \ + rm -f $$file.out; \ done @echo @echo "Build finished. The HTML pages are in `pwd`/$(BUILDDIR)/html." diff --git a/document/macros.rst b/document/macros.rst index 9a7825a55d..08927faf0c 100644 --- a/document/macros.rst +++ b/document/macros.rst @@ -4,9 +4,9 @@ .. Type-setting of names -.. X - (multi-letter) variables (non-terminals) +.. X - (multi-letter) variables / non-terminals .. F - functions (meta-level) -.. K - keywords (terminals) +.. K - keywords / terminals .. |X| mathmacro:: \mathit .. |F| mathmacro:: \mathrm @@ -81,7 +81,7 @@ .. |memtype| mathmacro:: \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} .. |externtype| mathmacro:: \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} .. |limits| mathmacro:: \href{../syntax/types.html#syntax-limits}{\mathit{limits}} -.. |mut| mathmacro:: \href{../syntax/types.html#syntax-mut}{\mathit{mutability}} +.. |mut| mathmacro:: \href{../syntax/types.html#syntax-mut}{\mathit{mut}} .. Indices @@ -143,8 +143,17 @@ .. |export| mathmacro:: \href{../syntax/modules.html#syntax-export}{\mathit{export}} .. |importdesc| mathmacro:: \href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}} .. |exportdesc| mathmacro:: \href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}} -.. |elemseg| mathmacro:: \href{../syntax/modules.html#syntax-elemseg}{\mathit{elemseg}} -.. |dataseg| mathmacro:: \href{../syntax/modules.html#syntax-dataseg}{\mathit{dataseg}} +.. |elem| mathmacro:: \href{../syntax/modules.html#syntax-elemseg}{\mathit{elem}} +.. |data| mathmacro:: \href{../syntax/modules.html#syntax-dataseg}{\mathit{data}} +.. |start| mathmacro:: \href{../syntax/modules.html#syntax-start}{\mathit{start}} + + +.. Modules, meta functions + +.. |funcs| mathmacro:: \href{../syntax/types.html#syntax-externtype}{\mathrm{funcs}} +.. |tables| mathmacro:: \href{../syntax/types.html#syntax-externtype}{\mathrm{tables}} +.. |mems| mathmacro:: \href{../syntax/types.html#syntax-externtype}{\mathrm{mems}} +.. |globals| mathmacro:: \href{../syntax/types.html#syntax-externtype}{\mathrm{globals}} .. Instructions, terminals @@ -181,7 +190,14 @@ .. Instructions, non-terminals +.. |unop| mathmacro:: \mathit{unop} +.. |binop| mathmacro:: \mathit{binop} +.. |testop| mathmacro:: \mathit{testop} +.. |relop| mathmacro:: \mathit{relop} +.. |cvtop| mathmacro:: \mathit{cvtop} + .. |sx| mathmacro:: \href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} .. |memarg| mathmacro:: \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} + .. |instr| mathmacro:: \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} .. |expr| mathmacro:: \href{../syntax/modules.html#syntax-expr}{\mathit{expr}} diff --git a/document/modules/code-section.rst b/document/modules/code-section.rst deleted file mode 100644 index f5dbcf05f6..0000000000 --- a/document/modules/code-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Code Section ------------- - -.. index:: - pair: code; section - single: modules; code section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/custom-section.rst b/document/modules/custom-section.rst deleted file mode 100644 index afab01b947..0000000000 --- a/document/modules/custom-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Custom Section --------------- - -.. index:: - pair: custom; section - single: modules; custom section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/data-section.rst b/document/modules/data-section.rst deleted file mode 100644 index 5c53ac2811..0000000000 --- a/document/modules/data-section.rst +++ /dev/null @@ -1,11 +0,0 @@ -Data Section ------------- - -.. index:: - pair: data; section - single: modules; data section - -.. todo:: - - Describe - \ No newline at end of file diff --git a/document/modules/element-section.rst b/document/modules/element-section.rst deleted file mode 100644 index bc4cc95f18..0000000000 --- a/document/modules/element-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Element Section ---------------- - -.. index:: - pair: element; section - single: modules; element section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/export-section.rst b/document/modules/export-section.rst deleted file mode 100644 index ffb454fbbc..0000000000 --- a/document/modules/export-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Export Section --------------- - -.. index:: - pair: export; section - single: modules; export section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/function-section.rst b/document/modules/function-section.rst deleted file mode 100644 index 89639369ff..0000000000 --- a/document/modules/function-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Function Section ----------------- - -.. index:: - pair: function; section - single: modules; function section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/global-section.rst b/document/modules/global-section.rst deleted file mode 100644 index ff981a1616..0000000000 --- a/document/modules/global-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Global Section --------------- - -.. index:: - pair: global; section - single: modules; global section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/import-section.rst b/document/modules/import-section.rst deleted file mode 100644 index 758eaec9ca..0000000000 --- a/document/modules/import-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Import Section --------------- - -.. index:: - pair: import; section - single: modules; import section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/index.rst b/document/modules/index.rst deleted file mode 100644 index da864ca296..0000000000 --- a/document/modules/index.rst +++ /dev/null @@ -1,23 +0,0 @@ -Modules -======= - -.. index:: !modules - -.. toctree:: - :maxdepth: 2 - - overview - type-section - import-section - function-section - table-section - memory-section - global-section - export-section - start-section - element-section - code-section - data-section - custom-section - instantiation - invocation diff --git a/document/modules/instantiation.rst b/document/modules/instantiation.rst deleted file mode 100644 index bc59891d64..0000000000 --- a/document/modules/instantiation.rst +++ /dev/null @@ -1,10 +0,0 @@ -Instantiation -------------- - -.. index:: !instantiation -.. index:: - single: module; instantiation - -.. todo:: - - Describe the semantics of module instantiation diff --git a/document/modules/invocation.rst b/document/modules/invocation.rst deleted file mode 100644 index f2bedee189..0000000000 --- a/document/modules/invocation.rst +++ /dev/null @@ -1,10 +0,0 @@ -Invocation ----------- - -.. index:: !invocation -.. index:: - single: exports; invocation - -.. todo:: - - Describe the semantics of invoking exports diff --git a/document/modules/memory-section.rst b/document/modules/memory-section.rst deleted file mode 100644 index a8db91637d..0000000000 --- a/document/modules/memory-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Memory Section --------------- - -.. index:: - pair: memory; section - single: modules; memory section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/overview.rst b/document/modules/overview.rst deleted file mode 100644 index cc6aba5803..0000000000 --- a/document/modules/overview.rst +++ /dev/null @@ -1,24 +0,0 @@ -Overview --------- - -.. todo:: - - Describe general structure of modules - - -Indices -~~~~~~~ - -Definitions in a module or function are referenced by index. -All indices are encoded as |u32| numbers. - -.. math:: - \begin{array}{llll} - \production{(type indices)} & \typeidx &::=& \u32 \\ - \production{(function indices)} & \funcidx &::=& \u32 \\ - \production{(table indices)} & \tableidx &::=& \u32 \\ - \production{(memory indices)} & \memidx &::=& \u32 \\ - \production{(global indices)} & \globalidx &::=& \u32 \\ - \production{(local indices)} & \localidx &::=& \u32 \\ - \production{(label indices)} & \labelidx &::=& \u32 \\ - \end{array} diff --git a/document/modules/start-section.rst b/document/modules/start-section.rst deleted file mode 100644 index f250e2b7af..0000000000 --- a/document/modules/start-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Start Section -------------- - -.. index:: - pair: start; section - single: modules; start section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/summary-execution.rst b/document/modules/summary-execution.rst deleted file mode 100644 index df95ab5677..0000000000 --- a/document/modules/summary-execution.rst +++ /dev/null @@ -1,27 +0,0 @@ -Summary: Execution of Modules ------------------------------ - -Instantiation -~~~~~~~~~~~~~ - -.. index:: - single: instantiation - single: modules; instantiation - single: execution; modules (instantiation) - -.. todo:: - - Summary of instantiation rules - - -Invocation -~~~~~~~~~~ - -.. index:: - single: invocation - single: exports; invocation - single: execution; exports (invocation) - -.. todo:: - - Summary of invocation rules diff --git a/document/modules/table-section.rst b/document/modules/table-section.rst deleted file mode 100644 index c90f6d58d7..0000000000 --- a/document/modules/table-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Table Section -------------- - -.. index:: - pair: table; section - single: modules; table section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/modules/type-section.rst b/document/modules/type-section.rst deleted file mode 100644 index e00271eb28..0000000000 --- a/document/modules/type-section.rst +++ /dev/null @@ -1,10 +0,0 @@ -Type Section ------------- - -.. index:: - pair: type; section - single: modules; type section - -.. todo:: - - Describe \ No newline at end of file diff --git a/document/syntax/conventions.rst b/document/syntax/conventions.rst index d540339f4d..63413f5459 100644 --- a/document/syntax/conventions.rst +++ b/document/syntax/conventions.rst @@ -34,6 +34,8 @@ The following conventions are adopted in defining grammar rules for abstract syn (This is a shorthand for :math:`A^n` where :math:`n \leq 1`.) +.. _syntax-record: + Auxiliary Notation ~~~~~~~~~~~~~~~~~~ diff --git a/document/syntax/instructions.rst b/document/syntax/instructions.rst index fa15c2a33a..d6b7e43b93 100644 --- a/document/syntax/instructions.rst +++ b/document/syntax/instructions.rst @@ -25,7 +25,7 @@ The following sections group instructions into a number of different categories. .. _syntax-sx: .. _syntax-instr-numeric: -.. index:: ! memory instructions +.. index:: ! numeric instruction pair: abstract syntax; instruction Numeric Instructions @@ -117,7 +117,7 @@ For the other integer instructions, the sign interpretation is irrelevant under .. _syntax-instr-parametric: -.. index:: ! parametric instructions +.. index:: ! parametric instruction pair: abstract syntax; instruction Parametric Instructions @@ -139,7 +139,7 @@ The |SELECT| operator selects one of its first two operands based on whether its .. _syntax-instr-variable: -.. index:: ! variable instructions, local, global, local index, global index +.. index:: ! variable instruction, local, global, local index, global index pair: abstract syntax; instruction Variable Instructions @@ -164,7 +164,7 @@ The |TEELOCAL| instruction is like |SETLOCAL| but also returns its argument. .. _syntax-instr-memory: .. _syntax-memarg: -.. index:: ! memory instructions, memory index +.. index:: ! memory instruction, memory index pair: abstract syntax; instruction Memory Instructions @@ -218,7 +218,7 @@ The precise semantics of memory instructions is :ref:`described ` and :r \TABLES~\vec(\table), \\&&&& \MEMS~\vec(\mem), \\&&&& \GLOBALS~\vec(\global), \\&&&& - \ELEM~\vec(\elemseg), \\&&&& - \DATA~\vec(\dataseg), \\&&&& - \START~\funcidx^?, \\&&&& + \ELEM~\vec(\elem), \\&&&& + \DATA~\vec(\data), \\&&&& + \START~\start^?, \\&&&& \IMPORTS~\vec(\import), \\&&&& \EXPORTS~\vec(\export) \quad\} \\ \end{array} @@ -29,6 +29,7 @@ and provide initialization logic in the form of :ref:`data ` and :r Each of the vectors -- and thus the entire module -- may be empty. +.. _syntax-index: .. _syntax-typeidx: .. _syntax-funcidx: .. _syntax-tableidx: @@ -82,7 +83,7 @@ Conventions * The meta variable :math:`l` ranges over label indices. -* The meta variable :math:`x` ranges over indices in any of the other index spaces. +* The meta variables :math:`x, y` ranges over indices in any of the other index spaces. .. _syntax-expr: @@ -123,7 +124,7 @@ They are referenced by :ref:`type indices `. .. _syntax-func: .. _syntax-local: -.. index:: ! function, ! local, function index, type index, value type, expression, import +.. index:: ! function, ! local, function index, local index, type index, value type, expression, import pair: abstract syntax; function Functions @@ -248,7 +249,7 @@ The |ELEM| component of a module defines a vector of *element segments* that ini .. math:: \begin{array}{llll} - \production{element segments} & \elemseg &::=& + \production{element segments} & \elem &::=& \{ \TABLE~\tableidx, \OFFSET~\expr, \INIT~\vec(\funcidx) \} \\ \end{array} @@ -273,7 +274,7 @@ The |DATA| component of a module defines a vector of *data segments* that initia .. math:: \begin{array}{llll} - \production{data segments} & \dataseg &::=& + \production{data segments} & \data &::=& \{ \MEM~\memidx, \OFFSET~\expr, \INIT~\vec(\by) \} \\ \end{array} @@ -291,7 +292,13 @@ The |OFFSET| is given by a :ref:`constant ` :ref:`expression ` of an optional *start function* that is automatically invoked when the module is :ref:`instantiated `, after tables and memories have been initialized. +The |START| component of a module optionally declares the :ref:`function index ` of a *start function* that is automatically invoked when the module is :ref:`instantiated `, after tables and memories have been initialized. + +.. math:: + \begin{array}{llll} + \production{start function} & \start &::=& + \{ \FUNC~\funcidx \} \\ + \end{array} .. _syntax-export: diff --git a/document/syntax/types.rst b/document/syntax/types.rst index 75ee225fcd..deb9fd354c 100644 --- a/document/syntax/types.rst +++ b/document/syntax/types.rst @@ -33,6 +33,9 @@ Conventions * The meta variable :math:`t` ranges over value types where clear from context. +* The notation :math:`|t|` denotes the *width* of a value type in bytes. + (That is, :math:`|\I32| = |\F32| = 4` and :math:`|\I64| = |\F64| = 8`.) + .. _syntax-resulttype: .. index:: ! result type, value type @@ -57,7 +60,7 @@ which is a sequence of values. .. _syntax-functype: -.. index:: ! function type, valut type, result type +.. index:: ! function type, value type, result type pair: abstract syntax; function type pair: function; type @@ -65,14 +68,19 @@ Function Types ~~~~~~~~~~~~~~ *Function types* classify the signature of functions, -mapping a sequence of parameters to a sequence of results. +mapping a vector of parameters to a vector of results. .. math:: \begin{array}{llll} \production{function types} & \functype &::=& - \valtype^\ast \to \resulttype \\ + [\vec(\valtype)] \to [\vec(\valtype)] \\ \end{array} +.. note:: + In the current version of WebAssembly, + the length of the result type vector of a function may be at most :math:`1`. + This restriction may be removed in future versions. + .. _syntax-memtype: .. _syntax-limits: @@ -133,7 +141,7 @@ A table of that type thus contains references to functions of heterogeneous type .. _syntax-globaltype: -.. index:: ! global type, value type +.. index:: ! global type, ! mutability, value type pair: abstract syntax; global type pair: abstract syntax; mutability pair: global; type @@ -147,7 +155,10 @@ Global Types .. math:: \begin{array}{llll} \production{global types} & \globaltype &::=& - \MUT^?~\valtype \\ + \mut^?~\valtype \\ + \production{mutability} & \mut &::=& + \CONST ~|~ + \MUT \\ \end{array} @@ -169,3 +180,17 @@ External Types \MEM~\memtype ~|~ \\&&& \GLOBAL~\globaltype \\ \end{array} + + +Conventions +........... + +The following auxiliary notation is defined for sequences of external types, filtering out entries of a specific kind in an order-preserving fashion: + +* :math:`\funcs(\externtype^\ast) = [\functype ~|~ \FUNC~\functype \in \externtype^\ast]` + +* :math:`\tables(\externtype^\ast) = [\tabletype ~|~ \TABLE~\tabletype \in \externtype^\ast]` + +* :math:`\mems(\externtype^\ast) = [\memtype ~|~ \MEM~\memtype \in \externtype^\ast]` + +* :math:`\globals(\externtype^\ast) = [\globaltype ~|~ \GLOBAL~\globaltype \in \externtype^\ast]` diff --git a/document/syntax/values.rst b/document/syntax/values.rst index 6095f9cb05..f20627e59d 100644 --- a/document/syntax/values.rst +++ b/document/syntax/values.rst @@ -103,24 +103,18 @@ Conventions Vectors ~~~~~~~ -*Vectors* are self-contained sequences of the form :math:`A^n` (or :math:`A^\ast`), +*Vectors* are bounded sequences of the form :math:`A^n` (or :math:`A^\ast`), where the :math:`A`-s can either be values or complex constructions. +A vector can have at most :math:`2^{32}-1` elements. .. math:: - \begin{array}{llll} + \begin{array}{lllll} \production{vectors} & \vec(A) &::=& - A^\ast \\ + A^n + & (n < 2^{32})\\ \end{array} -Conventions -........... - -* :math:`|V|` denotes the length of a vector :math:`V`. - -* :math:`V[i]` denotes the :math:`i`-th element of a vector :math:`V`, starting from :math:`0`. - - .. _syntax-name: .. index:: ! name, byte pair: abstract syntax; name diff --git a/document/validation/conventions.rst b/document/validation/conventions.rst new file mode 100644 index 0000000000..a081117679 --- /dev/null +++ b/document/validation/conventions.rst @@ -0,0 +1,177 @@ +.. index:: ! validation, ! type system, function type, table type, memory type, globaltype, valtype, resulttype, index space + +Conventions +----------- + +Validation checks that a WebAssembly module is well-formed. +Only valid modules can be :ref:`instantiated `. + +Validity is defined by a *type system* over the :ref:`abstract syntax ` of both instructions and modules. +For each piece of abstract syntax, there is a typing rule that specifies the constraints that apply to it. +All rules are given in two *equivalent* forms: + +1. In *prose*, describing the meaning in intuitive form. +2. In *formal notation*, describing the rule in mathematical form. + +.. note:: + The prose and formal rules are equivalent, + so that understanding of the formal notation is *not* required to read this specification. + The formalism offers a more concise description in notation that is used widely in programming languages semantics and is readily amenable to mathematical proof. + +In both cases, the rules are formulated in a *declarative* manner. +That is, they only formulate the constraints, they do not define an algorithm. +A sound and complete algorithm for type-checking instruction sequences according to this specification is provided in the :ref:`appendix `. + + +.. _context: +.. index:: ! context, function type, table type, memory type, global type, value type, result type, index space + +Contexts +~~~~~~~~ + +Validity of an individual definition is specified relative to a *context*, +which collects relevant information about the surrounding :ref:`module ` and other definitions in scope: + +* *Types*: the list of types defined in the current module. +* *Functions*: the list of functions declared in the current module, represented by their function type. +* *Tables*: the list of tables declared in the current module, represented by their table type. +* *Memories*: the list of memories declared in the current module, represented by their memory type. +* *Globals*: the list of globals declared in the current module, represented by their global type. +* *Locals*: the list of locals declared in the current function (including parameters), represented by their value type. +* *Labels*: the stack of labels accessible from the current position, represented by their result type. + +In other words, a context contains a sequence of suitable :ref:`types ` for each :ref:`index space `, +describing each defined entry in that space. +Locals and labels are only used for validating :ref:`instructions ` in :ref:`function bodies `, and are left empty elsewhere. +The label stack is the only part of the context that changes as validation of an instruction sequence proceeds. + +It is convenient to define contexts as :ref:`records ` :math:`C` with abstract syntax: + +.. math:: + \begin{array}{llll} + \production{(context)} & C &::=& + \begin{array}[t]{l@{~}ll} + \{ & \TYPES & \functype^\ast, \\ + & \FUNCS & \functype^\ast, \\ + & \TABLES & \tabletype^\ast, \\ + & \MEMS & \memtype^\ast, \\ + & \GLOBALS & \globaltype^\ast, \\ + & \LOCALS & \valtype^\ast, \\ + & \LABELS & \resulttype^\ast ~\} \\ + \end{array} + \end{array} + +.. note:: + The fields of a context are not defined as :ref:`vectors `, + since their lengths are not bounded by the maximum vector size. + +In addition to field access :math:`C.\K{field}` the following notation is adopted for manipulating contexts: + +* When spelling out a context, empty fields are omitted. + +* :math:`C,\K{field}\,A^\ast` denotes the same context as :math:`C` but with the elements :math:`A^\ast` prepended to its :math:`\K{field}` component sequence. + +.. note:: + This notation is defined to *prepend* not *append*. + It is only used in situations where the original :math:`C.\K{field}` is either empty + or :math:`\K{field}` is :math:`\K{labels}`. + In the latter case adding to the front is desired + because the :ref:`label index ` space is indexed relatively, that is, in reverse order of addition. + + +Textual Notation +~~~~~~~~~~~~~~~~ + +Validation is specified by stylised rules for each relevant part of the :ref:`abstract syntax `. +The rules not only state constraints defining when a phrase is valid, +they also classify it with a type. +A phrase :math:`A` is said to be "valid with type :math:`T`", +if all constraints expressed by the respective rules are met. +The form of :math:`T` depends on what :math:`A` is. + +.. note:: + For example, if :math:`A` is a :ref:`function `, + then :math:`T` is a :ref:`function type `; + for an :math:`A` that is a :ref:`global `, + :math:`T` is a :ref:`global type `; + and so on. + +The rules implicitly assume a given :ref:`context ` :math:`C`. +In some places, this context is locally extended to a context :math:`C'` with additional entries. +The formulation "Under context :math:`C'`, ... *statement* ..." is adopted to express that the following statement must apply under the assumptions embodied in the extended context. + + +Formal Notation +~~~~~~~~~~~~~~~ + +.. note:: + This section gives a brief explanation of the notation for specifying typing rules formally. + For the interested reader, a more thorough introduction can be found in respective text books. [#tapl]_ + +The proposition that a phrase :math:`A` has a respective type :math:`T` is written :math:`A : T`. +In general, however, typing is dependent on the context :math:`C`. +To express this explicitly, the complete form is a *judgement* :math:`C \vdash A : T`, +which says that :math:`A : T` holds under the assumptions encoded in :math:`C`. + +The formal typing rules use a standard approach for specifying type systems, rendering them into *deduction rules*. +Every rule has the following general form: + +.. math:: + \frac{ + \X{premise}_1 \qquad \X{premise}_2 \qquad \dots \qquad \X{premise}_n + }{ + \X{conclusion} + } + +Such a rule is read as a big implication: if all premises hold, then the conclusion holds. +Some rules have no premises; they are *axioms* whose conclusion holds unconditionally. +The conclusion always is a judgment :math:`C \vdash A : T`, +and there is one respective rule for each relevant construct :math:`A` of the abstract syntax. + +.. note:: + For example, the typing rule for the :ref:`instruction ` :math:`\K{i32.add}` can be given as an axiom: + + .. math:: + \frac{ + }{ + C \vdash \K{i32.add} : [\I32~\I32] \to [\I32] + } + + The instruction is always valid with type :math:`[\I32~\I32] \to [\I32`] + (saying that it consumes two |I32| values and produces one), + independent from any side conditions. + + An instruction like |GETLOCAL| can be typed as follows: + + .. math:: + \frac{ + C.\LOCAL[x] = t + }{ + C \vdash \GETLOCAL~x : [] \to [t] + } + + Here, the premise enforces that the immediate :ref:`local index ` :math:`x` exists in the context. + The instruction produces a value of its respective type :math:`t` + (and does not consume any values). + If :math:`C.\LOCAL[x]` does not exist then the premise does not hold, + and the instruction is ill-typed. + + Finally, a :ref:`structured ` instruction requires + a recursive rule, where the premise is itself a typing judgement: + + .. math:: + \frac{ + C,\LABEL\,(t^?) \vdash \instr^\ast : [] \to [t^?] + }{ + C \vdash \BLOCK~t^?~\instr^\ast~\END : [] \to [t^?] + } + + A |BLOCK| instruction is only valid when the instruction sequence in its body is. + Moreover, the result type must match the block's annotation :math:`t^?`. + If so, then the |BLOCK| instruction has the same type as the body. + Inside the body an additional label of the same type is available, + which is expressed by locally extending the context :math:`C` with the additional label information for the premise. + + +.. [#tapl] + For example: Benjamin Pierce. `Types and Programming Languages `_. The MIT Press 2002 diff --git a/document/validation/index.rst b/document/validation/index.rst index 40c9eaee1f..3606f529fc 100644 --- a/document/validation/index.rst +++ b/document/validation/index.rst @@ -5,5 +5,5 @@ Validation :maxdepth: 2 conventions - modules instructions + modules diff --git a/document/validation/instructions.rst b/document/validation/instructions.rst new file mode 100644 index 0000000000..2b5e983dc4 --- /dev/null +++ b/document/validation/instructions.rst @@ -0,0 +1,708 @@ +.. _valid-instr +.. index:: function type, context + +Instructions +------------ + +:ref:`Instructions ` are classified by :ref:`function types ` :math:`[t_1^\ast] \to [t_2^\ast]`. +The types describe which types :math:`t_1^\ast` of argument values an instruction pops off the operand stack and which types :math:`t_2^\ast` of result values it pushes back to it. + +.. note:: + For example, the instruction :math:`\K{i32.add}` has type :math:`[\I32~\I32] \to [\I32]`, + consuming two |I32| values and producing one. + +Typing extends to :ref:`instruction sequences ` :math:`\instr^\ast`. +Such a sequence has a :ref:`function types ` :math:`[t_1^\ast] \to [t_2^\ast]` if the accumulative effect of executing the instructions is consuming values of types :math:`t_1^\ast` off the operand stack and pushing new values of types :math:`t_2^\ast`. + +.. _polymorphism: + +For some instructions, the typing rules do not fully constrain the type, +and therefor allow for multiple types. +Such instructions are called *polymorphic*. +Two degrees of polymorphism can be distinguished: + +* *value-polymorphic*: + the :ref:`value type ` :math:`t` of one or several individual operands is unconstrained. + That is the case for all :ref:`parametric instructions ` like |DROP| and |SELECT|. + + +* *stack-polymorphic*: + the entire (or most of the) :ref:`function type ` :math:`[t_1^\ast] \to [t_2^\ast]` of the instruction is unconstrained. + That is the case for all :ref:`control instructions ` that perform an *unconditional control transfer*, such as |UNREACHABLE|, |BR|, |BRTABLE|, and |RETURN|. + +In both cases, the unconstrained types or type sequences can be chosen arbitrarily, as long as they meet the constraints imposed for the surrounding parts of the program. + +.. note:: + For example, the |SELECT| instruction is valid with type :math:`[t~t~\I32] \to [t]`, for any possible :ref:`value type ` :math:`t`. Consequently, both instruction sequences + + .. math:: + (\K{i32.const}~1)~~(\K{i32.const}~2)~~(\K{i32.const}~3)~~\SELECT{} + + and + + .. math:: + (\K{f64.const}~1.0)~~(\K{f64.const}~2.0)~~(\K{i32.const}~3)~~\SELECT{} + + are valid, with :math:`t` in the typing of |SELECT| being instantiated to |I32| or |F64|, respectively. + + The |UNREACHABLE| instruction is valid with type :math:`[t_1^\ast] \to [t_2^\ast]` for any possible sequences of value types :math:`t_1^\ast` and :math:`t_2^\ast`. + Consequently, + + .. math:: + \UNREACHABLE~~\K{i32.add} + + is valid by assuming type :math:`[] \to [\I32~\I32]` for the |UNREACHABLE| instruction. + In contrast, + + .. math:: + \UNREACHABLE~~(\K{i64.const}~0)~~\K{i32.add} + + is invalid, because there is no possible type to pick for the |UNREACHABLE| instruction that would make the sequence well-typed. + + +.. _valid-instr-numeric: +.. index:: numeric instruction + pair: validation; instruction + single: abstract syntax; instruction + +Numeric Instructions +~~~~~~~~~~~~~~~~~~~~ + +In this section, the following grammar shorthands are adopted: + +.. math:: + \begin{array}{llll} + \production{unary operators} & \unop &::=& + \K{clz} ~|~ + \K{ctz} ~|~ + \K{popcnt} ~|~ + \K{abs} ~|~ + \K{neg} ~|~ + \K{sqrt} ~|~ + \K{ceil} ~|~ + \K{floor} ~|~ + \K{trunc} ~|~ + \K{nearest} \\ + \production{binary operators} & \binop &::=& + \K{add} ~|~ + \K{sub} ~|~ + \K{mul} ~|~ + \K{div} ~|~ + \K{div\_}\sx ~|~ + \K{rem\_}\sx ~|~ + \K{min} ~|~ + \K{max} ~|~ + \K{copysign} ~|~ \\&&& + \K{and} ~|~ + \K{or} ~|~ + \K{xor} ~|~ + \K{shl} ~|~ + \K{shr\_}\sx ~|~ + \K{rotl} ~|~ + \K{rotr} \\ + \production{test operators} & \testop &::=& + \K{eqz} \\ + \production{relational operators} & \relop &::=& + \K{eq} ~|~ + \K{ne} ~|~ + \K{lt} ~|~ + \K{gt} ~|~ + \K{le} ~|~ + \K{ge} ~|~ + \K{lt\_}\sx ~|~ + \K{gt\_}\sx ~|~ + \K{le\_}\sx ~|~ + \K{ge\_}\sx \\ + \production{conversion operators} & \cvtop &::=& + \K{wrap} ~|~ + \K{extend\_}\sx ~|~ + \K{trunc\_}\sx ~|~ + \K{convert\_}\sx ~|~ + \K{demote} ~|~ + \K{promote} ~|~ + \K{reinterpret} \\ + \end{array} + + +:math:`t \K{.const}~c` +...................... + +* The instruction is valid with type :math:`[] \to [t]`. + +.. math:: + \frac{ + }{ + C \vdash t\K{.const}~c : [] \to [t] + } + + +:math:`t\K{.}\unop` +................... + +* The instruction is valid with type :math:`[t] \to [t]`. + +.. math:: + \frac{ + }{ + C \vdash t\K{.}\unop : [t] \to [t] + } + + +:math:`t\K{.}\binop` +.................... + +* The instruction is valid with type :math:`[t~t] \to [t]`. + +.. math:: + \frac{ + }{ + C \vdash t\K{.}\binop : [t~t] \to [t] + } + + +:math:`t\K{.}\testop` +..................... + +* The instruction is valid with type :math:`[t] \to [\I32]`. + +.. math:: + \frac{ + }{ + C \vdash t\K{.}\testop : [t] \to [\I32] + } + + +:math:`t\K{.}\relop` +.................... + +* The instruction is valid with type :math:`[t~t] \to [\I32]`. + +.. math:: + \frac{ + }{ + C \vdash t\K{.}\relop : [t~t] \to [\I32] + } + + +:math:`t_2\K{.}\cvtop/t_1` +.......................... + +* The instruction is valid with type :math:`[t_1] \to [t_2]`. + +.. math:: + \frac{ + }{ + C \vdash t_2\K{.}\cvtop/t_1 : [t_1] \to [t_2] + } + + +.. _syntax-instr-parametric: +.. index:: ! parametric instructions + pair: abstract syntax; instruction + + +.. _valid-parametric: +.. index:: value type, polymorphism + +Parametric Instructions +~~~~~~~~~~~~~~~~~~~~~~~ + +:math:`\DROP` +............. + +* The instruction is valid with type :math:`[t] \to []`, for any :ref:`value type ` :math:`t`. + +.. math:: + \frac{ + }{ + C \vdash \DROP : [t] \to [] + } + + +:math:`\SELECT` +............... + +* The instruction is valid with type :math:`[t~t~\I32] \to [t]`, for any :ref:`value type ` :math:`t`. + +.. math:: + \frac{ + }{ + C \vdash \SELECT : [t~t~\I32] \to [t] + } + +.. note:: + Both |DROP| and |SELECT| are :ref:`value-polymorphic ` instructions. + + +.. _valid-instr-variable: +.. index:: variable instructions, local index, global index + pair: validation; instruction + single: abstract syntax; instruction + +Variable Instructions +~~~~~~~~~~~~~~~~~~~~~ + +:math:`\GETLOCAL~x` +................... + +* The local :math:`C.\LOCALS[x]` must be defined in the context. + +* Let :math:`t` be the :ref:`value type ` :math:`C.\LOCALS[x]`. + +* Then the instruction is valid with type :math:`[] \to [t]`. + +.. math:: + \frac{ + C.\LOCALS[x] = t + }{ + C \vdash \GETLOCAL~x : [] \to [t] + } + + +:math:`\SETLOCAL~x` +................... + +* The local :math:`C.\LOCALS[x]` must be defined in the context. + +* Let :math:`t` be the :ref:`value type ` :math:`C.\LOCALS[x]`. + +* Then the instruction is valid with type :math:`[t] \to []`. + +.. math:: + \frac{ + C.\LOCALS[x] = t + }{ + C \vdash \SETLOCAL~x : [t] \to [] + } + + +:math:`\TEELOCAL~x` +................... + +* The local :math:`C.\LOCALS[x]` must be defined in the context. + +* Let :math:`t` be the :ref:`value type ` :math:`C.\LOCALS[x]`. + +* Then the instruction is valid with type :math:`[t] \to [t]`. + +.. math:: + \frac{ + C.\LOCALS[x] = t + }{ + C \vdash \TEELOCAL~x : [t] \to [t] + } + + +:math:`\GETGLOBAL~x` +.................... + +* The global :math:`C.\GLOBALS[x]` must be defined in the context. + +* Let :math:`\mut~t` be the :ref:`value type ` :math:`C.\LOCALS[x]`. + +* Then the instruction is valid with type :math:`[] \to [t]`. + +.. math:: + \frac{ + C.\GLOBALS[x] = \mut~t + }{ + C \vdash \GETGLOBAL~x : [] \to [t] + } + + +:math:`\SETGLOBAL~x` +.................... + +* The global :math:`C.\GLOBALS[x]` must be defined in the context. + +* Let :math:`\mut~t` be the :ref:`global type ` :math:`C.\GLOBALS[x]`. + +* The mutability :math:`\mut` must be |MUT|. + +* Then the instruction is valid with type :math:`[t] \to []`. + +.. math:: + \frac{ + C.\GLOBALS[x] = \MUT~t + }{ + C \vdash \SETGLOBAL~x : [t] \to [] + } + + +.. _valid-instr-memory: +.. _valid-memarg: +.. index:: memory instruction, memory index + pair: validation; instruction + single: abstract syntax; instruction + +Memory Instructions +~~~~~~~~~~~~~~~~~~~ + +:math:`t\K{.load}~\memarg` +.......................... + +* The memory :math:`C.\MEMS[0]` must be defined in the context. + +* The alignment :math:`2^{\memarg.\ALIGN}` must not be larger than the :ref:`width ` of :math:`t`. + +* Then the instruction is valid with type :math:`[\I32] \to [t]`. + +.. math:: + \frac{ + C.\MEMS[0] = \memtype + \qquad + 2^{\memarg.\ALIGN} \leq |t| + }{ + C \vdash t\K{.load}~\memarg : [\I32] \to [t] + } + + +:math:`t\K{.load}N\K{\_}\sx~\memarg` +.................................... + +* The memory :math:`C.\MEMS[0]` must be defined in the context. + +* The alignment :math:`2^{\memarg.\ALIGN}` must not be larger than :math:`N`. + +* Then the instruction is valid with type :math:`[\I32] \to [t]`. + +.. math:: + \frac{ + C.\MEMS[0] = \memtype + \qquad + 2^{\memarg.\ALIGN} \leq N + }{ + C \vdash t\K{.load}N\K{\_}\sx~\memarg : [\I32] \to [t] + } + + +:math:`t\K{.store}~\memarg` +........................... + +* The memory :math:`C.\MEMS[0]` must be defined in the context. + +* The alignment :math:`2^{\memarg.\ALIGN}` must not be larger than the :ref:`width ` of :math:`t`. + +* Then the instruction is valid with type :math:`[\I32~t] \to []`. + +.. math:: + \frac{ + C.\MEMS[0] = \memtype + \qquad + 2^{\memarg.\ALIGN} \leq |t| + }{ + C \vdash t\K{.store}~\memarg : [\I32~t] \to [] + } + + +:math:`t\K{.store}N~\memarg` +............................ + +* The memory :math:`C.\MEMS[0]` must be defined in the context. + +* The alignment :math:`2^{\memarg.\ALIGN}` must not be larger than :math:`N`. + +* Then the instruction is valid with type :math:`[\I32~t] \to []`. + +.. math:: + \frac{ + C.\MEMS[0] = \memtype + \qquad + 2^{\memarg.\ALIGN} \leq N + }{ + C \vdash t\K{.store}N~\memarg : [\I32~t] \to [] + } + + +:math:`\CURRENTMEMORY` +...................... + +* The memory :math:`C.\MEMS[0]` must be defined in the context. + +* Then the instruction is valid with type :math:`[] \to [\I32]`. + +.. math:: + \frac{ + C.\MEMS[0] = \memtype + }{ + C \vdash \CURRENTMEMORY : [] \to [\I32] + } + + +:math:`\GROWMEMORY` +................... + +* The memory :math:`C.\MEMS[0]` must be defined in the context. + +* Then the instruction is valid with type :math:`[\I32] \to [\I32]`. + +.. math:: + \frac{ + C.\MEMS[0] = \memtype + }{ + C \vdash \GROWMEMORY : [\I32] \to [\I32] + } + + +.. _valid-instr-control: +.. _valid-label: +.. index:: control instructions, structured control, label, block, branch, result type, label index, function index, type index, vector, polymorphism + pair: validation; instruction + single: abstract syntax; instruction + +Control Instructions +~~~~~~~~~~~~~~~~~~~~ + +:math:`\NOP` +............ + +* The instruction is valid with type :math:`[] \to []`. + +.. math:: + \frac{ + }{ + C \vdash \NOP : [] \to [] + } + + +:math:`\UNREACHABLE` +.................... + +* The instruction is valid with type :math:`[t_1^\ast] \to [t_2^\ast]`, for any sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. + +.. math:: + \frac{ + }{ + C \vdash \UNREACHABLE : [t_1^\ast] \to [t_2^\ast] + } + +.. note:: + The |UNREACHABLE| instruction is :ref:`stack-polymorphic `. + + +:math:`\BLOCK~t^?~\instr^\ast~\END` +................................... + +* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the :ref:`result type ` :math:`t^?` prepended to the |LABELS| vector. + +* Under context :math:`C'`, + the instruction sequence :math:`\instr^\ast` must be :ref:`valid ` with type :math:`[] \to [t^?]`. + +* Then the compound instruction is valid with type :math:`[] \to [t^?]`. + +.. math:: + \frac{ + C,\LABELS\,(t^?) \vdash \instr^\ast : [] \to [t^?] + }{ + C \vdash \BLOCK~t^?~\instr^\ast~\END : [] \to [t^?] + } + + +:math:`\LOOP~t^?~\instr^\ast~\END` +.................................. + +* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the empty :ref:`result type ` :math:`\epsilon` prepended to the |LABELS| vector. + +* Under context :math:`C'`, + the instruction sequence :math:`\instr^\ast` must be :ref:`valid ` with type :math:`[] \to [t^?]`. + +* Then the compound instruction is valid with type :math:`[] \to [t^?]`. + +.. math:: + \frac{ + C,\LABELS\,(\epsilon) \vdash \instr^\ast : [] \to [t^?] + }{ + C \vdash \LOOP~t^?~\instr^\ast~\END : [] \to [t^?] + } + + +:math:`\IF~t^?~\instr_1^\ast~\ELSE~\instr_2^\ast~\END` +...................................................... + +* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the empty :ref:`result type ` :math:`\epsilon` prepended to the |LABELS| vector. + +* Under context :math:`C'`, + the instruction sequence :math:`\instr_1^\ast` must be :ref:`valid ` with type :math:`[] \to [t^?]`. + +* Under context :math:`C'`, + the instruction sequence :math:`\instr_2^\ast` must be :ref:`valid ` with type :math:`[] \to [t^?]`. + +* Then the compound instruction is valid with type :math:`[] \to [t^?]`. + +.. math:: + \frac{ + C,\LABELS\,(t^?) \vdash \instr_1^\ast : [] \to [t^?] + \qquad + C,\LABELS\,(t^?) \vdash \instr_2^\ast : [] \to [t^?] + }{ + C \vdash \IF~t^?~\instr_1^\ast~\ELSE~\instr_2^\ast~\END : [\I32] \to [t^?] + } + + +:math:`\BR~l` +............. + +* The label :math:`C.\LABELS[l]` must be defined in the context. + +* Let :math:`t^?` be the :ref:`result type ` :math:`C.\LABELS[l]`. + +* Then the instruction is valid with type :math:`[t_1^\ast~t^?] \to [t_2^\ast]`, for any sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. + +.. math:: + \frac{ + C.\LABELS[l] = t^? + }{ + C \vdash \BR~l : [t_1^\ast~t^?] \to [t_2^\ast] + } + +.. note:: + The |BR| instruction is :ref:`stack-polymorphic `. + + +:math:`\BRIF~l` +............... + +* The label :math:`C.\LABELS[l]` must be defined in the context. + +* Let :math:`t^?` be the :ref:`result type ` :math:`C.\LABELS[l]`. + +* Then the instruction is valid with type :math:`[t^?~\I32] \to [t^?]`. + +.. math:: + \frac{ + C.\LABELS[l] = t^? + }{ + C \vdash \BRIF~l : [t^?~\I32] \to [t^?] + } + + +:math:`\BRTABLE~l^\ast~l'` +.......................... + +* The label :math:`C.\LABELS[l]` must be defined in the context. + +* Let :math:`t^?` be the :ref:`result type ` :math:`C.\LABELS[l']`. + +* For all :math:`l_i` in :math:`l^\ast`, + the label :math:`C.\LABELS[l_i]` must be defined in the context. + +* For all :math:`l_i` in :math:`l^\ast`, + :math:`C.\LABELS[l_i]` must be :math:`t^?`. + +* Then the instruction is valid with type :math:`[t_1^\ast~t^?] \to [t_2^\ast]`, for any sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. + +.. math:: + \frac{ + (C.\LABELS[l] = t^?)^\ast + \qquad + C.\LABELS[l'] = t^? + }{ + C \vdash \BRTABLE~l^\ast~l' : [t_1^\ast~t^?] \to [t_2^\ast] + } + +.. note:: + The |BRTABLE| instruction is :ref:`stack-polymorphic `. + + +:math:`\RETURN` +............... + +* The label vector :math:`C.\LABELS` must not be empty in the context. + +* Let :math:`t^?` be the :ref:`result type ` that is the last element of :math:`C.\LABELS`. + +* Then the instruction is valid with type :math:`[t_1^\ast~t^?] \to [t_2^\ast]`, for any sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. + +.. math:: + \frac{ + C.\LABELS[|C.\LABELS|-1] = t^? + }{ + C \vdash \RETURN : [t_1^\ast~t^?] \to [t_2^\ast] + } + +.. note:: + The |RETURN| instruction is :ref:`stack-polymorphic `. + + +:math:`\CALL~x` +............... + +* The function :math:`C.\FUNCS[x]` must be defined in the context. + +* Then the instruction is valid with type :math:`C.\FUNCS[x]`. + +.. math:: + \frac{ + C.\FUNCS[x] = [t_1^\ast] \to [t_2^\ast] + }{ + C \vdash \CALL~x : [t_1^\ast] \to [t_2^\ast] + } + + +:math:`\CALLINDIRECT~x` +....................... + +* The table :math:`C.\TABLES[0]` must be defined in the context. + +* Let :math:`\limits~\elemtype` be the :ref:`table type ` :math:`C.\TABLES[0]`. + +* The :ref:`element type ` :math:`\elemtype` must be |ANYFUNC|. + +* The type :math:`C.\TYPES[x]` must be defined in the context. + +* Then the instruction is valid with type :math:`C.\TYPES[x]`. + +.. math:: + \frac{ + C.\TABLES[0] = \limits~\ANYFUNC + \qquad + C.\TYPES[x] = [t_1^\ast] \to [t_2^\ast] + }{ + C \vdash \CALLINDIRECT~x : [t_1^\ast] \to [t_2^\ast] + } + + +.. _valid-instr-seq: +.. index:: instruction + +Instruction Sequences +~~~~~~~~~~~~~~~~~~~~~ + +Typing of instruction sequences is defined recursively. + + +Empty Instruction Sequence: :math:`\epsilon` +............................................ + +* The empty instruction sequence is valid with type :math:`[t^\ast] \to [t^\ast]`, + for any sequence of :ref:`value types ` :math:`t^\ast`. + +.. math:: + \frac{ + }{ + C \vdash \epsilon : [t^\ast] \to [t^\ast] + } + + +Non-empty Instruction Sequence: :math:`\instr^\ast~\instr'` +........................................................... + +* The instruction sequence :math:`\instr^\ast` must be valid with type :math:`[t_1^\ast] \to [t_2^\ast]`, + for some sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. + +* The instruction :math:`\instr'` must be valid with type :math:`[t^\ast] \to [t_3^\ast]`, + for some sequences of :ref:`value types ` :math:`t^\ast` and :math:`t_3^\ast`. + +* There must be a sequence of :ref:`value types ` :math:`t_0^\ast`, + such that :math:`t_2^\ast = t_0^\ast~t^\ast`. + +* Then the combined instruction sequence is valid with type :math:`[t_1^\ast] \to [t_0^\ast~t_3^\ast]`. + +.. math:: + \frac{ + C \vdash \instr^\ast : [t_1^\ast] \to [t_0^\ast~t^\ast] + \qquad + C \vdash \instr' : [t^\ast] \to [t_3^\ast] + }{ + C \vdash \instr^\ast~\instr' : [t_1^\ast] \to [t_0^\ast~t_3^\ast] + } diff --git a/document/validation/modules.rst b/document/validation/modules.rst new file mode 100644 index 0000000000..7127052204 --- /dev/null +++ b/document/validation/modules.rst @@ -0,0 +1,647 @@ +.. _valid-module: +.. index:: modules, type definition, function type, function, table, memory, global, element, data, start function, import, export, context + pair: validation; module + single: abstract syntax; module + +Modules +------- + +Modules are valid when all the definitions they contain are valid. +To that end, each definition is classified with a suitable type. + +A module is entirely *closed*, +that is, it only refers to definitions that appear in the module itself. +Consequently, no initial :ref:`context ` is required. +Instead, the context :math:`C` for validation of the module's content is constructed from the types of definitions in the module itself. + +* Let :math:`\module` be the module to validate. + +* Let :math:`C` be a :ref:`context ` where: + + * :math:`C.\TYPES` is :math:`\module.\TYPES`, + + * :math:`C.\FUNCS` is :math:`\funcs(\externtype_i^\ast)` concatenated with :math:`\functype_i^\ast`, + with the type sequences :math:`\externtype_i^\ast` and :math:`\functype_i^\ast` as determined below, + + * :math:`C.\TABLES` is :math:`\tables(\externtype_i^\ast)` concatenated with :math:`\tabletype_i^\ast`, + with the type sequences :math:`\externtype_i^\ast` and :math:`\tabletype_i^\ast` as determined below, + + * :math:`C.\MEMS` is :math:`\mems(\externtype_i^\ast)` concatenated with :math:`\memtype_i^\ast`, + with the type sequences :math:`\externtype_i^\ast` and :math:`\memtype_i^\ast` as determined below, + + * :math:`C.\GLOBALS` is :math:`\globals(\externtype_i^\ast)` concatenated with :math:`\globaltype_i^\ast`, + with the type sequences :math:`\externtype_i^\ast` and :math:`\globaltype_i^\ast` as determined below. + + * :math:`C.\LOCALS` is empty, + + * :math:`C.\LABELS` is empty. + +* Under the context :math:`C`: + + * For each :math:`\func_i` in :math:`\module.\FUNCS`, + the definition :math:`\func_i` must be :ref:`valid ` with a :ref:`function type ` :math:`\functype_i`. + + * For each :math:`\table_i` in :math:`\module.\TABLES`, + the definition :math:`\table_i` must be :ref:`valid ` with a :ref:`table type ` :math:`\tabletype_i`. + + * For each :math:`\mem_i` in :math:`\module.\MEMS`, + the definition :math:`\mem_i` must be :ref:`valid ` with a :ref:`memory type ` :math:`\memtype_i`. + + * For each :math:`\global_i` in :math:`\module.\GLOBALS`: + + * Let :math:`C_i` be the :ref:`context ` where :math:`C_i.\GLOBALS` is the sequence :math:`\globals(\externtype_i^\ast)` concatenated with :math:`\globaltype_0~\dots~\globaltype_{i-1}`, and all other fields are empty. + + * Under the context :math:`C_i`, + the definition :math:`\global_i` must be :ref:`valid ` with a :ref:`global type ` :math:`\globaltype_i`. + + * For each :math:`\elem_i` in :math:`\module.\ELEM`, + the segment :math:`\elem_i` must be :ref:`valid `. + + * For each :math:`\data_i` in :math:`\module.\DATA`, + the segment :math:`\elem_i` must be :ref:`valid `. + + * If :math:`\module.\START` is non-empty, + then :math:`\module.\START` must be :ref:`valid `. + + * For each :math:`\import_i` in :math:`\module.\IMPORTS`, + the segment :math:`\import_i` must be :ref:`valid ` with an :ref:`external type ` :math:`\externtype_i`. + + * For each :math:`\export_i` in :math:`\module.\EXPORTS`, + the segment :math:`\import_i` must be :ref:`valid ` with a :ref:`name ` :math:`\name_i`. + +* The length of :math:`C.\TABLES` must not be larger than :math:`1`. + +* The length of :math:`C.\MEMS` must not be larger than :math:`1`. + +* All export names :math:`\name_i` must be different. + +.. math:: + \frac{ + \begin{array}{@{}c@{}} + (C \vdash \func : \X{ft})^\ast + \quad + (C \vdash \table : \X{tt})^\ast + \quad + (C \vdash \mem : \X{mt})^\ast + \quad + (C_i \vdash \global : \X{gt})_i^\ast + \\ + (C \vdash \elem ~\F{ok})^\ast + \quad + (C \vdash \data ~\F{ok})^\ast + \quad + (C \vdash \start ~\F{ok})^? + \quad + (C \vdash \import : \X{it})^\ast + \quad + (C \vdash \export : \X{name})^\ast + \\ + \X{ift}^\ast = \funcs(\X{it}^\ast) + \qquad + \X{itt}^\ast = \tables(\X{it}^\ast) + \qquad + \X{imt}^\ast = \mems(\X{it}^\ast) + \qquad + \X{igt}^\ast = \globals(\X{it}^\ast) + \\ + C = \{ \TYPES~\functype^\ast, \FUNCS~\X{ift}^\ast~\X{ft}^\ast, \TABLES~\X{itt}^\ast~\X{tt}^\ast, \MEMS~\X{imt}^\ast~\X{mt}^\ast, \GLOBALS~\X{igt}^\ast~\X{gt}^\ast \} + \\ + |C.\TABLES| \leq 1 + \qquad + |C.\MEMS| \leq 1 + \qquad + \name^\ast ~\F{disjoint} + \qquad + (C_i = \{ \GLOBALS~[\X{igt}^\ast~\X{gt}^{i-1}] \})_i^\ast + \end{array} + }{ + \vdash \{ + \begin{array}[t]{@{}l@{}} + \TYPES~\functype^\ast, + \FUNCS~\func^\ast, + \TABLES~\table^\ast, + \MEMS~\mem^\ast, + \GLOBALS~\global^\ast, \\ + \ELEM~\elem^\ast, + \DATA~\data^\ast, + \START~\start^?, + \IMPORTS~\import^\ast, + \EXPORTS~\export^\ast \} ~\F{ok} \\ + \end{array} + } + +.. note:: + Most definitions in a module -- particularly functions -- are mutually recursive. + Consequently, the definition of the :ref:`context ` :math:`C` in this rule is recursive: + it depends on the outcome of validation of the function, table, memory, and global definitions contained in the module, + which itself depends on :math:`C`. + However, this recursion is just a specification device. + All types needed to construct :math:`C` can easily be determined from a simple pre-pass over the module that does not perform any actual validation. + + Globals, however, are not recursive. + The effect of defining the limited contexts :math:`C_i` for validating the module's globals is that their initialization expressions can only access imported and previously defined globals and nothing else. + +.. note:: + The restriction on the number of tables and memories may be lifted in future versions of WebAssembly. + + +Auxiliary Rules +~~~~~~~~~~~~~~~ + +.. _valid-limits: + +Limits :math:`\{ \MIN~n, \MAX~m^? \}` +..................................... + +* If the maximum :math:`m^?` is not empty, then its value must not be smaller than :math:`n`. + +* Then the limit is valid. + +.. math:: + \frac{ + (n \leq m)^? + }{ + \vdash \{ \MIN~n, \MAX~m^? \} ~\F{ok} + } + + +.. _valid-expr: +.. index:: expression + pair: validation; expression + single: abstract syntax; expression + single: expression; constant + +Expressions +~~~~~~~~~~~ + +Expressions :math:`\expr` are classified by :ref:`result types ` of the form :math:`t^?`. + + +:math:`\instr^\ast~\END` +........................ + +* The :ref:`instruction sequence ` must be :ref:`valid ` with type :math:`[] \to [t^?]`, + for some optional :ref:`value type ` :math:`t^?`. + +* Then the expression is valid with :ref:`result type ` :math:`t^?`. + +.. math:: + \frac{ + C \vdash \instr^\ast : [] \to [t^?] + }{ + C \vdash \instr^\ast~\END : t^? + } + + +.. _valid-const: +.. index:: ! constant + +Constant Expressions +.................... + +* In a *constant* expression :math:`\instr^\ast~\END` all instructions in :math:`\instr^\ast` must be constant. + +* A constant instruction :math:`\instr` must be: + + * either of the form :math:`t.\CONST~c`, + + * or of the form :math:`\GETGLOBAL~x`, in which case :math:`C.\GLOBALS[x]` must be a :ref:`global type ` of the form :math:`\CONST~t`. + +.. math:: + \frac{ + (C \vdash \instr ~\F{const})^\ast + }{ + C \vdash \instr~\END ~\F{const} + } + \qquad + \frac{ + }{ + C \vdash t.\CONST~c ~\F{const} + } + \qquad + \frac{ + C.\GLOBALS[x] = \CONST~t + }{ + C \vdash \GETGLOBAL~x ~\F{const} + } + +.. note:: + The definition of constant expression may be extended in future versions of WebAssembly. + + +.. _valid-func: +.. index:: function, local, function index, local index, type index, function type, value type, expression, import + pair: abstract syntax; function + +Functions +~~~~~~~~~ + +Functions :math:`\func` are classified by :ref:`function types ` of the form :math:`[t_1^\ast] \to [t_2^?]`. + + +:math:`\{ \TYPE~x, \LOCALS~t^\ast, \BODY~\expr \}` +.................................................... + +* The type :math:`C.\TYPES[x]` must be defined in the context. + +* Let :math:`[t_1^\ast] \to [t_2^\ast]` be the :ref:`function type ` :math:`C.\TYPES[x]`. + +* The length of :math:`t_2^\ast` must not be larger than :math:`1`. + +* Let :math:`C'` be the same :ref:`context ` as :math:`C`, + but with: + + * the |LOCALS| set to the sequence of :ref:`value types ` :math:`t_1^\ast~t^\ast`, concatenating parameters and locals, + + * the |LABELS| set to the singular sequence with :ref:`result type ` :math:`(t_2^\ast)`. + +* Under the context :math:`C'`, + the expression :math:`\expr` must be valid with type :math:`t_2^\ast`. + +* Then the function definition is valid with type :math:`[t_1^\ast] \to [t_2^\ast]`. + +.. math:: + \frac{ + C.\TYPES[x] = [t_1^\ast] \to [t_2^?] + \qquad + C,\LOCALS\,t_1^\ast~t^\ast,\LABELS~(t_2^?) \vdash \expr : t_2^? + }{ + C \vdash \{ \TYPE~x, \LOCALS~t^\ast, \BODY~\expr \} : t_2^? + } + +.. note:: + The restriction on the length of the result types :math:`t_2^\ast` may be lifted in future versions of WebAssembly. + + +.. _valid-table: +.. index:: table, table type, limits, element type + pair: validation; table + single: abstract syntax; table + +Tables +~~~~~~ + +Tables :math:`\table` are classified by :ref:`table types ` of the form :math:`\limits~\elemtype`. + + +:math:`\{ \TYPE~\limits~\elemtype \}` +..................................... + +* The limits :math:`\limits` must be :ref:`valid `. + +* Then the table definition is valid with type :math:`\limits~\elemtype`. + +.. math:: + \frac{ + \vdash \limits~\F{ok} + }{ + C \vdash \{ \TYPE~\limits~\elemtype \} : \limits~\elemtype + } + + +.. _valid-mem: +.. index:: memory, memory type, limits + pair: validation; memory + single: abstract syntax; memory + +Memories +~~~~~~~~ + +Memories :math:`\mem` are classified by :ref:`memory types ` of the form :math:`\limits`. + + +:math:`\{ \TYPE~\limits \}` +........................... + +* The limits :math:`\limits` must be :ref:`valid `. + +* Then the memory definition is valid with type :math:`\limits`. + +.. math:: + \frac{ + \vdash \limits~\F{ok} + }{ + C \vdash \{ \TYPE~\limits \} : \limits~\elemtype + } + + +.. _valid-global: +.. index:: global, global type, mutability, expression + pair: validation; global + single: abstract syntax; global + +Globals +~~~~~~~ + +Globals :math:`\global` are classified by :ref:`global types ` of the form :math:`\mut~t`. + + +:math:`\{ \TYPE~\mut~t, \INIT~\expr \}` +....................................... + +* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` :math:`t`. + +* The expression :math:`\expr` must be :ref:`constant `. + +* Then the global definition is valid with type :math:`\mut~t`. + +.. math:: + \frac{ + C \vdash \expr : t + \qquad + C \vdash \expr ~\F{const} + }{ + C \vdash \{ \TYPE~\mut~t, \INIT~\expr \} : \mut~t + } + + +.. _valid-elem: +.. index:: element, table, table index, expression, function index + pair: validation; element + single: abstract syntax; element + single: table; element + single: element; segment + +Element Segments +~~~~~~~~~~~~~~~~ + +Element segments :math:`\elem` are not classified by a type. + +:math:`\{ \TABLE~x, \OFFSET~\expr, \INIT~y^\ast \}` +................................................... + +* The table :math:`C.\TABLES[x]` must be defined in the context. + +* Let :math:`\limits~\elemtype` be the :ref:`table type ` :math:`C.\TABLES[x]`. + +* The :ref:`element type ` :math:`\elemtype` must be |ANYFUNC|. + +* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` |I32|. + +* The expression :math:`\expr` must be :ref:`constant `. + +* For each :math:`y_i` in :math:`y^\ast`, + the function :math:`C.\FUNCS[y]` must be defined in the context. + +* Then the element segment is valid. + + +.. math:: + \frac{ + C.\TABLES[x] = \limits~\ANYFUNC + \qquad + C \vdash \expr : \I32 + \qquad + C \vdash \expr ~\F{const} + \qquad + (C.\FUNCS[y] = \functype)^\ast + }{ + C \vdash \{ \TABLE~x, \OFFSET~\expr, \INIT~y^\ast \} ~\F{ok} + } + + +.. _valid-data: +.. index:: data, memory, memory index, expression, byte + pair: validation; data + single: abstract syntax; data + single: memory; data + single: data; segment + +Data Segments +~~~~~~~~~~~~~ + +Data segments :math:`\data` are not classified by any type. + +:math:`\{ \MEM~x, \OFFSET~\expr, \INIT~b^\ast \}` +................................................. + +* The memory :math:`C.\MEMS[x]` must be defined in the context. + +* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` |I32|. + +* The expression :math:`\expr` must be :ref:`constant `. + +* Then the data segment is valid. + + +.. math:: + \frac{ + C.\MEMS[x] = \limits + \qquad + C \vdash \expr : \I32 + \qquad + C \vdash \expr ~\F{const} + }{ + C \vdash \{ \MEM~x, \OFFSET~\expr, \INIT~b^\ast \} ~\F{ok} + } + + +.. _valid-start: +.. index:: start function, function index + pair: validation; start function + single: abstract syntax; start function + +Start Function +~~~~~~~~~~~~~~ + +Start function declarations :math:`\start` are not classified by any type. + +:math:`\{ \FUNC~x \}` +..................... + +* The function :math:`C.\FUNCS[x]` must be defined in the context. + +* The type of :math:`C.\FUNCS[x]` must be :math:`[] \to []`. + +* Then the start function is valid. + + +.. math:: + \frac{ + C.\FUNCS[x] = [] \to [] + }{ + C \vdash \{ \FUNC~x \} ~\F{ok} + } + + +.. _valid-export: +.. index:: export, name, index, function index, table index, memory index, global index + validation: abstract syntax; export + single: abstract syntax; export + +Exports +~~~~~~~ + +Exports :math:`\export` are classified by their export :ref:`name `. +Export descriptions :math:`\exportdesc` are not classified by any type. + + +:math:`\{ \NAME~\name, \DESC~\exportdesc \}` +............................................ + +* The export description :math:`\exportdesc` must be valid with type :math:`\externtype`. + +* Then the export is valid with name :math:`\name`. + +.. math:: + \frac{ + C \vdash \exportdesc ~\F{ok} + }{ + C \vdash \{ \NAME~\name, \DESC~\exportdesc \} : \name + } + + +:math:`\FUNC~x` +............... + +* The function :math:`C.\FUNCS[x]` must be defined in the context. + +* Then the export description is valid. + +.. math:: + \frac{ + C.\FUNCS[x] = \functype + }{ + C \vdash \FUNC~x ~\F{ok} + } + + +:math:`\TABLE~x` +................ + +* The table :math:`C.\TABLES[x]` must be defined in the context. + +* Then the export description is valid. + +.. math:: + \frac{ + C.\TABLES[x] = \tabletype + }{ + C \vdash \TABLE~x ~\F{ok} + } + + +:math:`\MEM~x` +.............. + +* The memory :math:`C.\MEMS[x]` must be defined in the context. + +* Then the export description is valid. + +.. math:: + \frac{ + C.\MEMS[x] = \memtype + }{ + C \vdash \MEM~x ~\F{ok} + } + + +:math:`\GLOBAL~x` +................. + +* The global :math:`C.\GLOBALS[x]` must be defined in the context. + +* Let :math:`\mut~t` be the :ref:`global type ` :math:`C.\GLOBALS[x]`. + +* The mutability :math:`\mut` must be |CONST|. + +* Then the export description is valid. + +.. math:: + \frac{ + C.\GLOBALS[x] = \CONST~t + }{ + C \vdash \GLOBAL~x ~\F{ok} + } + + +.. _valid-import: +.. index:: import, name, function type, table type, memory type, global type + pair: validation; import + single: abstract syntax; import + +Imports +~~~~~~~ + +Imports :math:`\import` and import descriptions :math:`\importdesc` are classified by :ref:`external types `. + + +:math:`\{ \MODULE~\name_1, \NAME~\name_2, \DESC~\importdesc \}` +............................................................... + +* The import description :math:`\importdesc` must be valid with type :math:`\externtype`. + +* Then the import is valid with type :math:`\externtype`. + +.. math:: + \frac{ + C \vdash \importdesc : \externtype + }{ + C \vdash \{ \MODULE~\name_1, \NAME~\name_2, \DESC~\importdesc \} : \externtype + } + + +:math:`\FUNC~x` +............... + +* The function :math:`C.\TYPES[x]` must be defined in the context. + +* Let :math:`[t_1^\ast] \to [t_2^\ast]` be the :ref:`function type ` :math:`C.\TYPES[x]`. + +* The length of :math:`t_2^\ast` must not be larger than :math:`1`. + +* Then the import description is valid with type :math:`\FUNC~[t_1^\ast] \to [t_2^\ast]`. + +.. math:: + \frac{ + C.\TYPES[x] = [t_1^\ast] \to [t_2^?] + }{ + C \vdash \FUNC~x : \FUNC~[t_1^\ast] \to [t_2^?] + } + +.. note:: + The restriction on the length of the result types :math:`t_2^\ast` may be lifted in future versions of WebAssembly. + + +:math:`\TABLE~\limits~\elemtype` +................................ + +* The limits :math:`\limits` must be valid. + +* Then the import description is valid with type :math:`\TABLE~\limits~\elemtype`. + +.. math:: + \frac{ + \vdash \limits ~\F{ok} + }{ + C \vdash \TABLE~\limits~\elemtype : \TABLE~\limits~\elemtype + } + + +:math:`\MEM~\limits` +.................... + +* The limits :math:`\limits` must be valid. + +* Then the import description is valid with type :math:`\MEM~\limits`. + +.. math:: + \frac{ + \vdash \limits ~\F{ok} + }{ + C \vdash \MEM~\limits : \MEM~\limits + } + + +:math:`\GLOBAL~\mut~t` +...................... + +* The mutability :math:`\mut` must be |CONST|. + +* Then the import description is valid with type :math:`\GLOBAL~t`. + +.. math:: + \frac{ + }{ + C \vdash \GLOBAL~t : \GLOBAL~t + } From b576a00ce99357769040b3598d03a1d6d7de63ba Mon Sep 17 00:00:00 2001 From: rossberg-chromium Date: Fri, 17 Mar 2017 16:21:39 +0100 Subject: [PATCH 02/15] Tweaks --- document/syntax/instructions.rst | 19 ++++ document/syntax/modules.rst | 19 ---- document/syntax/types.rst | 2 +- document/validation/conventions.rst | 4 +- document/validation/instructions.rst | 134 ++++++++++++++++++++------- document/validation/modules.rst | 76 ++------------- 6 files changed, 128 insertions(+), 126 deletions(-) diff --git a/document/syntax/instructions.rst b/document/syntax/instructions.rst index d6b7e43b93..f87a82eafb 100644 --- a/document/syntax/instructions.rst +++ b/document/syntax/instructions.rst @@ -287,3 +287,22 @@ the callee is dynamically checked against the :ref:`function type ` in In the current version of WebAssembly, |CALLINDIRECT| implicitly operates on :ref:`table ` :ref:`index ` :math:`0`. This restriction may be lifted in future versions. + + +.. _syntax-expr: +.. index:: ! expression, constant + pair: abstract syntax; expression + single: expression; constant + +Expressions +~~~~~~~~~~~ + +:ref:`Function ` bodies, initialization values for :ref:`globals ` and offsets of :ref:`element ` or :ref:`data ` segments are given as expressions, which are sequences of :ref:`instructions ` terminated by an |END| marker. + +.. math:: + \begin{array}{llll} + \production{expressions} & \expr &::=& + \instr^\ast~\END \\ + \end{array} + +In some places, validation :ref:`restricts ` expressions to be *constant*, which limits the set of allowable insructions. diff --git a/document/syntax/modules.rst b/document/syntax/modules.rst index 490a4f10ca..ad4a8a0529 100644 --- a/document/syntax/modules.rst +++ b/document/syntax/modules.rst @@ -86,25 +86,6 @@ Conventions * The meta variables :math:`x, y` ranges over indices in any of the other index spaces. -.. _syntax-expr: -.. index:: ! expression - pair: abstract syntax; expression - single: expression; constant - -Expressions -~~~~~~~~~~~ - -:ref:`Function ` bodies, initialization values for :ref:`globals ` and offsets of :ref:`element ` or :ref:`data ` segments are given as expressions, which are sequences of :ref:`instructions ` terminated by an |END| marker. - -.. math:: - \begin{array}{llll} - \production{expressions} & \expr &::=& - \instr^\ast~\END \\ - \end{array} - -In some places, validation :ref:`restricts ` expressions to be *constant*, which limits the set of allowable insructions. - - .. _syntax-type: .. index:: ! type definition, type index pair: abstract syntax; type definition diff --git a/document/syntax/types.rst b/document/syntax/types.rst index deb9fd354c..b53694c713 100644 --- a/document/syntax/types.rst +++ b/document/syntax/types.rst @@ -51,7 +51,7 @@ which is a sequence of values. .. math:: \begin{array}{llll} \production{result types} & \resulttype &::=& - \valtype^? \\ + [\valtype^?] \\ \end{array} .. note:: diff --git a/document/validation/conventions.rst b/document/validation/conventions.rst index a081117679..bb7944aa4a 100644 --- a/document/validation/conventions.rst +++ b/document/validation/conventions.rst @@ -161,9 +161,9 @@ and there is one respective rule for each relevant construct :math:`A` of the ab .. math:: \frac{ - C,\LABEL\,(t^?) \vdash \instr^\ast : [] \to [t^?] + C,\LABEL\,[t^?] \vdash \instr^\ast : [] \to [t^?] }{ - C \vdash \BLOCK~t^?~\instr^\ast~\END : [] \to [t^?] + C \vdash \BLOCK~[t^?]~\instr^\ast~\END : [] \to [t^?] } A |BLOCK| instruction is only valid when the instruction sequence in its body is. diff --git a/document/validation/instructions.rst b/document/validation/instructions.rst index 2b5e983dc4..46fbe9a320 100644 --- a/document/validation/instructions.rst +++ b/document/validation/instructions.rst @@ -4,8 +4,10 @@ Instructions ------------ -:ref:`Instructions ` are classified by :ref:`function types ` :math:`[t_1^\ast] \to [t_2^\ast]`. -The types describe which types :math:`t_1^\ast` of argument values an instruction pops off the operand stack and which types :math:`t_2^\ast` of result values it pushes back to it. +:ref:`Instructions ` are classified by :ref:`function types ` :math:`[t_1^\ast] \to [t_2^\ast]` +that describe how they manipulate the :ref:`operand stack `. +The types describe the required input stack with argument values of types :math:`t_1^\ast` that an instruction pops off +and the provided output stack with result values of types :math:`t_2^\ast` that it pushes back. .. note:: For example, the instruction :math:`\K{i32.add}` has type :math:`[\I32~\I32] \to [\I32]`, @@ -480,10 +482,10 @@ Control Instructions The |UNREACHABLE| instruction is :ref:`stack-polymorphic `. -:math:`\BLOCK~t^?~\instr^\ast~\END` -................................... +:math:`\BLOCK~[t^?]~\instr^\ast~\END` +..................................... -* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the :ref:`result type ` :math:`t^?` prepended to the |LABELS| vector. +* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the :ref:`result type ` :math:`[t^?]` prepended to the |LABELS| vector. * Under context :math:`C'`, the instruction sequence :math:`\instr^\ast` must be :ref:`valid ` with type :math:`[] \to [t^?]`. @@ -492,16 +494,16 @@ Control Instructions .. math:: \frac{ - C,\LABELS\,(t^?) \vdash \instr^\ast : [] \to [t^?] + C,\LABELS\,[t^?] \vdash \instr^\ast : [] \to [t^?] }{ - C \vdash \BLOCK~t^?~\instr^\ast~\END : [] \to [t^?] + C \vdash \BLOCK~[^?]~\instr^\ast~\END : [] \to [t^?] } -:math:`\LOOP~t^?~\instr^\ast~\END` -.................................. +:math:`\LOOP~[t^?]~\instr^\ast~\END` +.................................... -* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the empty :ref:`result type ` :math:`\epsilon` prepended to the |LABELS| vector. +* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the empty :ref:`result type ` :math:`[]` prepended to the |LABELS| vector. * Under context :math:`C'`, the instruction sequence :math:`\instr^\ast` must be :ref:`valid ` with type :math:`[] \to [t^?]`. @@ -510,16 +512,16 @@ Control Instructions .. math:: \frac{ - C,\LABELS\,(\epsilon) \vdash \instr^\ast : [] \to [t^?] + C,\LABELS\,[] \vdash \instr^\ast : [] \to [t^?] }{ - C \vdash \LOOP~t^?~\instr^\ast~\END : [] \to [t^?] + C \vdash \LOOP~[t^?]~\instr^\ast~\END : [] \to [t^?] } -:math:`\IF~t^?~\instr_1^\ast~\ELSE~\instr_2^\ast~\END` +:math:`\IF~[t^?]~\instr_1^\ast~\ELSE~\instr_2^\ast~\END` ...................................................... -* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the empty :ref:`result type ` :math:`\epsilon` prepended to the |LABELS| vector. +* Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the empty :ref:`result type ` :math:`[t^?]` prepended to the |LABELS| vector. * Under context :math:`C'`, the instruction sequence :math:`\instr_1^\ast` must be :ref:`valid ` with type :math:`[] \to [t^?]`. @@ -531,11 +533,11 @@ Control Instructions .. math:: \frac{ - C,\LABELS\,(t^?) \vdash \instr_1^\ast : [] \to [t^?] + C,\LABELS\,[t^?] \vdash \instr_1^\ast : [] \to [t^?] \qquad - C,\LABELS\,(t^?) \vdash \instr_2^\ast : [] \to [t^?] + C,\LABELS\,[t^?] \vdash \instr_2^\ast : [] \to [t^?] }{ - C \vdash \IF~t^?~\instr_1^\ast~\ELSE~\instr_2^\ast~\END : [\I32] \to [t^?] + C \vdash \IF~[t^?]~\instr_1^\ast~\ELSE~\instr_2^\ast~\END : [\I32] \to [t^?] } @@ -544,13 +546,13 @@ Control Instructions * The label :math:`C.\LABELS[l]` must be defined in the context. -* Let :math:`t^?` be the :ref:`result type ` :math:`C.\LABELS[l]`. +* Let :math:`[t^?]` be the :ref:`result type ` :math:`C.\LABELS[l]`. * Then the instruction is valid with type :math:`[t_1^\ast~t^?] \to [t_2^\ast]`, for any sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. .. math:: \frac{ - C.\LABELS[l] = t^? + C.\LABELS[l] = [t^?] }{ C \vdash \BR~l : [t_1^\ast~t^?] \to [t_2^\ast] } @@ -564,24 +566,24 @@ Control Instructions * The label :math:`C.\LABELS[l]` must be defined in the context. -* Let :math:`t^?` be the :ref:`result type ` :math:`C.\LABELS[l]`. +* Let :math:`[t^?]` be the :ref:`result type ` :math:`C.\LABELS[l]`. * Then the instruction is valid with type :math:`[t^?~\I32] \to [t^?]`. .. math:: \frac{ - C.\LABELS[l] = t^? + C.\LABELS[l] = [t^?] }{ C \vdash \BRIF~l : [t^?~\I32] \to [t^?] } -:math:`\BRTABLE~l^\ast~l'` -.......................... +:math:`\BRTABLE~l^\ast~l_N` +........................... * The label :math:`C.\LABELS[l]` must be defined in the context. -* Let :math:`t^?` be the :ref:`result type ` :math:`C.\LABELS[l']`. +* Let :math:`[t^?]` be the :ref:`result type ` :math:`C.\LABELS[l_N]`. * For all :math:`l_i` in :math:`l^\ast`, the label :math:`C.\LABELS[l_i]` must be defined in the context. @@ -593,11 +595,11 @@ Control Instructions .. math:: \frac{ - (C.\LABELS[l] = t^?)^\ast + (C.\LABELS[l] = [t^?])^\ast \qquad - C.\LABELS[l'] = t^? + C.\LABELS[l_N] = [t^?] }{ - C \vdash \BRTABLE~l^\ast~l' : [t_1^\ast~t^?] \to [t_2^\ast] + C \vdash \BRTABLE~l^\ast~l_N : [t_1^\ast~t^?] \to [t_2^\ast] } .. note:: @@ -609,13 +611,13 @@ Control Instructions * The label vector :math:`C.\LABELS` must not be empty in the context. -* Let :math:`t^?` be the :ref:`result type ` that is the last element of :math:`C.\LABELS`. +* Let :math:`[t^?]` be the :ref:`result type ` that is the last element of :math:`C.\LABELS`. * Then the instruction is valid with type :math:`[t_1^\ast~t^?] \to [t_2^\ast]`, for any sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. .. math:: \frac{ - C.\LABELS[|C.\LABELS|-1] = t^? + C.\LABELS[|C.\LABELS|-1] = [t^?] }{ C \vdash \RETURN : [t_1^\ast~t^?] \to [t_2^\ast] } @@ -684,13 +686,13 @@ Empty Instruction Sequence: :math:`\epsilon` } -Non-empty Instruction Sequence: :math:`\instr^\ast~\instr'` -........................................................... +Non-empty Instruction Sequence: :math:`\instr^\ast~\instr_N` +............................................................ * The instruction sequence :math:`\instr^\ast` must be valid with type :math:`[t_1^\ast] \to [t_2^\ast]`, for some sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. -* The instruction :math:`\instr'` must be valid with type :math:`[t^\ast] \to [t_3^\ast]`, +* The instruction :math:`\instr_N` must be valid with type :math:`[t^\ast] \to [t_3^\ast]`, for some sequences of :ref:`value types ` :math:`t^\ast` and :math:`t_3^\ast`. * There must be a sequence of :ref:`value types ` :math:`t_0^\ast`, @@ -702,7 +704,71 @@ Non-empty Instruction Sequence: :math:`\instr^\ast~\instr'` \frac{ C \vdash \instr^\ast : [t_1^\ast] \to [t_0^\ast~t^\ast] \qquad - C \vdash \instr' : [t^\ast] \to [t_3^\ast] + C \vdash \instr_N : [t^\ast] \to [t_3^\ast] }{ - C \vdash \instr^\ast~\instr' : [t_1^\ast] \to [t_0^\ast~t_3^\ast] + C \vdash \instr^\ast~\instr_N : [t_1^\ast] \to [t_0^\ast~t_3^\ast] } + + +.. _valid-expr: +.. index:: expression + pair: validation; expression + single: abstract syntax; expression + single: expression; constant + +Expressions +~~~~~~~~~~~ + +Expressions :math:`\expr` are classified by :ref:`result types ` of the form :math:`[t^?]`. + + +:math:`\instr^\ast~\END` +........................ + +* The :ref:`instruction sequence ` must be :ref:`valid ` with type :math:`[] \to [t^?]`, + for some optional :ref:`value type ` :math:`t^?`. + +* Then the expression is valid with :ref:`result type ` :math:`[t^?]`. + +.. math:: + \frac{ + C \vdash \instr^\ast : [] \to [t^?] + }{ + C \vdash \instr^\ast~\END : [t^?] + } + + +.. _valid-const: +.. index:: ! constant + +Constant Expressions +.................... + +* In a *constant* expression :math:`\instr^\ast~\END` all instructions in :math:`\instr^\ast` must be constant. + +* A constant instruction :math:`\instr` must be: + + * either of the form :math:`t.\CONST~c`, + + * or of the form :math:`\GETGLOBAL~x`, in which case :math:`C.\GLOBALS[x]` must be a :ref:`global type ` of the form :math:`\CONST~t`. + +.. math:: + \frac{ + (C \vdash \instr ~\F{const})^\ast + }{ + C \vdash \instr~\END ~\F{const} + } + \qquad + \frac{ + }{ + C \vdash t.\CONST~c ~\F{const} + } + \qquad + \frac{ + C.\GLOBALS[x] = \CONST~t + }{ + C \vdash \GETGLOBAL~x ~\F{const} + } + +.. note:: + The definition of constant expression may be extended in future versions of WebAssembly. diff --git a/document/validation/modules.rst b/document/validation/modules.rst index 7127052204..44b3fd563a 100644 --- a/document/validation/modules.rst +++ b/document/validation/modules.rst @@ -165,70 +165,6 @@ Limits :math:`\{ \MIN~n, \MAX~m^? \}` } -.. _valid-expr: -.. index:: expression - pair: validation; expression - single: abstract syntax; expression - single: expression; constant - -Expressions -~~~~~~~~~~~ - -Expressions :math:`\expr` are classified by :ref:`result types ` of the form :math:`t^?`. - - -:math:`\instr^\ast~\END` -........................ - -* The :ref:`instruction sequence ` must be :ref:`valid ` with type :math:`[] \to [t^?]`, - for some optional :ref:`value type ` :math:`t^?`. - -* Then the expression is valid with :ref:`result type ` :math:`t^?`. - -.. math:: - \frac{ - C \vdash \instr^\ast : [] \to [t^?] - }{ - C \vdash \instr^\ast~\END : t^? - } - - -.. _valid-const: -.. index:: ! constant - -Constant Expressions -.................... - -* In a *constant* expression :math:`\instr^\ast~\END` all instructions in :math:`\instr^\ast` must be constant. - -* A constant instruction :math:`\instr` must be: - - * either of the form :math:`t.\CONST~c`, - - * or of the form :math:`\GETGLOBAL~x`, in which case :math:`C.\GLOBALS[x]` must be a :ref:`global type ` of the form :math:`\CONST~t`. - -.. math:: - \frac{ - (C \vdash \instr ~\F{const})^\ast - }{ - C \vdash \instr~\END ~\F{const} - } - \qquad - \frac{ - }{ - C \vdash t.\CONST~c ~\F{const} - } - \qquad - \frac{ - C.\GLOBALS[x] = \CONST~t - }{ - C \vdash \GETGLOBAL~x ~\F{const} - } - -.. note:: - The definition of constant expression may be extended in future versions of WebAssembly. - - .. _valid-func: .. index:: function, local, function index, local index, type index, function type, value type, expression, import pair: abstract syntax; function @@ -339,7 +275,7 @@ Globals :math:`\global` are classified by :ref:`global types :math:`\{ \TYPE~\mut~t, \INIT~\expr \}` ....................................... -* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` :math:`t`. +* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` :math:`[t]`. * The expression :math:`\expr` must be :ref:`constant `. @@ -347,7 +283,7 @@ Globals :math:`\global` are classified by :ref:`global types .. math:: \frac{ - C \vdash \expr : t + C \vdash \expr : [t] \qquad C \vdash \expr ~\F{const} }{ @@ -376,7 +312,7 @@ Element segments :math:`\elem` are not classified by a type. * The :ref:`element type ` :math:`\elemtype` must be |ANYFUNC|. -* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` |I32|. +* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` :math:`[\I32]`. * The expression :math:`\expr` must be :ref:`constant `. @@ -390,7 +326,7 @@ Element segments :math:`\elem` are not classified by a type. \frac{ C.\TABLES[x] = \limits~\ANYFUNC \qquad - C \vdash \expr : \I32 + C \vdash \expr : [\I32] \qquad C \vdash \expr ~\F{const} \qquad @@ -417,7 +353,7 @@ Data segments :math:`\data` are not classified by any type. * The memory :math:`C.\MEMS[x]` must be defined in the context. -* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` |I32|. +* The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` :math:`[\I32]`. * The expression :math:`\expr` must be :ref:`constant `. @@ -428,7 +364,7 @@ Data segments :math:`\data` are not classified by any type. \frac{ C.\MEMS[x] = \limits \qquad - C \vdash \expr : \I32 + C \vdash \expr : [\I32] \qquad C \vdash \expr ~\F{const} }{ From 3d892b0f3223695ea1c4dbe1b3ff41f684b6fbfc Mon Sep 17 00:00:00 2001 From: Andreas Rossberg Date: Sat, 18 Mar 2017 03:45:06 +0100 Subject: [PATCH 03/15] Move modules --- document/syntax/index.rst | 2 +- document/validation/instructions.rst | 8 +- document/validation/modules.rst | 298 ++++++++++++++------------- 3 files changed, 156 insertions(+), 152 deletions(-) diff --git a/document/syntax/index.rst b/document/syntax/index.rst index f8fb18b8a6..0eb625b358 100644 --- a/document/syntax/index.rst +++ b/document/syntax/index.rst @@ -7,5 +7,5 @@ Structure conventions values types - modules instructions + modules diff --git a/document/validation/instructions.rst b/document/validation/instructions.rst index 46fbe9a320..9baba9f56c 100644 --- a/document/validation/instructions.rst +++ b/document/validation/instructions.rst @@ -1,4 +1,4 @@ -.. _valid-instr +.. _valid-instr: .. index:: function type, context Instructions @@ -203,7 +203,7 @@ In this section, the following grammar shorthands are adopted: pair: abstract syntax; instruction -.. _valid-parametric: +.. _valid-instr-parametric: .. index:: value type, polymorphism Parametric Instructions @@ -519,7 +519,7 @@ Control Instructions :math:`\IF~[t^?]~\instr_1^\ast~\ELSE~\instr_2^\ast~\END` -...................................................... +........................................................ * Let :math:`C'` be the same :ref:`context ` as :math:`C`, but with the empty :ref:`result type ` :math:`[t^?]` prepended to the |LABELS| vector. @@ -725,7 +725,7 @@ Expressions :math:`\expr` are classified by :ref:`result types ` must be :ref:`valid ` with type :math:`[] \to [t^?]`, +* The instruction sequence :math:`\instr^\ast` must be :ref:`valid ` with type :math:`[] \to [t^?]`, for some optional :ref:`value type ` :math:`t^?`. * Then the expression is valid with :ref:`result type ` :math:`[t^?]`. diff --git a/document/validation/modules.rst b/document/validation/modules.rst index 44b3fd563a..ea9aed0864 100644 --- a/document/validation/modules.rst +++ b/document/validation/modules.rst @@ -1,149 +1,9 @@ -.. _valid-module: -.. index:: modules, type definition, function type, function, table, memory, global, element, data, start function, import, export, context - pair: validation; module - single: abstract syntax; module - Modules ------- Modules are valid when all the definitions they contain are valid. To that end, each definition is classified with a suitable type. -A module is entirely *closed*, -that is, it only refers to definitions that appear in the module itself. -Consequently, no initial :ref:`context ` is required. -Instead, the context :math:`C` for validation of the module's content is constructed from the types of definitions in the module itself. - -* Let :math:`\module` be the module to validate. - -* Let :math:`C` be a :ref:`context ` where: - - * :math:`C.\TYPES` is :math:`\module.\TYPES`, - - * :math:`C.\FUNCS` is :math:`\funcs(\externtype_i^\ast)` concatenated with :math:`\functype_i^\ast`, - with the type sequences :math:`\externtype_i^\ast` and :math:`\functype_i^\ast` as determined below, - - * :math:`C.\TABLES` is :math:`\tables(\externtype_i^\ast)` concatenated with :math:`\tabletype_i^\ast`, - with the type sequences :math:`\externtype_i^\ast` and :math:`\tabletype_i^\ast` as determined below, - - * :math:`C.\MEMS` is :math:`\mems(\externtype_i^\ast)` concatenated with :math:`\memtype_i^\ast`, - with the type sequences :math:`\externtype_i^\ast` and :math:`\memtype_i^\ast` as determined below, - - * :math:`C.\GLOBALS` is :math:`\globals(\externtype_i^\ast)` concatenated with :math:`\globaltype_i^\ast`, - with the type sequences :math:`\externtype_i^\ast` and :math:`\globaltype_i^\ast` as determined below. - - * :math:`C.\LOCALS` is empty, - - * :math:`C.\LABELS` is empty. - -* Under the context :math:`C`: - - * For each :math:`\func_i` in :math:`\module.\FUNCS`, - the definition :math:`\func_i` must be :ref:`valid ` with a :ref:`function type ` :math:`\functype_i`. - - * For each :math:`\table_i` in :math:`\module.\TABLES`, - the definition :math:`\table_i` must be :ref:`valid ` with a :ref:`table type ` :math:`\tabletype_i`. - - * For each :math:`\mem_i` in :math:`\module.\MEMS`, - the definition :math:`\mem_i` must be :ref:`valid ` with a :ref:`memory type ` :math:`\memtype_i`. - - * For each :math:`\global_i` in :math:`\module.\GLOBALS`: - - * Let :math:`C_i` be the :ref:`context ` where :math:`C_i.\GLOBALS` is the sequence :math:`\globals(\externtype_i^\ast)` concatenated with :math:`\globaltype_0~\dots~\globaltype_{i-1}`, and all other fields are empty. - - * Under the context :math:`C_i`, - the definition :math:`\global_i` must be :ref:`valid ` with a :ref:`global type ` :math:`\globaltype_i`. - - * For each :math:`\elem_i` in :math:`\module.\ELEM`, - the segment :math:`\elem_i` must be :ref:`valid `. - - * For each :math:`\data_i` in :math:`\module.\DATA`, - the segment :math:`\elem_i` must be :ref:`valid `. - - * If :math:`\module.\START` is non-empty, - then :math:`\module.\START` must be :ref:`valid `. - - * For each :math:`\import_i` in :math:`\module.\IMPORTS`, - the segment :math:`\import_i` must be :ref:`valid ` with an :ref:`external type ` :math:`\externtype_i`. - - * For each :math:`\export_i` in :math:`\module.\EXPORTS`, - the segment :math:`\import_i` must be :ref:`valid ` with a :ref:`name ` :math:`\name_i`. - -* The length of :math:`C.\TABLES` must not be larger than :math:`1`. - -* The length of :math:`C.\MEMS` must not be larger than :math:`1`. - -* All export names :math:`\name_i` must be different. - -.. math:: - \frac{ - \begin{array}{@{}c@{}} - (C \vdash \func : \X{ft})^\ast - \quad - (C \vdash \table : \X{tt})^\ast - \quad - (C \vdash \mem : \X{mt})^\ast - \quad - (C_i \vdash \global : \X{gt})_i^\ast - \\ - (C \vdash \elem ~\F{ok})^\ast - \quad - (C \vdash \data ~\F{ok})^\ast - \quad - (C \vdash \start ~\F{ok})^? - \quad - (C \vdash \import : \X{it})^\ast - \quad - (C \vdash \export : \X{name})^\ast - \\ - \X{ift}^\ast = \funcs(\X{it}^\ast) - \qquad - \X{itt}^\ast = \tables(\X{it}^\ast) - \qquad - \X{imt}^\ast = \mems(\X{it}^\ast) - \qquad - \X{igt}^\ast = \globals(\X{it}^\ast) - \\ - C = \{ \TYPES~\functype^\ast, \FUNCS~\X{ift}^\ast~\X{ft}^\ast, \TABLES~\X{itt}^\ast~\X{tt}^\ast, \MEMS~\X{imt}^\ast~\X{mt}^\ast, \GLOBALS~\X{igt}^\ast~\X{gt}^\ast \} - \\ - |C.\TABLES| \leq 1 - \qquad - |C.\MEMS| \leq 1 - \qquad - \name^\ast ~\F{disjoint} - \qquad - (C_i = \{ \GLOBALS~[\X{igt}^\ast~\X{gt}^{i-1}] \})_i^\ast - \end{array} - }{ - \vdash \{ - \begin{array}[t]{@{}l@{}} - \TYPES~\functype^\ast, - \FUNCS~\func^\ast, - \TABLES~\table^\ast, - \MEMS~\mem^\ast, - \GLOBALS~\global^\ast, \\ - \ELEM~\elem^\ast, - \DATA~\data^\ast, - \START~\start^?, - \IMPORTS~\import^\ast, - \EXPORTS~\export^\ast \} ~\F{ok} \\ - \end{array} - } - -.. note:: - Most definitions in a module -- particularly functions -- are mutually recursive. - Consequently, the definition of the :ref:`context ` :math:`C` in this rule is recursive: - it depends on the outcome of validation of the function, table, memory, and global definitions contained in the module, - which itself depends on :math:`C`. - However, this recursion is just a specification device. - All types needed to construct :math:`C` can easily be determined from a simple pre-pass over the module that does not perform any actual validation. - - Globals, however, are not recursive. - The effect of defining the limited contexts :math:`C_i` for validating the module's globals is that their initialization expressions can only access imported and previously defined globals and nothing else. - -.. note:: - The restriction on the number of tables and memories may be lifted in future versions of WebAssembly. - Auxiliary Rules ~~~~~~~~~~~~~~~ @@ -176,7 +36,7 @@ Functions :math:`\func` are classified by :ref:`function types :math:`\{ \TYPE~x, \LOCALS~t^\ast, \BODY~\expr \}` -.................................................... +.................................................. * The type :math:`C.\TYPES[x]` must be defined in the context. @@ -189,7 +49,7 @@ Functions :math:`\func` are classified by :ref:`function types * the |LOCALS| set to the sequence of :ref:`value types ` :math:`t_1^\ast~t^\ast`, concatenating parameters and locals, - * the |LABELS| set to the singular sequence with :ref:`result type ` :math:`(t_2^\ast)`. + * the |LABELS| set to the singular sequence with :ref:`result type ` :math:`[t_2^\ast][t_1^\ast] \to [t_2^?]`. * Under the context :math:`C'`, the expression :math:`\expr` must be valid with type :math:`t_2^\ast`. @@ -200,9 +60,9 @@ Functions :math:`\func` are classified by :ref:`function types \frac{ C.\TYPES[x] = [t_1^\ast] \to [t_2^?] \qquad - C,\LOCALS\,t_1^\ast~t^\ast,\LABELS~(t_2^?) \vdash \expr : t_2^? + C,\LOCALS\,t_1^\ast~t^\ast,\LABELS~[t_2^?] \vdash \expr : [t_2^?] }{ - C \vdash \{ \TYPE~x, \LOCALS~t^\ast, \BODY~\expr \} : t_2^? + C \vdash \{ \TYPE~x, \LOCALS~t^\ast, \BODY~\expr \} : [t_1^\ast] \to [t_2^?] } .. note:: @@ -277,7 +137,7 @@ Globals :math:`\global` are classified by :ref:`global types * The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` :math:`[t]`. -* The expression :math:`\expr` must be :ref:`constant `. +* The expression :math:`\expr` must be :ref:`constant `. * Then the global definition is valid with type :math:`\mut~t`. @@ -314,7 +174,7 @@ Element segments :math:`\elem` are not classified by a type. * The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` :math:`[\I32]`. -* The expression :math:`\expr` must be :ref:`constant `. +* The expression :math:`\expr` must be :ref:`constant `. * For each :math:`y_i` in :math:`y^\ast`, the function :math:`C.\FUNCS[y]` must be defined in the context. @@ -355,7 +215,7 @@ Data segments :math:`\data` are not classified by any type. * The expression :math:`\expr` must be :ref:`valid ` with :ref:`result type ` :math:`[\I32]`. -* The expression :math:`\expr` must be :ref:`constant `. +* The expression :math:`\expr` must be :ref:`constant `. * Then the data segment is valid. @@ -581,3 +441,147 @@ Imports :math:`\import` and import descriptions :math:`\importdesc` are classifi }{ C \vdash \GLOBAL~t : \GLOBAL~t } + + +.. _valid-module: +.. index:: modules, type definition, function type, function, table, memory, global, element, data, start function, import, export, context + pair: validation; module + single: abstract syntax; module + +Modules +~~~~~~~ + +A module is entirely *closed*, +that is, it only refers to definitions that appear in the module itself. +Consequently, no initial :ref:`context ` is required. +Instead, the context :math:`C` for validation of the module's content is constructed from the types of definitions in the module itself. + +* Let :math:`\module` be the module to validate. + +* Let :math:`C` be a :ref:`context ` where: + + * :math:`C.\TYPES` is :math:`\module.\TYPES`, + + * :math:`C.\FUNCS` is :math:`\funcs(\externtype_i^\ast)` concatenated with :math:`\functype_i^\ast`, + with the type sequences :math:`\externtype_i^\ast` and :math:`\functype_i^\ast` as determined below, + + * :math:`C.\TABLES` is :math:`\tables(\externtype_i^\ast)` concatenated with :math:`\tabletype_i^\ast`, + with the type sequences :math:`\externtype_i^\ast` and :math:`\tabletype_i^\ast` as determined below, + + * :math:`C.\MEMS` is :math:`\mems(\externtype_i^\ast)` concatenated with :math:`\memtype_i^\ast`, + with the type sequences :math:`\externtype_i^\ast` and :math:`\memtype_i^\ast` as determined below, + + * :math:`C.\GLOBALS` is :math:`\globals(\externtype_i^\ast)` concatenated with :math:`\globaltype_i^\ast`, + with the type sequences :math:`\externtype_i^\ast` and :math:`\globaltype_i^\ast` as determined below. + + * :math:`C.\LOCALS` is empty, + + * :math:`C.\LABELS` is empty. + +* Under the context :math:`C`: + + * For each :math:`\func_i` in :math:`\module.\FUNCS`, + the definition :math:`\func_i` must be :ref:`valid ` with a :ref:`function type ` :math:`\functype_i`. + + * For each :math:`\table_i` in :math:`\module.\TABLES`, + the definition :math:`\table_i` must be :ref:`valid ` with a :ref:`table type ` :math:`\tabletype_i`. + + * For each :math:`\mem_i` in :math:`\module.\MEMS`, + the definition :math:`\mem_i` must be :ref:`valid ` with a :ref:`memory type ` :math:`\memtype_i`. + + * For each :math:`\global_i` in :math:`\module.\GLOBALS`: + + * Let :math:`C_i` be the :ref:`context ` where :math:`C_i.\GLOBALS` is the sequence :math:`\globals(\externtype_i^\ast)` concatenated with :math:`\globaltype_0~\dots~\globaltype_{i-1}`, and all other fields are empty. + + * Under the context :math:`C_i`, + the definition :math:`\global_i` must be :ref:`valid ` with a :ref:`global type ` :math:`\globaltype_i`. + + * For each :math:`\elem_i` in :math:`\module.\ELEM`, + the segment :math:`\elem_i` must be :ref:`valid `. + + * For each :math:`\data_i` in :math:`\module.\DATA`, + the segment :math:`\elem_i` must be :ref:`valid `. + + * If :math:`\module.\START` is non-empty, + then :math:`\module.\START` must be :ref:`valid `. + + * For each :math:`\import_i` in :math:`\module.\IMPORTS`, + the segment :math:`\import_i` must be :ref:`valid ` with an :ref:`external type ` :math:`\externtype_i`. + + * For each :math:`\export_i` in :math:`\module.\EXPORTS`, + the segment :math:`\import_i` must be :ref:`valid ` with a :ref:`name ` :math:`\name_i`. + +* The length of :math:`C.\TABLES` must not be larger than :math:`1`. + +* The length of :math:`C.\MEMS` must not be larger than :math:`1`. + +* All export names :math:`\name_i` must be different. + +.. math:: + \frac{ + \begin{array}{@{}c@{}} + (C \vdash \func : \X{ft})^\ast + \quad + (C \vdash \table : \X{tt})^\ast + \quad + (C \vdash \mem : \X{mt})^\ast + \quad + (C_i \vdash \global : \X{gt})_i^\ast + \\ + (C \vdash \elem ~\F{ok})^\ast + \quad + (C \vdash \data ~\F{ok})^\ast + \quad + (C \vdash \start ~\F{ok})^? + \quad + (C \vdash \import : \X{it})^\ast + \quad + (C \vdash \export : \X{name})^\ast + \\ + \X{ift}^\ast = \funcs(\X{it}^\ast) + \qquad + \X{itt}^\ast = \tables(\X{it}^\ast) + \qquad + \X{imt}^\ast = \mems(\X{it}^\ast) + \qquad + \X{igt}^\ast = \globals(\X{it}^\ast) + \\ + C = \{ \TYPES~\functype^\ast, \FUNCS~\X{ift}^\ast~\X{ft}^\ast, \TABLES~\X{itt}^\ast~\X{tt}^\ast, \MEMS~\X{imt}^\ast~\X{mt}^\ast, \GLOBALS~\X{igt}^\ast~\X{gt}^\ast \} + \\ + |C.\TABLES| \leq 1 + \qquad + |C.\MEMS| \leq 1 + \qquad + \name^\ast ~\F{disjoint} + \qquad + (C_i = \{ \GLOBALS~[\X{igt}^\ast~\X{gt}^{i-1}] \})_i^\ast + \end{array} + }{ + \vdash \{ + \begin{array}[t]{@{}l@{}} + \TYPES~\functype^\ast, + \FUNCS~\func^\ast, + \TABLES~\table^\ast, + \MEMS~\mem^\ast, + \GLOBALS~\global^\ast, \\ + \ELEM~\elem^\ast, + \DATA~\data^\ast, + \START~\start^?, + \IMPORTS~\import^\ast, + \EXPORTS~\export^\ast \} ~\F{ok} \\ + \end{array} + } + +.. note:: + Most definitions in a module -- particularly functions -- are mutually recursive. + Consequently, the definition of the :ref:`context ` :math:`C` in this rule is recursive: + it depends on the outcome of validation of the function, table, memory, and global definitions contained in the module, + which itself depends on :math:`C`. + However, this recursion is just a specification device. + All types needed to construct :math:`C` can easily be determined from a simple pre-pass over the module that does not perform any actual validation. + + Globals, however, are not recursive. + The effect of defining the limited contexts :math:`C_i` for validating the module's globals is that their initialization expressions can only access imported and previously defined globals and nothing else. + +.. note:: + The restriction on the number of tables and memories may be lifted in future versions of WebAssembly. From 525c1ccd067237ebf6547d70f0e564db28d3d15e Mon Sep 17 00:00:00 2001 From: rossberg-chromium Date: Mon, 20 Mar 2017 15:56:59 +0100 Subject: [PATCH 04/15] Add instruction index --- document/index.rst | 9 ++ document/syntax/instrindex.rst | 201 +++++++++++++++++++++++++++ document/validation/instructions.rst | 64 ++++++++- 3 files changed, 272 insertions(+), 2 deletions(-) create mode 100644 document/syntax/instrindex.rst diff --git a/document/index.rst b/document/index.rst index 83ba5cf642..d14440892b 100644 --- a/document/index.rst +++ b/document/index.rst @@ -20,6 +20,15 @@ WebAssembly Specification appendix-textual/index appendix-names/index +.. only:: latex + + .. toctree:: + :maxdepth: 2 + + syntax/instrindex + .. only:: html + * :ref:`instrindex` + * :ref:`genindex` diff --git a/document/syntax/instrindex.rst b/document/syntax/instrindex.rst new file mode 100644 index 0000000000..d6f5054267 --- /dev/null +++ b/document/syntax/instrindex.rst @@ -0,0 +1,201 @@ +.. _instrindex: + +Index of Instructions +--------------------- + +=================================== ================ ========================================== ======================================== ================ +Instruction Opcode Type Validation Execution +=================================== ================ ========================================== ======================================== ================ +:math:`\UNREACHABLE` :math:`\hex{00}` :math:`[t_1^\ast] \to [t_2^\ast]` :ref:`validation ` +:math:`\NOP` :math:`\hex{01}` :math:`[] \to []` :ref:`validation ` +:math:`\BLOCK~[t^?]` :math:`\hex{02}` :math:`[] \to [t^\ast]` :ref:`validation ` +:math:`\LOOP~[t^?]` :math:`\hex{03}` :math:`[] \to [t^\ast]` :ref:`validation ` +:math:`\IF~[t^?]` :math:`\hex{04}` :math:`[] \to [t^\ast]` :ref:`validation ` +:math:`\ELSE` :math:`\hex{05}` +(reserved) :math:`\hex{06}` +(reserved) :math:`\hex{07}` +(reserved) :math:`\hex{08}` +(reserved) :math:`\hex{09}` +(reserved) :math:`\hex{0A}` +:math:`\END` :math:`\hex{0B}` +:math:`\BR~l` :math:`\hex{0C}` :math:`[t_1^\ast~t^?] \to [t_2^\ast]` :ref:`validation ` +:math:`\BRIF~l` :math:`\hex{0D}` :math:`[t^?~\I32] \to [t^?]` :ref:`validation ` +:math:`\BRTABLE~l^\ast~l` :math:`\hex{0E}` :math:`[t_1^\ast~t^?~\I32] \to [t_2^\ast]` :ref:`validation ` +:math:`\RETURN` :math:`\hex{0F}` :math:`[t_1^\ast~t^?] \to [t_2^\ast]` :ref:`validation ` +:math:`\CALL~x` :math:`\hex{10}` :math:`[t_1^\ast] \to [t_2^\ast]` :ref:`validation ` +:math:`\CALLINDIRECT~x` :math:`\hex{11}` :math:`[t_1^\ast~\I32] \to [t_2^\ast]` :ref:`validation ` +(reserved) :math:`\hex{12}` +(reserved) :math:`\hex{13}` +(reserved) :math:`\hex{14}` +(reserved) :math:`\hex{15}` +(reserved) :math:`\hex{16}` +(reserved) :math:`\hex{17}` +(reserved) :math:`\hex{18}` +(reserved) :math:`\hex{19}` +:math:`\DROP` :math:`\hex{1A}` :math:`[t] \to []` :ref:`validation ` +:math:`\SELECT` :math:`\hex{1B}` :math:`[t~t~\I32] \to [t]` :ref:`validation ` +(reserved) :math:`\hex{1C}` +(reserved) :math:`\hex{1D}` +(reserved) :math:`\hex{1E}` +(reserved) :math:`\hex{1F}` +:math:`\GETLOCAL~x` :math:`\hex{20}` :math:`[] \to [t]` :ref:`validation ` +:math:`\SETLOCAL~x` :math:`\hex{21}` :math:`[t] \to []` :ref:`validation ` +:math:`\TEELOCAL~x` :math:`\hex{22}` :math:`[t] \to [t]` :ref:`validation ` +:math:`\GETGLOBAL~x` :math:`\hex{23}` :math:`[\I32] \to [t]` :ref:`validation ` +:math:`\SETGLOBAL~x` :math:`\hex{24}` :math:`[\I32~t] \to []` :ref:`validation ` +(reserved) :math:`\hex{25}` +(reserved) :math:`\hex{26}` +(reserved) :math:`\hex{27}` +:math:`\I32.\LOAD~\memarg` :math:`\hex{28}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I64.\LOAD~\memarg` :math:`\hex{29}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\F32.\LOAD~\memarg` :math:`\hex{2A}` :math:`[\I32] \to [\F32]` :ref:`validation ` +:math:`\F64.\LOAD~\memarg` :math:`\hex{2B}` :math:`[\I32] \to [\F64]` :ref:`validation ` +:math:`\I32.\LOAD\K{8\_s}~\memarg` :math:`\hex{2C}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\LOAD\K{8\_u}~\memarg` :math:`\hex{2D}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\LOAD\K{16\_s}~\memarg` :math:`\hex{2E}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\LOAD\K{16\_u}~\memarg` :math:`\hex{2F}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I64.\LOAD\K{8\_s}~\memarg` :math:`\hex{30}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\I64.\LOAD\K{8\_u}~\memarg` :math:`\hex{31}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\I64.\LOAD\K{16\_s}~\memarg` :math:`\hex{32}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\I64.\LOAD\K{16\_u}~\memarg` :math:`\hex{33}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\I64.\LOAD\K{32\_s}~\memarg` :math:`\hex{34}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\I64.\LOAD\K{32\_u}~\memarg` :math:`\hex{35}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\I32.\STORE~\memarg` :math:`\hex{36}` :math:`[\I32~\I32] \to []` :ref:`validation ` +:math:`\I64.\STORE~\memarg` :math:`\hex{37}` :math:`[\I32~\I64] \to []` :ref:`validation ` +:math:`\F32.\STORE~\memarg` :math:`\hex{38}` :math:`[\I32~\F32] \to []` :ref:`validation ` +:math:`\F64.\STORE~\memarg` :math:`\hex{39}` :math:`[\I32~\F64] \to []` :ref:`validation ` +:math:`\I32.\STORE\K{8}~\memarg` :math:`\hex{3A}` :math:`[\I32~\I32] \to []` :ref:`validation ` +:math:`\I32.\STORE\K{16}~\memarg` :math:`\hex{3B}` :math:`[\I32~\I32] \to []` :ref:`validation ` +:math:`\I64.\STORE\K{8}~\memarg` :math:`\hex{3C}` :math:`[\I32~\I64] \to []` :ref:`validation ` +:math:`\I64.\STORE\K{16}~\memarg` :math:`\hex{3D}` :math:`[\I32~\I64] \to []` :ref:`validation ` +:math:`\I64.\STORE\K{32}~\memarg` :math:`\hex{3E}` :math:`[\I32~\I64] \to []` :ref:`validation ` +:math:`\CURRENTMEMORY` :math:`\hex{3F}` :math:`[] \to [\I32]` :ref:`validation ` +:math:`\GROWMEMORY` :math:`\hex{40}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\CONST~\i32` :math:`\hex{41}` :math:`[] \to [\I32]` :ref:`validation ` +:math:`\I64.\CONST~\i64` :math:`\hex{42}` :math:`[] \to [\I64]` :ref:`validation ` +:math:`\F32.\CONST~\f32` :math:`\hex{43}` :math:`[] \to [\F32]` :ref:`validation ` +:math:`\F64.\CONST~\f64` :math:`\hex{44}` :math:`[] \to [\F64]` :ref:`validation ` +:math:`\I32.\K{eqz}` :math:`\hex{45}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{eq}` :math:`\hex{46}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{ne}` :math:`\hex{47}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{lt\_s}` :math:`\hex{48}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{lt\_u}` :math:`\hex{49}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{gt\_s}` :math:`\hex{4A}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{gt\_u}` :math:`\hex{4B}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{le\_s}` :math:`\hex{4C}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{le\_u}` :math:`\hex{4D}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{ge\_s}` :math:`\hex{4E}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{ge\_u}` :math:`\hex{4F}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{eqz}` :math:`\hex{50}` :math:`[\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{eq}` :math:`\hex{51}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{ne}` :math:`\hex{52}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{lt\_s}` :math:`\hex{53}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{lt\_u}` :math:`\hex{54}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{gt\_s}` :math:`\hex{55}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{gt\_u}` :math:`\hex{56}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{le\_s}` :math:`\hex{57}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{le\_u}` :math:`\hex{58}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{ge\_s}` :math:`\hex{59}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{ge\_u}` :math:`\hex{5A}` :math:`[\I64~\I64] \to [\I32]` :ref:`validation ` +:math:`\F32.\K{eq}` :math:`\hex{5B}` :math:`[\F32~\F32] \to [\I32]` :ref:`validation ` +:math:`\F32.\K{ne}` :math:`\hex{5C}` :math:`[\F32~\F32] \to [\I32]` :ref:`validation ` +:math:`\F32.\K{lt}` :math:`\hex{5D}` :math:`[\F32~\F32] \to [\I32]` :ref:`validation ` +:math:`\F32.\K{gt}` :math:`\hex{5E}` :math:`[\F32~\F32] \to [\I32]` :ref:`validation ` +:math:`\F32.\K{le}` :math:`\hex{5F}` :math:`[\F32~\F32] \to [\I32]` :ref:`validation ` +:math:`\F32.\K{ge}` :math:`\hex{60}` :math:`[\F32~\F32] \to [\I32]` :ref:`validation ` +:math:`\F64.\K{eq}` :math:`\hex{61}` :math:`[\F64~\F64] \to [\I32]` :ref:`validation ` +:math:`\F64.\K{ne}` :math:`\hex{62}` :math:`[\F64~\F64] \to [\I32]` :ref:`validation ` +:math:`\F64.\K{lt}` :math:`\hex{63}` :math:`[\F64~\F64] \to [\I32]` :ref:`validation ` +:math:`\F64.\K{gt}` :math:`\hex{64}` :math:`[\F64~\F64] \to [\I32]` :ref:`validation ` +:math:`\F64.\K{le}` :math:`\hex{65}` :math:`[\F64~\F64] \to [\I32]` :ref:`validation ` +:math:`\F64.\K{ge}` :math:`\hex{66}` :math:`[\F64~\F64] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{clz}` :math:`\hex{67}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{ctz}` :math:`\hex{68}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{popcnt}` :math:`\hex{69}` :math:`[\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{add}` :math:`\hex{6A}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{sub}` :math:`\hex{6B}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{mul}` :math:`\hex{6C}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{div\_s}` :math:`\hex{6D}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{div\_u}` :math:`\hex{6E}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{rem\_s}` :math:`\hex{6F}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{rem\_u}` :math:`\hex{70}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{and}` :math:`\hex{71}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{or}` :math:`\hex{72}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{xor}` :math:`\hex{73}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{shl}` :math:`\hex{74}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{shr\_s}` :math:`\hex{75}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{shr\_u}` :math:`\hex{76}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{rotl}` :math:`\hex{77}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{rotr}` :math:`\hex{78}` :math:`[\I32~\I32] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{clz}` :math:`\hex{79}` :math:`[\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{ctz}` :math:`\hex{7A}` :math:`[\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{popcnt}` :math:`\hex{7B}` :math:`[\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{add}` :math:`\hex{7C}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{sub}` :math:`\hex{7D}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{mul}` :math:`\hex{7E}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{div\_s}` :math:`\hex{7F}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{div\_u}` :math:`\hex{80}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{rem\_s}` :math:`\hex{81}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{rem\_u}` :math:`\hex{82}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{and}` :math:`\hex{83}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{or}` :math:`\hex{84}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{xor}` :math:`\hex{85}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{shl}` :math:`\hex{86}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{shr\_s}` :math:`\hex{87}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{shr\_u}` :math:`\hex{88}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{rotl}` :math:`\hex{89}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{rotr}` :math:`\hex{8A}` :math:`[\I64~\I64] \to [\I64]` :ref:`validation ` +:math:`\F32.\K{abs}` :math:`\hex{8B}` :math:`[\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{neg}` :math:`\hex{8C}` :math:`[\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{ceil}` :math:`\hex{8D}` :math:`[\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{floor}` :math:`\hex{8E}` :math:`[\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{trunc}` :math:`\hex{8F}` :math:`[\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{nearest}` :math:`\hex{90}` :math:`[\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{sqrt}` :math:`\hex{91}` :math:`[\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{add}` :math:`\hex{92}` :math:`[\F32~\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{sub}` :math:`\hex{93}` :math:`[\F32~\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{mul}` :math:`\hex{94}` :math:`[\F32~\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{div}` :math:`\hex{95}` :math:`[\F32~\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{min}` :math:`\hex{96}` :math:`[\F32~\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{max}` :math:`\hex{97}` :math:`[\F32~\F32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{copysign}` :math:`\hex{98}` :math:`[\F32~\F32] \to [\F32]` :ref:`validation ` +:math:`\F64.\K{abs}` :math:`\hex{99}` :math:`[\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{neg}` :math:`\hex{9A}` :math:`[\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{ceil}` :math:`\hex{9B}` :math:`[\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{floor}` :math:`\hex{9C}` :math:`[\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{trunc}` :math:`\hex{9D}` :math:`[\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{nearest}` :math:`\hex{9E}` :math:`[\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{sqrt}` :math:`\hex{9F}` :math:`[\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{add}` :math:`\hex{A0}` :math:`[\F64~\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{sub}` :math:`\hex{A1}` :math:`[\F64~\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{mul}` :math:`\hex{A2}` :math:`[\F64~\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{div}` :math:`\hex{A3}` :math:`[\F64~\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{min}` :math:`\hex{A4}` :math:`[\F64~\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{max}` :math:`\hex{A5}` :math:`[\F64~\F64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{copysign}` :math:`\hex{A6}` :math:`[\F64~\F64] \to [\F64]` :ref:`validation ` +:math:`\I32.\K{wrap/i64}` :math:`\hex{A7}` :math:`[\I64] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{trunc\_s/f32}` :math:`\hex{A8}` :math:`[\F32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{trunc\_u/f32}` :math:`\hex{A9}` :math:`[\F32] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{trunc\_s/f64}` :math:`\hex{AA}` :math:`[\F64] \to [\I32]` :ref:`validation ` +:math:`\I32.\K{trunc\_u/f64}` :math:`\hex{AB}` :math:`[\F64] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{extend\_s/i32}` :math:`\hex{AC}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{extend\_u/i32}` :math:`\hex{AD}` :math:`[\I32] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{trunc\_s/f32}` :math:`\hex{AE}` :math:`[\F32] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{trunc\_u/f32}` :math:`\hex{AF}` :math:`[\F32] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{trunc\_s/f64}` :math:`\hex{B0}` :math:`[\F64] \to [\I64]` :ref:`validation ` +:math:`\I64.\K{trunc\_u/f64}` :math:`\hex{B1}` :math:`[\F64] \to [\I64]` :ref:`validation ` +:math:`\F32.\K{convert\_s/i32}` :math:`\hex{B2}` :math:`[\I32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{convert\_u/i32}` :math:`\hex{B3}` :math:`[\I32] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{convert\_s/i64}` :math:`\hex{B4}` :math:`[\I64] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{convert\_u/i64}` :math:`\hex{B5}` :math:`[\I64] \to [\F32]` :ref:`validation ` +:math:`\F32.\K{demote/f64}` :math:`\hex{B6}` :math:`[\F64] \to [\F32]` :ref:`validation ` +:math:`\F64.\K{convert\_s/i32}` :math:`\hex{B7}` :math:`[\I32] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{convert\_u/i32}` :math:`\hex{B8}` :math:`[\I32] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{convert\_s/i64}` :math:`\hex{B9}` :math:`[\I64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{convert\_u/i64}` :math:`\hex{BA}` :math:`[\I64] \to [\F64]` :ref:`validation ` +:math:`\F64.\K{promote/f32}` :math:`\hex{BB}` :math:`[\F32] \to [\F64]` :ref:`validation ` +:math:`\I32.\K{reinterpret/f32}` :math:`\hex{BC}` :math:`[\F32] \to [\I32]` :ref:`validation ` +:math:`\I64.\K{reinterpret/f64}` :math:`\hex{BD}` :math:`[\F64] \to [\I64]` :ref:`validation ` +:math:`\F32.\K{reinterpret/i32}` :math:`\hex{BE}` :math:`[\I32] \to [\F32]` :ref:`validation ` +:math:`\F64.\K{reinterpret/i64}` :math:`\hex{BF}` :math:`[\I64] \to [\F64]` :ref:`validation ` +=================================== ================ ========================================== ======================================== ================ diff --git a/document/validation/instructions.rst b/document/validation/instructions.rst index 239c749ef1..aee3379663 100644 --- a/document/validation/instructions.rst +++ b/document/validation/instructions.rst @@ -126,6 +126,8 @@ In this section, the following grammar shorthands are adopted: \end{array} +.. _valid-const: + :math:`t \K{.const}~c` ...................... @@ -138,6 +140,8 @@ In this section, the following grammar shorthands are adopted: } +.. _valid-unop: + :math:`t\K{.}\unop` ................... @@ -150,6 +154,8 @@ In this section, the following grammar shorthands are adopted: } +.. _valid-binop: + :math:`t\K{.}\binop` .................... @@ -162,6 +168,8 @@ In this section, the following grammar shorthands are adopted: } +.. _valid-testop: + :math:`t\K{.}\testop` ..................... @@ -174,6 +182,8 @@ In this section, the following grammar shorthands are adopted: } +.. _valid-relop: + :math:`t\K{.}\relop` .................... @@ -186,6 +196,8 @@ In this section, the following grammar shorthands are adopted: } +.. _valid-cvtop: + :math:`t_2\K{.}\cvtop/t_1` .......................... @@ -209,6 +221,8 @@ In this section, the following grammar shorthands are adopted: Parametric Instructions ~~~~~~~~~~~~~~~~~~~~~~~ +.. _valid-drop: + :math:`\DROP` ............. @@ -221,6 +235,8 @@ Parametric Instructions } +.. _valid-select: + :math:`\SELECT` ............... @@ -244,6 +260,8 @@ Parametric Instructions Variable Instructions ~~~~~~~~~~~~~~~~~~~~~ +.. _valid-get_local: + :math:`\GETLOCAL~x` ................... @@ -261,6 +279,8 @@ Variable Instructions } +.. _valid-set_local: + :math:`\SETLOCAL~x` ................... @@ -278,6 +298,8 @@ Variable Instructions } +.. _valid-tee_local: + :math:`\TEELOCAL~x` ................... @@ -295,6 +317,8 @@ Variable Instructions } +.. _valid-get_global: + :math:`\GETGLOBAL~x` .................... @@ -312,6 +336,8 @@ Variable Instructions } +.. _valid-set_global: + :math:`\SETGLOBAL~x` .................... @@ -340,6 +366,8 @@ Variable Instructions Memory Instructions ~~~~~~~~~~~~~~~~~~~ +.. _valid-load: + :math:`t\K{.load}~\memarg` .......................... @@ -359,6 +387,8 @@ Memory Instructions } +.. _valid-loadn: + :math:`t\K{.load}N\K{\_}\sx~\memarg` .................................... @@ -378,6 +408,8 @@ Memory Instructions } +.. _valid-store: + :math:`t\K{.store}~\memarg` ........................... @@ -397,6 +429,8 @@ Memory Instructions } +.. _valid-storen: + :math:`t\K{.store}N~\memarg` ............................ @@ -416,6 +450,8 @@ Memory Instructions } +.. _valid-current_memory: + :math:`\CURRENTMEMORY` ...................... @@ -431,6 +467,8 @@ Memory Instructions } +.. _valid-grow_memory: + :math:`\GROWMEMORY` ................... @@ -455,6 +493,8 @@ Memory Instructions Control Instructions ~~~~~~~~~~~~~~~~~~~~ +.. _valid-nop: + :math:`\NOP` ............ @@ -467,6 +507,8 @@ Control Instructions } +.. _valid-unreachable: + :math:`\UNREACHABLE` .................... @@ -482,6 +524,8 @@ Control Instructions The |UNREACHABLE| instruction is :ref:`stack-polymorphic `. +.. _valid-block: + :math:`\BLOCK~[t^?]~\instr^\ast~\END` ..................................... @@ -500,6 +544,8 @@ Control Instructions } +.. _valid-loop: + :math:`\LOOP~[t^?]~\instr^\ast~\END` .................................... @@ -518,6 +564,8 @@ Control Instructions } +.. _valid-if: + :math:`\IF~[t^?]~\instr_1^\ast~\ELSE~\instr_2^\ast~\END` ........................................................ @@ -541,6 +589,8 @@ Control Instructions } +.. _valid-br: + :math:`\BR~l` ............. @@ -561,6 +611,8 @@ Control Instructions The |BR| instruction is :ref:`stack-polymorphic `. +.. _valid-br_if: + :math:`\BRIF~l` ............... @@ -578,6 +630,8 @@ Control Instructions } +.. _valid-br_table: + :math:`\BRTABLE~l^\ast~l_N` ........................... @@ -591,7 +645,7 @@ Control Instructions * For all :math:`l_i` in :math:`l^\ast`, :math:`C.\LABELS[l_i]` must be :math:`t^?`. -* Then the instruction is valid with type :math:`[t_1^\ast~t^?] \to [t_2^\ast]`, for any sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. +* Then the instruction is valid with type :math:`[t_1^\ast~t^?~\I32] \to [t_2^\ast]`, for any sequences of :ref:`value types ` :math:`t_1^\ast` and :math:`t_2^\ast`. .. math:: \frac{ @@ -599,13 +653,15 @@ Control Instructions \qquad C.\LABELS[l_N] = [t^?] }{ - C \vdash \BRTABLE~l^\ast~l_N : [t_1^\ast~t^?] \to [t_2^\ast] + C \vdash \BRTABLE~l^\ast~l_N : [t_1^\ast~t^?~\I32] \to [t_2^\ast] } .. note:: The |BRTABLE| instruction is :ref:`stack-polymorphic `. +.. _valid-return: + :math:`\RETURN` ............... @@ -626,6 +682,8 @@ Control Instructions The |RETURN| instruction is :ref:`stack-polymorphic `. +.. _valid-call: + :math:`\CALL~x` ............... @@ -641,6 +699,8 @@ Control Instructions } +.. _valid-call_indirect: + :math:`\CALLINDIRECT~x` ....................... From 5f92ccf69ff227ea6c12ed956f2cc545cc47b210 Mon Sep 17 00:00:00 2001 From: rossberg-chromium Date: Mon, 20 Mar 2017 16:11:19 +0100 Subject: [PATCH 05/15] Fix xref --- document/math.def | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/document/math.def b/document/math.def index 46aa686e19..c177e9752c 100644 --- a/document/math.def +++ b/document/math.def @@ -201,4 +201,4 @@ .. |memarg| mathdef:: \xref{syntax/instructions}{syntax-memarg}{\X{memarg}} .. |instr| mathdef:: \xref{syntax/instructions}{syntax-instr}{\X{instr}} -.. |expr| mathdef:: \xref{syntax/modules}{syntax-expr}{\X{expr}} +.. |expr| mathdef:: \xref{syntax/instructions}{syntax-expr}{\X{expr}} From f250abe6795914db61936343d91555d228e902b6 Mon Sep 17 00:00:00 2001 From: rossberg-chromium Date: Mon, 20 Mar 2017 16:19:06 +0100 Subject: [PATCH 06/15] Fix typing rule for global imports --- document/validation/modules.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/document/validation/modules.rst b/document/validation/modules.rst index ea9aed0864..d6a2213d48 100644 --- a/document/validation/modules.rst +++ b/document/validation/modules.rst @@ -439,7 +439,7 @@ Imports :math:`\import` and import descriptions :math:`\importdesc` are classifi .. math:: \frac{ }{ - C \vdash \GLOBAL~t : \GLOBAL~t + C \vdash \GLOBAL~\CONST~t : \GLOBAL~\CONST~t } From bbb26c42b62096baff86089767531c3b1f108a85 Mon Sep 17 00:00:00 2001 From: rossberg-chromium Date: Tue, 21 Mar 2017 14:15:14 +0100 Subject: [PATCH 07/15] Add PLDI paper --- papers/pldi2017.pdf | Bin 0 -> 2485248 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 papers/pldi2017.pdf diff --git a/papers/pldi2017.pdf b/papers/pldi2017.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4af4d7323750cd8ea54b98055013c38f420624a8 GIT binary patch literal 2485248 zcmbT8W0d6UvgXUSU0JqmS9KX(?6RxNwryKowr$&8wrv~J``okd>{)X^oSFO->s=Y~ z#y>w~uICp|B$kfIYy6G^N9y60xuqj=;31PR}IU4iv 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