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spec-wasmfx.patch
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spec-wasmfx.patch
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diff --git a/.github/workflows/ci-interpreter.yml b/.github/workflows/ci-interpreter.yml
deleted file mode 100644
index 8f7b02c0..00000000
--- a/.github/workflows/ci-interpreter.yml
+++ /dev/null
@@ -1,36 +0,0 @@
-name: CI for interpreter & tests
-
-on:
- push:
- branches: [ main ]
- paths: [ interpreter/**, test/** ]
-
- pull_request:
- branches: [ main ]
- paths: [ interpreter/**, test/** ]
-
- # Allows you to run this workflow manually from the Actions tab
- workflow_dispatch:
-
-jobs:
- interpreter:
- runs-on: ubuntu-latest
- steps:
- - name: Checkout repo
- uses: actions/checkout@v2
- - name: Setup OCaml
- uses: ocaml/setup-ocaml@v2
- with:
- ocaml-compiler: 4.14.x
- - name: Setup OCaml tools
- run: opam install --yes ocamlbuild.0.14.0 ocamlfind.1.9.5 js_of_ocaml.4.0.0 js_of_ocaml-ppx.4.0.0
- - name: Setup Node.js
- uses: actions/setup-node@v2
- with:
- node-version: 19.x
- - name: Build interpreter
- run: cd interpreter && opam exec make
- - name: Run tests
- # TODO: disable node.js run until it fully implements proposal
- # run: cd interpreter && opam exec make JS=node ci
- run: cd interpreter && opam exec make ci
diff --git a/.github/workflows/ci-spec.yml b/.github/workflows/ci-spec.yml
deleted file mode 100644
index 7610b33b..00000000
--- a/.github/workflows/ci-spec.yml
+++ /dev/null
@@ -1,101 +0,0 @@
-name: CI for specs
-
-on:
- push:
- branches: [ main ]
- paths: [ document/** ]
-
- pull_request:
- branches: [ main ]
- paths: [ document/** ]
-
- # Allows you to run this workflow manually from the Actions tab
- workflow_dispatch:
-
-jobs:
- build-core-spec:
- runs-on: ubuntu-latest
- steps:
- - name: Checkout repo
- uses: actions/checkout@v2
- with:
- submodules: "recursive"
- - name: Setup Node.js
- uses: actions/setup-node@v3
- with:
- node-version: 16
- - name: Setup Bikeshed
- run: pip install bikeshed && bikeshed update
- - name: Setup TexLive
- run: sudo apt-get update -y && sudo apt-get install -y latexmk texlive-latex-recommended texlive-latex-extra texlive-fonts-recommended
- - name: Setup Sphinx
- run: pip install six && pip install sphinx==5.1.0
- - name: Build main spec
- run: cd document/core && make main
- - name: Run Bikeshed
- run: cd document/core && make bikeshed
- - name: Upload artifact
- uses: actions/upload-artifact@v2
- with:
- name: core-rendered
- path: document/core/_build/html
-
- build-js-api-spec:
- runs-on: ubuntu-latest
- steps:
- - name: Checkout repo
- uses: actions/checkout@v2
- - name: Setup Bikeshed
- run: pip install bikeshed && bikeshed update
- - name: Run Bikeshed
- run: bikeshed spec "document/js-api/index.bs" "document/js-api/index.html"
- - name: Upload artifact
- uses: actions/upload-artifact@v2
- with:
- name: js-api-rendered
- path: document/js-api/index.html
-
- build-web-api-spec:
- runs-on: ubuntu-latest
- steps:
- - name: Checkout repo
- uses: actions/checkout@v2
- - name: Setup Bikeshed
- run: pip install bikeshed && bikeshed update
- - name: Run Bikeshed
- run: bikeshed spec "document/web-api/index.bs" "document/web-api/index.html"
- - name: Upload artifact
- uses: actions/upload-artifact@v2
- with:
- name: web-api-rendered
- path: document/web-api/index.html
-
- publish-spec:
- runs-on: ubuntu-latest
- needs: [build-core-spec, build-js-api-spec, build-web-api-spec]
- steps:
- - name: Checkout repo
- uses: actions/checkout@v2
- - name: Create output directory
- run: mkdir _output && cp document/index.html _output/index.html
- - name: Download core spec artifact
- uses: actions/download-artifact@v2
- with:
- name: core-rendered
- path: _output/core
- - name: Download JS API spec artifact
- uses: actions/download-artifact@v2
- with:
- name: js-api-rendered
- path: _output/js-api
- - name: Download Web API spec artifact
- uses: actions/download-artifact@v2
- with:
- name: web-api-rendered
- path: _output/web-api
- - name: Publish to GitHub Pages
- if: github.ref == 'refs/heads/main'
- uses: peaceiris/actions-gh-pages@v3
- with:
- publish_dir: ./_output
- github_token: ${{ secrets.GITHUB_TOKEN }}
diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
new file mode 100644
index 00000000..e20e3db4
--- /dev/null
+++ b/.github/workflows/main.yml
@@ -0,0 +1,105 @@
+name: CI
+
+on:
+ push:
+ branches: [ main ]
+ pull_request:
+ branches: [ main ]
+
+ # Allows you to run this workflow manually from the Actions tab
+ workflow_dispatch:
+
+jobs:
+ ref-interpreter:
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@v3
+ - name: Setup OCaml
+ uses: ocaml/setup-ocaml@v2
+ with:
+ ocaml-compiler: 4.13.x
+ - run: opam install --yes ocamlbuild.0.14.0
+ - name: Setup Node.js
+ uses: actions/setup-node@v1
+ with:
+ node-version: 19.x
+ # TODO: disable node.js run until it fully implements proposal
+ # - run: cd interpreter && opam exec make JS=node all
+ - run: cd interpreter && opam exec make all
+
+ ref-interpreter-js-library:
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@v2
+ - name: Setup OCaml
+ uses: ocaml/setup-ocaml@v2
+ with:
+ ocaml-compiler: 4.13.x
+ - run: opam install --yes ocamlbuild.0.14.0 ocamlfind.1.9.5 js_of_ocaml.4.0.0 js_of_ocaml-ppx.4.0.0
+ - run: cd interpreter && opam exec make wast.js
+
+ build-js-api-spec:
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@v2
+ - run: pip install bikeshed && bikeshed update
+ - run: bikeshed spec "document/js-api/index.bs" "document/js-api/index.html"
+ - uses: actions/upload-artifact@v2
+ with:
+ name: js-api-rendered
+ path: document/js-api/index.html
+
+ build-web-api-spec:
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@v2
+ - run: pip install bikeshed && bikeshed update
+ - run: bikeshed spec "document/web-api/index.bs" "document/web-api/index.html"
+ - uses: actions/upload-artifact@v2
+ with:
+ name: web-api-rendered
+ path: document/web-api/index.html
+
+ build-core-spec:
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@v2
+ with:
+ submodules: "recursive"
+ - uses: actions/setup-node@v3
+ with:
+ node-version: 16
+ - run: pip install bikeshed && bikeshed update
+ - run: pip install six
+ - run: sudo apt-get update -y && sudo apt-get install -y latexmk texlive-latex-recommended texlive-latex-extra texlive-fonts-recommended
+ - run: pip install sphinx==5.1.0
+ - run: cd document/core && make all
+ - uses: actions/upload-artifact@v2
+ with:
+ name: core-api-rendered
+ path: document/core/_build/html
+
+ publish-spec:
+ runs-on: ubuntu-latest
+ needs: [build-core-spec, build-js-api-spec, build-web-api-spec]
+ steps:
+ - uses: actions/checkout@v2
+ - run: mkdir _output && cp document/index.html _output/index.html
+ - uses: actions/download-artifact@v2
+ with:
+ name: js-api-rendered
+ path: _output/js-api
+ - uses: actions/download-artifact@v2
+ with:
+ name: web-api-rendered
+ path: _output/web-api
+ - uses: actions/download-artifact@v2
+ with:
+ name: core-api-rendered
+ path: _output/core
+ - name: Publish HTML to GitHub Pages
+ if: github.ref == 'refs/heads/main'
+ uses: peaceiris/actions-gh-pages@v3
+ with:
+ publish_dir: ./_output
+ github_token: ${{ secrets.GITHUB_TOKEN }}
diff --git a/.github/workflows/mirror-to-master.yml b/.github/workflows/mirror.yml
similarity index 81%
rename from .github/workflows/mirror-to-master.yml
rename to .github/workflows/mirror.yml
index 7849af75..5c470757 100644
--- a/.github/workflows/mirror-to-master.yml
+++ b/.github/workflows/mirror.yml
@@ -1,5 +1,3 @@
-name: Mirror main branch to master branch
-
on:
push:
branches:
@@ -10,7 +8,8 @@ jobs:
runs-on: ubuntu-latest
name: Mirror main branch to master branch
steps:
- - name: Mirror branch
+ - name: Mirror action step
+ id: mirror
uses: google/[email protected]
with:
github-token: ${{ secrets.GITHUB_TOKEN }}
diff --git a/README.md b/README.md
index b204e475..d9d4412d 100644
--- a/README.md
+++ b/README.md
@@ -1,18 +1,20 @@
-[](https://github.com/WebAssembly/function-references/actions/workflows/ci-spec.yml)
-[](https://github.com/WebAssembly/function-references/actions/workflows/ci-interpreter.yml)
+# Typed Continuations Proposal for WebAssembly
-# Function Reference Types Proposal for WebAssembly
+This repository is a clone of
+[github.com/WebAssembly/spec/](https://github.com/WebAssembly/spec/).
+It is meant for discussion, prototype specification and implementation
+of a proposal to add support for different patterns of non-local
+control flow to WebAssembly.
-This repository is a clone of [github.com/WebAssembly/spec/](https://github.com/WebAssembly/spec/).
-It is meant for discussion, prototype specification and implementation of a proposal to add support for basic function reference types to WebAssembly.
+The proposal is fully implemented as part of the reference interpreter.
-* See the [overview](proposals/function-references/Overview.md) for a summary of the proposal.
+* See the [explainer](proposals/continuations/Explainer.md) for a high-level summary of the proposal.
-* See the [modified spec](https://webassembly.github.io/function-references/core) for details.
+* See the [overview](proposals/continuations/Overview.md) for a more formal description of the proposal.
-The repository is now based on the [bulk operations proposal](proposals/bulk-memory-operations/Overview.md) and includes all respective changes.
+* See the [examples](proposals/continuations/examples) for Wasm code for implementing various different features including lightweight threads, actors, and async/await.
-Original README from upstream repository follows...
+Original `README` from upstream repository follows.
# spec
diff --git a/document/core/.gitignore b/document/core/.gitignore
index b932ec28..d21e55e3 100644
--- a/document/core/.gitignore
+++ b/document/core/.gitignore
@@ -1,3 +1,4 @@
_build
_static
document/*.pyc
+appendix/index-instructions.rst
diff --git a/document/core/Makefile b/document/core/Makefile
index 8a3650ec..d8b357c7 100644
--- a/document/core/Makefile
+++ b/document/core/Makefile
@@ -89,14 +89,12 @@ bikeshed-keep:
echo Downloaded Bikeshed.
-GENERATED = appendix/index-instructions.rst
-.INTERMEDIATE: $(GENERATED)
-
-%.rst: %.py
- (cd `dirname $@`; ./`basename $^`)
+.PHONY: index
+index:
+ (cd appendix; ./index-instructions.py)
.PHONY: pdf
-pdf: $(GENERATED) latexpdf
+pdf: index latexpdf
mkdir -p $(BUILDDIR)/html/$(DOWNLOADDIR)
ln -f $(BUILDDIR)/latex/$(NAME).pdf $(BUILDDIR)/html/$(DOWNLOADDIR)/$(NAME).pdf
@@ -105,10 +103,10 @@ pdf: $(GENERATED) latexpdf
clean:
rm -rf $(BUILDDIR)
rm -rf $(STATICDIR)
- rm -f $(GENERATED)
+ rm -f appendix/index-instructions.rst
.PHONY: html
-html: $(GENERATED)
+html: index
$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
for file in `ls $(BUILDDIR)/html/*.html`; \
do \
@@ -124,34 +122,28 @@ html: $(GENERATED)
@echo "Build finished. The HTML pages are in `pwd`/$(BUILDDIR)/html/."
.PHONY: dirhtml
-dirhtml: $(GENERATED)
+dirhtml:
$(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
@echo
@echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
.PHONY: singlehtml
-singlehtml: $(GENERATED)
+singlehtml:
$(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml
@echo
@echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml."
.PHONY: bikeshed
-bikeshed: $(GENERATED)
+bikeshed:
$(SPHINXBUILD) -b singlehtml -c util/bikeshed \
$(ALLSPHINXOPTS) $(BUILDDIR)/bikeshed_singlehtml
- python3 util/bikeshed_fixup.py $(BUILDDIR)/bikeshed_singlehtml/index.html \
+ python util/bikeshed_fixup.py $(BUILDDIR)/bikeshed_singlehtml/index.html \
>$(BUILDDIR)/bikeshed_singlehtml/index_fixed.html
- @echo ==== Showing contents of _build/bikeshed_singlehtml/index_fixed.html ====
- @head -n10 _build/bikeshed_singlehtml/index_fixed.html
- @echo ... skipping $$(expr `cat _build/bikeshed_singlehtml/index_fixed.html | wc -l` - 20) lines ...
- @tail -n10 _build/bikeshed_singlehtml/index_fixed.html
- @echo
- @echo =========================================================================
mkdir -p $(BUILDDIR)/bikeshed_mathjax/
bikeshed spec index.bs $(BUILDDIR)/bikeshed_mathjax/index.html
mkdir -p $(BUILDDIR)/html/bikeshed/
(cd util/katex/ && yarn && yarn build && npm install --only=prod)
- python3 util/mathjax2katex.py $(BUILDDIR)/bikeshed_mathjax/index.html \
+ python util/mathjax2katex.py $(BUILDDIR)/bikeshed_mathjax/index.html \
>$(BUILDDIR)/html/bikeshed/index.html
mkdir -p $(BUILDDIR)/html/bikeshed/katex/dist/
cp -r util/katex/dist/* $(BUILDDIR)/html/bikeshed/katex/dist/
@@ -268,7 +260,7 @@ latex:
"(use \`make latexpdf' here to do that automatically)."
.PHONY: latexpdf
-latexpdf: $(GENERATED)
+latexpdf:
$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
@echo "Running LaTeX files through pdflatex..."
$(MAKE) -C $(BUILDDIR)/latex LATEXMKOPTS=" </dev/null" all-pdf >$(BUILDDIR)/latex/LOG 2>&1 || cat $(BUILDDIR)/latex/LOG
diff --git a/document/core/appendix/embedding.rst b/document/core/appendix/embedding.rst
index c94f8753..dda85673 100644
--- a/document/core/appendix/embedding.rst
+++ b/document/core/appendix/embedding.rst
@@ -167,7 +167,7 @@ Modules
:math:`\F{module\_imports}(\module) : (\name, \name, \externtype)^\ast`
.......................................................................
-1. Pre-condition: :math:`\module` is :ref:`valid <valid-module>` with the external import types :math:`\externtype^\ast` and external export types :math:`{\externtype'}^\ast`.
+1. Pre-condition: :math:`\module` is :ref:`valid <valid-module>` with the :ref:`dynamic <syntax-type-dyn>` external import types :math:`\externtype^\ast` and external export types :math:`{\externtype'}^\ast`.
2. Let :math:`\import^\ast` be the :ref:`imports <syntax-import>` :math:`\module.\MIMPORTS`.
@@ -179,7 +179,7 @@ Modules
5. Return the concatenation of all :math:`\X{result}_i`, in index order.
-6. Post-condition: each :math:`\externtype_i` is :ref:`valid <valid-externtype>` under the empty :ref:`context <context>`.
+6. Post-condition: each :ref:`dynamic <syntax-type-dyn>` :math:`\externtype_i` is :ref:`valid <valid-externtype>`.
.. math::
~ \\
@@ -195,7 +195,7 @@ Modules
:math:`\F{module\_exports}(\module) : (\name, \externtype)^\ast`
................................................................
-1. Pre-condition: :math:`\module` is :ref:`valid <valid-module>` with the external import types :math:`\externtype^\ast` and external export types :math:`{\externtype'}^\ast`.
+1. Pre-condition: :math:`\module` is :ref:`valid <valid-module>` with the :ref:`dynamic <syntax-type-dyn>` external import types :math:`\externtype^\ast` and external export types :math:`{\externtype'}^\ast`.
2. Let :math:`\export^\ast` be the :ref:`exports <syntax-export>` :math:`\module.\MEXPORTS`.
@@ -207,7 +207,7 @@ Modules
5. Return the concatenation of all :math:`\X{result}_i`, in index order.
-6. Post-condition: each :math:`\externtype'_i` is :ref:`valid <valid-externtype>` under the empty :ref:`context <context>`.
+6. Post-condition: each :ref:`dynamic <syntax-type-dyn>` :math:`\externtype'_i` is :ref:`valid <valid-externtype>`.
.. math::
~ \\
@@ -246,6 +246,29 @@ Module Instances
\end{array}
+.. index:: type, type instance, function type
+.. _embed-type:
+
+Types
+~~~~~
+
+.. _embed-type-alloc:
+
+:math:`\F{type\_alloc}(\store, \functype) : (\store, \typeaddr)`
+...........................................................................
+
+1. Pre-condition: the :ref:`dynamic <syntax-type-dyn>` :math:`\functype` is :ref:`valid <valid-functype>`.
+
+2. Let :math:`\typeaddr` be the result of :ref:`allocating a type <alloc-type>` in :math:`\store` for :ref:`function type <syntax-functype>` :math:`\functype`.
+
+3. Return the new store paired with :math:`\typeaddr`.
+
+.. math::
+ \begin{array}{lclll}
+ \F{type\_alloc}(S, \X{ft}) &=& (S', \X{a}) && (\iff \alloctype(S, \X{ft}) = S', \X{a}) \\
+ \end{array}
+
+
.. index:: function, host function, function address, function instance, function type, store
.. _embed-func:
@@ -254,12 +277,12 @@ Functions
.. _embed-func-alloc:
-:math:`\F{func\_alloc}(\store, \functype, \hostfunc) : (\store, \funcaddr)`
+:math:`\F{func\_alloc}(\store, \typeaddr, \hostfunc) : (\store, \funcaddr)`
...........................................................................
-1. Pre-condition: the :math:`\functype` is :ref:`valid <valid-functype>` under the empty :ref:`context <context>`.
+1. Pre-condition: the :ref:`dynamic <syntax-type-dyn>` :math:`\functype` is :ref:`valid <valid-functype>`.
-2. Let :math:`\funcaddr` be the result of :ref:`allocating a host function <alloc-func>` in :math:`\store` with :ref:`function type <syntax-functype>` :math:`\functype` and host function code :math:`\hostfunc`.
+2. Let :math:`\funcaddr` be the result of :ref:`allocating a host function <alloc-func>` in :math:`\store` with :ref:`type address <syntax-typeaddr>` :math:`\typeaddr` and host function code :math:`\hostfunc`.
3. Return the new store paired with :math:`\funcaddr`.
@@ -279,15 +302,15 @@ Functions
:math:`\F{func\_type}(\store, \funcaddr) : \functype`
.....................................................
-1. Let :math:`\functype` be the :ref:`function type <syntax-functype>` :math:`S.\SFUNCS[a].\FITYPE`.
+1. Let :math:`\typeaddr` be the :ref:`type address <syntax-typeaddr>` :math:`S.\SFUNCS[a].\FITYPE`.
-2. Return :math:`\functype`.
+2. Return :math:`S.\STYPES[\typeaddr]`.
-3. Post-condition: the returned :ref:`function type <syntax-functype>` is :ref:`valid <valid-functype>`.
+3. Post-condition: the returned :ref:`dynamic <syntax-type-dyn>` :ref:`function type <syntax-functype>` is :ref:`valid <valid-functype>`.
.. math::
\begin{array}{lclll}
- \F{func\_type}(S, a) &=& S.\SFUNCS[a].\FITYPE \\
+ \F{func\_type}(S, a) &=& S.\STYPES[S.\SFUNCS[a].\FITYPE] \\
\end{array}
@@ -327,7 +350,7 @@ Tables
:math:`\F{table\_alloc}(\store, \tabletype) : (\store, \tableaddr, \reff)`
..........................................................................
-1. Pre-condition: the :math:`\tabletype` is :ref:`valid <valid-tabletype>` under the empty :ref:`context <context>`.
+1. Pre-condition: the :ref:`dynamic <syntax-type-dyn>` :math:`\tabletype` is :ref:`valid <valid-tabletype>`.
2. Let :math:`\tableaddr` be the result of :ref:`allocating a table <alloc-table>` in :math:`\store` with :ref:`table type <syntax-tabletype>` :math:`\tabletype` and initialization value :math:`\reff`.
@@ -346,7 +369,7 @@ Tables
1. Return :math:`S.\STABLES[a].\TITYPE`.
-2. Post-condition: the returned :ref:`table type <syntax-tabletype>` is :ref:`valid <valid-tabletype>` under the empty :ref:`context <context>`.
+2. Post-condition: the returned :ref:`dynamic <syntax-type-dyn>` :ref:`table type <syntax-tabletype>` is :ref:`valid <valid-tabletype>`.
.. math::
\begin{array}{lclll}
@@ -439,7 +462,7 @@ Memories
:math:`\F{mem\_alloc}(\store, \memtype) : (\store, \memaddr)`
................................................................
-1. Pre-condition: the :math:`\memtype` is :ref:`valid <valid-memtype>` under the empty :ref:`context <context>`.
+1. Pre-condition: the :ref:`dynamic <syntax-type-dyn>` :math:`\memtype` is :ref:`valid <valid-memtype>`.
2. Let :math:`\memaddr` be the result of :ref:`allocating a memory <alloc-mem>` in :math:`\store` with :ref:`memory type <syntax-memtype>` :math:`\memtype`.
@@ -458,7 +481,7 @@ Memories
1. Return :math:`S.\SMEMS[a].\MITYPE`.
-2. Post-condition: the returned :ref:`memory type <syntax-memtype>` is :ref:`valid <valid-memtype>` under the empty :ref:`context <context>`.
+2. Post-condition: the returned :ref:`dynamic <syntax-type-dyn>` :ref:`memory type <syntax-memtype>` is :ref:`valid <valid-memtype>`.
.. math::
\begin{array}{lclll}
@@ -552,7 +575,7 @@ Globals
:math:`\F{global\_alloc}(\store, \globaltype, \val) : (\store, \globaladdr)`
............................................................................
-1. Pre-condition: the :math:`\globaltype` is :ref:`valid <valid-globaltype>` under the empty :ref:`context <context>`.
+1. Pre-condition: the :ref:`dynamic <syntax-type-dyn>` :math:`\globaltype` is :ref:`valid <valid-globaltype>`.
2. Let :math:`\globaladdr` be the result of :ref:`allocating a global <alloc-global>` in :math:`\store` with :ref:`global type <syntax-globaltype>` :math:`\globaltype` and initialization value :math:`\val`.
@@ -571,7 +594,7 @@ Globals
1. Return :math:`S.\SGLOBALS[a].\GITYPE`.
-2. Post-condition: the returned :ref:`global type <syntax-globaltype>` is :ref:`valid <valid-globaltype>` under the empty :ref:`context <context>`.
+2. Post-condition: the returned :ref:`dynamic <syntax-type-dyn>` :ref:`global type <syntax-globaltype>` is :ref:`valid <valid-globaltype>`.
.. math::
\begin{array}{lclll}
diff --git a/document/core/appendix/index-rules.rst b/document/core/appendix/index-rules.rst
index 64f91a51..ba337a76 100644
--- a/document/core/appendix/index-rules.rst
+++ b/document/core/appendix/index-rules.rst
@@ -29,7 +29,7 @@ Construct Judgement
:ref:`Instruction <valid-instr>` :math:`S;C \vdashinstr \instr : \functype`
:ref:`Instruction sequence <valid-instr-seq>` :math:`S;C \vdashinstrseq \instr^\ast : \functype`
:ref:`Expression <valid-expr>` :math:`C \vdashexpr \expr : \resulttype`
-:ref:`Function <valid-func>` :math:`C \vdashfunc \func : \functype`
+:ref:`Function <valid-func>` :math:`C \vdashfunc \func : \typeid`
:ref:`Local <valid-local>` :math:`C \vdashlocal \local : \localtype`
:ref:`Table <valid-table>` :math:`C \vdashtable \table : \tabletype`
:ref:`Memory <valid-mem>` :math:`C \vdashmem \mem : \memtype`
@@ -58,6 +58,7 @@ Construct Judgement
:ref:`Value <valid-val>` :math:`S \vdashval \val : \valtype`
:ref:`Result <valid-result>` :math:`S \vdashresult \result : \resulttype`
:ref:`External value <valid-externval>` :math:`S \vdashexternval \externval : \externtype`
+:ref:`Type instance <valid-typeinst>` :math:`S \vdashtypeinst \typeinst \ok`
:ref:`Function instance <valid-funcinst>` :math:`S \vdashfuncinst \funcinst : \functype`
:ref:`Table instance <valid-tableinst>` :math:`S \vdashtableinst \tableinst : \tabletype`
:ref:`Memory instance <valid-meminst>` :math:`S \vdashmeminst \meminst : \memtype`
@@ -121,6 +122,7 @@ Store Extension
=============================================== ===============================================================================
Construct Judgement
=============================================== ===============================================================================
+:ref:`Type instance <extend-typeinst>` :math:`\vdashtypeinstextends \typeinst_1 \extendsto \typeinst_2`
:ref:`Function instance <extend-funcinst>` :math:`\vdashfuncinstextends \funcinst_1 \extendsto \funcinst_2`
:ref:`Table instance <extend-tableinst>` :math:`\vdashtableinstextends \tableinst_1 \extendsto \tableinst_2`
:ref:`Memory instance <extend-meminst>` :math:`\vdashmeminstextends \meminst_1 \extendsto \meminst_2`
diff --git a/document/core/appendix/properties.rst b/document/core/appendix/properties.rst
index 45e3084b..cd52c399 100644
--- a/document/core/appendix/properties.rst
+++ b/document/core/appendix/properties.rst
@@ -26,14 +26,14 @@ In order to state and prove soundness precisely, the typing rules must be extend
Results
~~~~~~~
-:ref:`Results <syntax-result>` can be classified by :ref:`result types <syntax-resulttype>` as follows.
+:ref:`Results <syntax-result>` can be classified by :ref:`dynamic <syntax-type-dyn>` :ref:`result types <syntax-resulttype>` as follows.
:ref:`Results <syntax-result>` :math:`\val^\ast`
................................................
* For each :ref:`value <syntax-val>` :math:`\val_i` in :math:`\val^\ast`:
- * The value :math:`\val_i` is :ref:`valid <valid-val>` with some :ref:`value type <syntax-valtype>` :math:`t_i`.
+ * The value :math:`\val_i` is :ref:`valid <valid-val>` with some :ref:`dynamic <syntax-type-dyn>` :ref:`value type <syntax-valtype>` :math:`t_i`.
* Let :math:`t^\ast` be the concatenation of all :math:`t_i`.
@@ -50,11 +50,11 @@ Results
:ref:`Results <syntax-result>` :math:`\TRAP`
............................................
-* The result is valid with :ref:`result type <syntax-resulttype>` :math:`[t^\ast]`, for any :ref:`valid <valid-resulttype>` :ref:`closed <type-closed>` :ref:`result types <syntax-resulttype>`.
+* The result is valid with :ref:`result type <syntax-resulttype>` :math:`[t^\ast]`, for any :ref:`valid <valid-resulttype>` :ref:`dynamic <syntax-type-dyn>` :ref:`result types <syntax-resulttype>`.
.. math::
\frac{
- \vdashresulttype [t^\ast] \ok
+ S \vdashresulttype [t^\ast] \ok
}{
S \vdashresult \TRAP : [t^\ast]
}
@@ -80,7 +80,9 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
:ref:`Store <syntax-store>` :math:`S`
.....................................
-* Each :ref:`function instance <syntax-funcinst>` :math:`\funcinst_i` in :math:`S.\SFUNCS` must be :ref:`valid <valid-funcinst>` with some :ref:`function type <syntax-functype>` :math:`\functype_i`.
+* Each :ref:`type instance <syntax-typeinst>` :math:`\typeinst_i` in :math:`S.\STYPES` must be :ref:`valid <valid-functype>` in a store :math:`S'_i` only containing the sequence :math:`\typeinst_0 \dots \typeinst_{i-1}` of preceding type instances.
+
+* Each :ref:`function instance <syntax-funcinst>` :math:`\funcinst_i` in :math:`S.\SFUNCS` must be :ref:`valid <valid-funcinst>` with some :ref:`type address <syntax-typeaddr>` :math:`\typeaddr_i`.
* Each :ref:`table instance <syntax-tableinst>` :math:`\tableinst_i` in :math:`S.\STABLES` must be :ref:`valid <valid-tableinst>` with some :ref:`table type <syntax-tabletype>` :math:`\tabletype_i`.
@@ -98,7 +100,11 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
~\\[-1ex]
\frac{
\begin{array}{@{}c@{}}
- (S \vdashfuncinst \funcinst : \functype)^\ast
+ a^n = 0 \dots (n-1)
+ \qquad
+ (\{\STYPES~\typeinst^n[0 \slice a]\} \vdashtypeinst \typeinst \ok)^n
+ \\
+ (S \vdashfuncinst \funcinst : \typeaddr)^\ast
\qquad
(S \vdashtableinst \tableinst : \tabletype)^\ast
\\
@@ -112,6 +118,7 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
\\
S = \{
\begin{array}[t]{@{}l@{}}
+ \STYPES~\typeinst^n,
\SFUNCS~\funcinst^\ast,
\SGLOBALS~\globalinst^\ast, \\
\STABLES~\tableinst^\ast,
@@ -128,49 +135,63 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
The validity condition on type instances ensures the absence of cyclic types.
+.. index:: function type, type instance
+.. _valid-typeinst:
+
+:ref:`Type Instances <syntax-typeinst>` :math:`\functype`
+.........................................................
+
+* The :ref:`dynamic <syntax-type-dyn>` :ref:`function type <syntax-functype>` :math:`\functype` must be :ref:`valid <valid-functype>`.
+
+* Then it is valid as a type instance.
+
+.. math::
+ \frac{
+ S \vdashfunctype \functype \ok
+ }{
+ S \vdashtypeinst \functype \ok
+ }
+
+
.. index:: function type, function instance
.. _valid-funcinst:
-:ref:`Function Instances <syntax-funcinst>` :math:`\{\FITYPE~\functype, \FIMODULE~\moduleinst, \FICODE~\func\}`
+:ref:`Function Instances <syntax-funcinst>` :math:`\{\FITYPE~\typeaddr, \FIMODULE~\moduleinst, \FICODE~\func\}`
.......................................................................................................................
-* The :ref:`function type <syntax-functype>` :math:`\functype` must be :ref:`valid <valid-functype>` under an empty :ref:`context <context>`.
-
* The :ref:`module instance <syntax-moduleinst>` :math:`\moduleinst` must be :ref:`valid <valid-moduleinst>` with some :ref:`context <context>` :math:`C`.
* Under :ref:`context <context>` :math:`C`:
- * The :ref:`function <syntax-func>` :math:`\func` must be :ref:`valid <valid-func>` with some :ref:`function type <syntax-functype>` :math:`\functype'`.
+ * The :ref:`function <syntax-func>` :math:`\func` must be :ref:`valid <valid-func>` with :ref:`static <syntax-type-stat>` :ref:`type identifier <syntax-typeid>` :math:`\typeidx`.
- * The :ref:`function type <syntax-functype>` :math:`\functype'` must :ref:`match <match-functype>` :math:`\functype`.
+ * The :ref:`static <syntax-type-stat>` :ref:`heap type <syntax-heaptype>` :math:`\typeidx` must :ref:`match <match-heaptype>` the :ref:`dynamic <syntax-type-dyn>` :ref:`heap type <syntax-heaptype>` :math:`\typeaddr`.
-* Then the function instance is valid with :ref:`function type <syntax-functype>` :math:`\functype`.
+* Then the function instance is valid with :ref:`type address <syntax-typeaddr>` :math:`\typeaddr`.
.. math::
\frac{
\begin{array}{@{}c@{}}
- \vdashfunctype \functype \ok
- \qquad
S \vdashmoduleinst \moduleinst : C
\\
- C \vdashfunc \func : \functype'
+ C \vdashfunc \func : \typeidx
\qquad
- C \vdashfunctypematch \functype' \matchesfunctype \functype
+ C; S \vdashheaptypematch \typeidx \matchesheaptype \typeaddr
\end{array}
}{
- S \vdashfuncinst \{\FITYPE~\functype, \FIMODULE~\moduleinst, \FICODE~\func\} : \functype
+ S \vdashfuncinst \{\FITYPE~\typeaddr, \FIMODULE~\moduleinst, \FICODE~\func\} : \typeaddr
}
.. index:: function type, function instance, host function
.. _valid-hostfuncinst:
-:ref:`Host Function Instances <syntax-funcinst>` :math:`\{\FITYPE~\functype, \FIHOSTCODE~\X{hf}\}`
+:ref:`Host Function Instances <syntax-funcinst>` :math:`\{\FITYPE~\typeaddr, \FIHOSTCODE~\X{hf}\}`
..................................................................................................
-* The :ref:`function type <syntax-functype>` :math:`\functype` must be :ref:`valid <valid-functype>` under an empty :ref:`context <context>`.
+* The :ref:`type instance <syntax-typeinst>` :math:`S.\STYPES[\typeaddr]` must exist.
-* Let :math:`[t_1^\ast] \toF [t_2^\ast]` be the :ref:`function type <syntax-functype>` :math:`\functype`.
+* Let the :ref:`dynamic <syntax-type-dyn>` :ref:`function type <syntax-functype>` :math:`[t_1^\ast] \toF [t_2^\ast]` be the :ref:`type instance <syntax-typeinst>` :math:`S.\STYPES[\typeaddr]`.
* For every :ref:`valid <valid-store>` :ref:`store <syntax-store>` :math:`S_1` :ref:`extending <extend-store>` :math:`S` and every sequence :math:`\val^\ast` of :ref:`values <syntax-val>` whose :ref:`types <valid-val>` coincide with :math:`t_1^\ast`:
@@ -182,12 +203,12 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
* Or :math:`R` consists of a :ref:`valid <valid-store>` :ref:`store <syntax-store>` :math:`S_2` :ref:`extending <extend-store>` :math:`S_1` and a :ref:`result <syntax-result>` :math:`\result` whose :ref:`type <valid-result>` coincides with :math:`[t_2^\ast]`.
-* Then the function instance is valid with :ref:`function type <syntax-functype>` :math:`\functype`.
+* Then the function instance is valid with :ref:`type address <syntax-typeaddr>` :math:`\typeaddr`.
.. math::
\frac{
\begin{array}[b]{@{}l@{}}
- \vdashfunctype [t_1^\ast] \toF [t_2^\ast] \ok \\
+ S.\STYPES[\typeaddr] = [t_1^\ast] \toF [t_2^\ast] \\
\end{array}
\quad
\begin{array}[b]{@{}l@{}}
@@ -206,7 +227,7 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
R = (S_2; \result)
\end{array}
}{
- S \vdashfuncinst \{\FITYPE~[t_1^\ast] \to [t_2^\ast], \FIHOSTCODE~\X{hf}\} : [t_1^\ast] \to [t_2^\ast]
+ S \vdashfuncinst \{\FITYPE~\typeaddr, \FIHOSTCODE~\X{hf}\} : \typeaddr
}
.. note::
@@ -223,7 +244,7 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
:ref:`Table Instances <syntax-tableinst>` :math:`\{ \TITYPE~(\limits~t), \TIELEM~\reff^\ast \}`
...............................................................................................
-* The :ref:`table type <syntax-tabletype>` :math:`\limits~t` must be :ref:`valid <valid-tabletype>` under the empty :ref:`context <context>`.
+* The :ref:`dynamic <syntax-type-dyn>` :ref:`table type <syntax-tabletype>` :math:`\limits~t` must be :ref:`valid <valid-tabletype>`.
* The length of :math:`\reff^\ast` must equal :math:`\limits.\LMIN`.
@@ -237,13 +258,13 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
.. math::
\frac{
- \vdashtabletype \limits~t \ok
+ S \vdashtabletype \limits~t \ok
\qquad
n = \limits.\LMIN
\qquad
(S \vdash \reff : t')^n
\qquad
- (\vdashreftypematch t' \matchesvaltype t)^n
+ (S \vdashreftypematch t' \matchesvaltype t)^n
}{
S \vdashtableinst \{ \TITYPE~(\limits~t), \TIELEM~\reff^n \} : \limits~t
}
@@ -255,7 +276,7 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
:ref:`Memory Instances <syntax-meminst>` :math:`\{ \MITYPE~\limits, \MIDATA~b^\ast \}`
......................................................................................
-* The :ref:`memory type <syntax-memtype>` :math:`\limits` must be :ref:`valid <valid-memtype>` under the empty :ref:`context <context>`.
+* The :ref:`dynamic <syntax-type-dyn>` :ref:`memory type <syntax-memtype>` :math:`\limits` must be :ref:`valid <valid-memtype>`.
* The length of :math:`b^\ast` must equal :math:`\limits.\LMIN` multiplied by the :ref:`page size <page-size>` :math:`64\,\F{Ki}`.
@@ -263,7 +284,7 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
.. math::
\frac{
- \vdashmemtype \limits \ok
+ S \vdashmemtype \limits \ok
\qquad
n = \limits.\LMIN \cdot 64\,\F{Ki}
}{
@@ -277,7 +298,7 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
:ref:`Global Instances <syntax-globalinst>` :math:`\{ \GITYPE~(\mut~t), \GIVALUE~\val \}`
.........................................................................................
-* The :ref:`global type <syntax-globaltype>` :math:`\mut~t` must be :ref:`valid <valid-globaltype>` under the empty :ref:`context <context>`.
+* The :ref:`dynamic <syntax-type-dyn>` :ref:`global type <syntax-globaltype>` :math:`\mut~t` must be :ref:`valid <valid-globaltype>`.
* The :ref:`value <syntax-val>` :math:`\val` must be :ref:`valid <valid-val>` with some :ref:`value type <syntax-valtype>` :math:`t'`.
@@ -287,11 +308,11 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
.. math::
\frac{
- \vdashglobaltype \mut~t \ok
+ S \vdashglobaltype \mut~t \ok
\qquad
S \vdashval \val : t'
\qquad
- \vdashvaltypematch t' \matchesvaltype t
+ S \vdashvaltypematch t' \matchesvaltype t
}{
S \vdashglobalinst \{ \GITYPE~(\mut~t), \GIVALUE~\val \} : \mut~t
}
@@ -303,7 +324,7 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
:ref:`Element Instances <syntax-eleminst>` :math:`\{ \EIELEM~\X{fa}^\ast \}`
............................................................................
-* The :ref:`reference type <syntax-reftype>` :math:`t` must be :ref:`valid <valid-reftype>` under the empty :ref:`context <context>`.
+* The :ref:`dynamic <syntax-type-dyn>` :ref:`reference type <syntax-reftype>` :math:`t` must be :ref:`valid <valid-reftype>`.
* For each :ref:`reference <syntax-ref>` :math:`\reff_i` in the elements :math:`\reff^n`:
@@ -315,11 +336,11 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
.. math::
\frac{
- \vdashreftype t \ok
+ S \vdashreftype t \ok
\qquad
(S \vdash \reff : t')^\ast
\qquad
- (\vdashreftypematch t' \matchesvaltype t)^\ast
+ (S \vdashreftypematch t' \matchesvaltype t)^\ast
}{
S \vdasheleminst \{ \EITYPE~t, \EIELEM~\reff^\ast \} : t
}
@@ -364,9 +385,9 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
:ref:`Module Instances <syntax-moduleinst>` :math:`\moduleinst`
...............................................................
-* Each :ref:`defined type <syntax-deftype>` :math:`\deftype_i` in :math:`\moduleinst.\MITYPES` must be :ref:`valid <valid-deftype>`.
+* For each :ref:`type address <syntax-typeaddr>` :math:`\typeaddr_i` in :math:`\moduleinst.\MITYPES`, the :ref:`type instance <syntax-typeinst>` :math:`\typeinst_i` at :math:`S.\STYPES[\typeaddr_i]` must be :ref:`valid <valid-typeinst>`.
-* For each :ref:`function address <syntax-funcaddr>` :math:`\funcaddr_i` in :math:`\moduleinst.\MIFUNCS`, the :ref:`external value <syntax-externval>` :math:`\EVFUNC~\funcaddr_i` must be :ref:`valid <valid-externval-func>` with some :ref:`external type <syntax-externtype>` :math:`\ETFUNC~\functype_i`.
+* For each :ref:`function address <syntax-funcaddr>` :math:`\funcaddr_i` in :math:`\moduleinst.\MIFUNCS`, the :ref:`external value <syntax-externval>` :math:`\EVFUNC~\funcaddr_i` must be :ref:`valid <valid-externval-func>` with some :ref:`external type <syntax-externtype>` :math:`\ETFUNC~\typeaddr'_i`.
* For each :ref:`table address <syntax-tableaddr>` :math:`\tableaddr_i` in :math:`\moduleinst.\MITABLES`, the :ref:`external value <syntax-externval>` :math:`\EVTABLE~\tableaddr_i` must be :ref:`valid <valid-externval-table>` with some :ref:`external type <syntax-externtype>` :math:`\ETTABLE~\tabletype_i`.
@@ -382,9 +403,9 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
* For each :ref:`export instance <syntax-exportinst>` :math:`\exportinst_i` in :math:`\moduleinst.\MIEXPORTS`, the :ref:`name <syntax-name>` :math:`\exportinst_i.\EINAME` must be different from any other name occurring in :math:`\moduleinst.\MIEXPORTS`.
-* Let :math:`\deftype^\ast` be the concatenation of all :math:`\deftype_i` in order.
+* Let :math:`\typeinst^\ast` be the concatenation of all :math:`\typeinst_i` in order.
-* Let :math:`\functype^\ast` be the concatenation of all :math:`\functype_i` in order.
+* Let :math:`\typeaddr'^\ast` be the concatenation of all :math:`\typeaddr'_i` in order.
* Let :math:`\tabletype^\ast` be the concatenation of all :math:`\tabletype_i` in order.
@@ -397,15 +418,15 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
* Let :math:`n` be the length of :math:`\moduleinst.\MIDATAS`.
* Then the module instance is valid with :ref:`context <context>`
- :math:`\{\CTYPES~\deftype^\ast,` :math:`\CFUNCS~\functype^\ast,` :math:`\CTABLES~\tabletype^\ast,` :math:`\CMEMS~\memtype^\ast,` :math:`\CGLOBALS~\globaltype^\ast,` :math:`\CELEMS~\reftype^\ast,` :math:`\CDATAS~{\ok}^n\}`.
+ :math:`\{\CTYPES~\typeinst^\ast,` :math:`\CFUNCS~{\typeaddr'}^\ast,` :math:`\CTABLES~\tabletype^\ast,` :math:`\CMEMS~\memtype^\ast,` :math:`\CGLOBALS~\globaltype^\ast,` :math:`\CELEMS~\reftype^\ast,` :math:`\CDATAS~{\ok}^n\}`.
.. math::
~\\[-1ex]
\frac{
\begin{array}{@{}c@{}}
- (\vdashdeftype \deftype \ok)^\ast
+ (S \vdashtypeinst S.\STYPES[\typeaddr] \ok)^\ast
\\
- (S \vdashexternval \EVFUNC~\funcaddr : \ETFUNC~\functype)^\ast
+ (S \vdashexternval \EVFUNC~\funcaddr : \ETFUNC~\typeaddr')^\ast
\qquad
(S \vdashexternval \EVTABLE~\tableaddr : \ETTABLE~\tabletype)^\ast
\\
@@ -424,7 +445,7 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
}{
S \vdashmoduleinst \{
\begin{array}[t]{@{}l@{~}l@{}}
- \MITYPES & \deftype^\ast, \\
+ \MITYPES & \typeaddr^\ast, \\
\MIFUNCS & \funcaddr^\ast, \\
\MITABLES & \tableaddr^\ast, \\
\MIMEMS & \memaddr^\ast, \\
@@ -433,8 +454,8 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
\MIDATAS & \dataaddr^n, \\
\MIEXPORTS & \exportinst^\ast ~\} : \{
\begin{array}[t]{@{}l@{~}l@{}}
- \CTYPES & \deftype^\ast, \\
- \CFUNCS & \functype^\ast, \\
+ \CTYPES & S.\STYPES[\typeaddr]^\ast, \\
+ \CFUNCS & {\typeaddr'}^\ast, \\
\CTABLES & \tabletype^\ast, \\
\CMEMS & \memtype^\ast, \\
\CGLOBALS & \globaltype^\ast, \\
@@ -444,6 +465,9 @@ Module instances are classified by *module contexts*, which are regular :ref:`co
\end{array}
}
+.. note::
+ The context derived for a module instance consists of :ref:`dynamic types <syntax-type-dyn>`.
+
.. scratch
.. index:: context, store, frame
@@ -562,7 +586,7 @@ Finally, :ref:`frames <syntax-frame>` are classified with *frame contexts*, whic
:ref:`Frames <syntax-frame>` :math:`\{\ALOCALS~\val^\ast, \AMODULE~\moduleinst\}`
.................................................................................
-* The :ref:`module instance <syntax-moduleinst>` :math:`\moduleinst` must be :ref:`valid <valid-moduleinst>` with some :ref:`module context <module-context>` :math:`C`.
+* The :ref:`module instance <syntax-moduleinst>` :math:`\moduleinst` must be :ref:`valid <valid-moduleinst>` with some :ref:`dynamic <syntax-type-dyn>` :ref:`module context <module-context>` :math:`C`.
* Each :ref:`value <syntax-val>` :math:`\val_i` in :math:`\val^\ast` must be :ref:`valid <valid-val>` with some :ref:`value type <syntax-valtype>` :math:`t_i`.
@@ -599,11 +623,11 @@ To that end, all previous typing judgements :math:`C \vdash \X{prop}` are genera
:math:`\TRAP`
.............
-* The instruction is valid with any :ref:`valid <valid-instrtype>` :ref:`instruction type <syntax-instrtype>` of the form :math:`[t_1^\ast] \to [t_2^\ast]`.
+* The instruction is valid with any :ref:`valid <valid-instrtype>` :ref:`dynamic <syntax-type-dyn>` :ref:`instruction type <syntax-instrtype>` of the form :math:`[t_1^\ast] \to [t_2^\ast]`.
.. math::
\frac{
- C \vdashinstrtype [t_1^\ast] \to [t_2^\ast] \ok
+ S; C \vdashinstrtype [t_1^\ast] \to [t_2^\ast] \ok
}{
S; C \vdashadmininstr \TRAP : [t_1^\ast] \to [t_2^\ast]
}
@@ -628,32 +652,41 @@ To that end, all previous typing judgements :math:`C \vdash \X{prop}` are genera
:math:`\REFFUNCADDR~\funcaddr`
..............................
-* The :ref:`external function value <syntax-externval>` :math:`\EVFUNC~\funcaddr` must be :ref:`valid <valid-externval>` with :ref:`external function type <syntax-externtype>` :math:`\ETFUNC~\functype`.
+* The :ref:`external function value <syntax-externval>` :math:`\EVFUNC~\funcaddr` must be :ref:`valid <valid-externval>` with :ref:`dynamic <syntax-type-dyn>` :ref:`external function type <syntax-externtype>` :math:`\ETFUNC~a'`.
-* Then the instruction is valid with type :math:`[] \to [(\REF~\functype)]`.
+* Then the instruction is valid with type :math:`[] \to [(\REF~a')]`.
.. math::
\frac{
- S \vdashexternval \EVFUNC~a : \ETFUNC~\functype
+ S \vdashexternval \EVFUNC~a : \ETFUNC~a'
}{
- S; C \vdashadmininstr \REFFUNCADDR~a : [] \to [(\REF~\functype)]
+ S; C \vdashadmininstr \REFFUNCADDR~a : [] \to [(\REF~a')]
}
+.. note::
+ This typing rule yields a :ref:`dynamic <syntax-type-dyn>` type.
+ The function may originate from outside the current module,
+ so that a definition for its type may not exist in context :math:`C`.
+
.. index:: function address, extern value, extern type, function type
:math:`\INVOKE~\funcaddr`
.........................
-* The :ref:`external function value <syntax-externval>` :math:`\EVFUNC~\funcaddr` must be :ref:`valid <valid-externval-func>` with :ref:`external function type <syntax-externtype>` :math:`\ETFUNC \functype'`.
+* The :ref:`external function value <syntax-externval>` :math:`\EVFUNC~\funcaddr` must be :ref:`valid <valid-externval-func>` with :ref:`external function type <syntax-externtype>` :math:`\ETFUNC a'`.
+
+* Assert: The :ref:`type address <syntax-typeaddr>` :math:`S.\STYPES[a']` is defined in the store.
-* Let :math:`[t_1^\ast] \toF [t_2^\ast])` be the :ref:`function type <syntax-functype>` :math:`\functype`.
+* Let :math:`[t_1^\ast] \toF [t_2^\ast])` be the :ref:`function type <syntax-functype>` :math:`S.\STYPES[a']`.
* Then the instruction is valid with type :math:`[t_1^\ast] \to [t_2^\ast]`.
.. math::
\frac{
- S \vdashexternval \EVFUNC~\funcaddr : \ETFUNC~[t_1^\ast] \toF [t_2^\ast]
+ S \vdashexternval \EVFUNC~\funcaddr : \ETFUNC~a'
+ \qquad
+ S.\STYPES[a'] = [t_1^\ast] \toF [t_2^\ast]