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Elaboration of subtyping rule of struct and variant in SpecTec IL #2111

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Elaboration of subtyping rule of struct and variant in SpecTec IL #2111

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2067e36
fix: typo
jihongmin63 Mar 10, 2026
3791634
Merge branch 'WebAssembly:main' into main
jihongmin63 Mar 12, 2026
8cd0346
[spectec] elaborate subtyping rules for struct and variant
jihongmin63 Mar 13, 2026
f12cda1
Merge branch 'WebAssembly:main' into subtyp
jihongmin63 Mar 13, 2026
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5 changes: 5 additions & 0 deletions spectec/doc/semantics/il/0-aux.spectec
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Expand Up @@ -13,3 +13,8 @@ def $equiv_(syntax X, x_1*, x_2*) = false -- otherwise
def $transpose_(syntax X, X**) : X**
def $transpose_(syntax X, eps^n) = eps
def $transpose_(syntax X, (x_1 x*)*) = x_1* $transpose_(X, x**)


def $forall(bool*) : bool
def $forall(eps) = true
def $forall(bool_1 bool*) = bool_1 /\ $forall(bool*)
8 changes: 4 additions & 4 deletions spectec/doc/semantics/il/6-typing.spectec
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Expand Up @@ -45,16 +45,16 @@ rule Sub_typ/struct:
E |- t_1 <: t_2
-- Expand_typ: E |- t_1 => STRUCT tf_1*
-- Expand_typ: E |- t_2 => STRUCT tf_2*
-- (if (a `: t_2a `- `{q*} pr*) = tf_2)*
-- (if (a `: t_1a `- `{q*} pr*) <- tf_1*)*
-- (if (a `: t_2a `- `{q*} pr_2*) = tf_2)*
-- (if (a `: t_1a `- `{q*} pr_1*) <- tf_1* /\ $forall((pr_2 <- pr_1*)*))*
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@rossberg rossberg Mar 16, 2026

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Does this not work without the auxiliary forall?

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-- (if (a `: t_1a `- `{q*} pr_1*) <- tf_1* /\ $forall((pr_2 <- pr_1*)*))*
-- (if (a `: t_1a `- `{q*} pr_1*) <- tf_1*)*
-- (if pr_2 <- pr_1*)**

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@rossberg rossberg Mar 18, 2026

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Trying this myself I noted my suggestion works, but is ambiguous and may not have the intended semantics. When I put in explicit sizes to disambiguate, SpecTec dimension inference complains, because using x^n^m in a context []^n^k^m is too much for it to handle.

I also realised that this flexibility in the rule isn't really useful if it doesn't also allow subsetting the quantifier list. But that is rather tricky, due to possible dependencies and possible shadowing. It would at least need to take α-equivalence into account correctly.

Since the flexibility of weakening side conditions isn't currently needed for anything, I'd rather keep it simple, keep requiring equality and adjusting docs and implementation accordingly.

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@jihongmin63 jihongmin63 Mar 18, 2026

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I also initially thought that syntactic removal would be feasible, but I had concerns about whether it would preserve the intended semantics. If this flexibility is not actually required in practice, I agree that it is better not to introduce it.

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@rossberg rossberg Mar 18, 2026

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Done. I think you can close this one. But thanks for pointing out the discrepancy!

-- (Sub_typ: E |- t_1a <: t_2a)*

rule Sub_typ/variant:
E |- t_1 <: t_2
-- Expand_typ: E |- t_1 => VARIANT tc_1*
-- Expand_typ: E |- t_2 => VARIANT tc_2*
-- (if (m `: t_1a `- `{q*} pr*) = tc_1)*
-- (if (m `: t_2a `- `{q*} pr*) <- tc_2*)*
-- (if (m `: t_1a `- `{q*} pr_1*) = tc_1)*
-- (if (m `: t_2a `- `{q*} pr_2*) <- tc_2* /\ $forall((pr_2 <- pr_1*)*))*
-- (Sub_typ: E |- t_1a <: t_2a)*

rule Sub_typ/iter:
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