From 56c590438c71c12413e42e446e818cdf63461e32 Mon Sep 17 00:00:00 2001
From: Andreas Rossberg <rossberg@mpi-sws.org>
Date: Thu, 4 Jun 2026 11:58:19 +0200
Subject: [PATCH] [spectec] Equivalence tracking in IL validator

---
 specification/wasm-1.0/A-binary.spectec       |  2 +-
 specification/wasm-2.0/A-binary.spectec       |  2 +-
 .../wasm-3.0/5.1-binary.values.spectec        |  1 +
 .../wasm-latest/5.1-binary.values.spectec     |  1 +
 spectec/src/frontend/elab.ml                  |  1 +
 spectec/src/il/env.ml                         |  9 +++++
 spectec/src/il/eval.ml                        |  6 ++--
 spectec/src/il/valid.ml                       | 14 ++++++--
 spectec/test-frontend/TEST.md                 | 11 ++++---
 spectec/test-latex/TEST.md                    |  2 +-
 spectec/test-middlend/TEST.md                 | 33 ++++++++++---------
 11 files changed, 55 insertions(+), 27 deletions(-)

diff --git a/specification/wasm-1.0/A-binary.spectec b/specification/wasm-1.0/A-binary.spectec
index ce3ede9c73..db5de53d22 100644
--- a/specification/wasm-1.0/A-binary.spectec
+++ b/specification/wasm-1.0/A-binary.spectec
@@ -53,7 +53,7 @@ def $utf8(ch) = b  -- if ch < U+0080 /\ ch = b
 def $utf8(ch) = b_1 b_2  -- if U+0080 <= ch < U+0800 /\ ch = $(2^6*(b_1 - 0xC0) + (b_2 - 0x80))
 def $utf8(ch) = b_1 b_2 b_3  -- if (U+0800 <= ch < U+D800 \/ U+E000 <= ch < U+10000) /\ ch = $(2^12*(b_1 - 0xE0) + 2^6*(b_2 - 0x80) + (b_3 - 0x80))
 def $utf8(ch) = b_1 b_2 b_3 b_4  -- if (U+10000 <= ch < U+11000) /\ ch = $(2^18*(b_1 - 0xF0) + 2^12*(b_2 - 0x80) + 2^6*(b_3 - 0x80) + (b_4 - 0x80))
-def $utf8(ch*) = $concat_(byte, $utf8(ch)*)
+def $utf8(ch*) = $concat_(byte, $utf8(ch)*)  -- if |ch*| > 1
 
 grammar Bname : name =
   | b*:Blist(Bbyte) => name  -- if $utf8(name) = b*
diff --git a/specification/wasm-2.0/A-binary.spectec b/specification/wasm-2.0/A-binary.spectec
index 8570e0b2e7..9f364f38b5 100644
--- a/specification/wasm-2.0/A-binary.spectec
+++ b/specification/wasm-2.0/A-binary.spectec
@@ -55,7 +55,7 @@ def $utf8(ch) = b  -- if ch < U+0080 /\ ch = b
 def $utf8(ch) = b_1 b_2  -- if U+0080 <= ch < U+0800 /\ ch = $(2^6*(b_1 - 0xC0) + (b_2 - 0x80))
 def $utf8(ch) = b_1 b_2 b_3  -- if (U+0800 <= ch < U+D800 \/ U+E000 <= ch < U+10000) /\ ch = $(2^12*(b_1 - 0xE0) + 2^6*(b_2 - 0x80) + (b_3 - 0x80))
 def $utf8(ch) = b_1 b_2 b_3 b_4  -- if (U+10000 <= ch < U+11000) /\ ch = $(2^18*(b_1 - 0xF0) + 2^12*(b_2 - 0x80) + 2^6*(b_3 - 0x80) + (b_4 - 0x80))
-def $utf8(ch*) = $concat_(byte, $utf8(ch)*)
+def $utf8(ch*) = $concat_(byte, $utf8(ch)*)  -- if |ch*| > 1
 
 grammar Bname : name =
   | b*:Blist(Bbyte) => name  -- if $utf8(name) = b*
diff --git a/specification/wasm-3.0/5.1-binary.values.spectec b/specification/wasm-3.0/5.1-binary.values.spectec
index 6bb898de24..8740df8c69 100644
--- a/specification/wasm-3.0/5.1-binary.values.spectec
+++ b/specification/wasm-3.0/5.1-binary.values.spectec
@@ -50,6 +50,7 @@ def $cont(b) = $(b - 0x80) -- if (0x80 < b < 0xC0)
 
 ;; def $utf8(char*) : byte*
 def $utf8(ch*) = $concat_(byte, $utf8(ch)*)
+  -- if |ch*| > 1
 def $utf8(ch) = b
   -- if ch < U+0080
   -- if ch = b
diff --git a/specification/wasm-latest/5.1-binary.values.spectec b/specification/wasm-latest/5.1-binary.values.spectec
index 6bb898de24..8740df8c69 100644
--- a/specification/wasm-latest/5.1-binary.values.spectec
+++ b/specification/wasm-latest/5.1-binary.values.spectec
@@ -50,6 +50,7 @@ def $cont(b) = $(b - 0x80) -- if (0x80 < b < 0xC0)
 
 ;; def $utf8(char*) : byte*
 def $utf8(ch*) = $concat_(byte, $utf8(ch)*)
+  -- if |ch*| > 1
 def $utf8(ch) = b
   -- if ch < U+0080
   -- if ch = b
diff --git a/spectec/src/frontend/elab.ml b/spectec/src/frontend/elab.ml
index 686281dc3a..e4d79bd0d3 100644
--- a/spectec/src/frontend/elab.ml
+++ b/spectec/src/frontend/elab.ml
@@ -225,6 +225,7 @@ let to_il_env env =
     defs;
     rels = Map.empty;
     grams;
+    eqs = [];
   }
 
 
diff --git a/spectec/src/il/env.ml b/spectec/src/il/env.ml
index 044f5393ac..ce3d22776d 100644
--- a/spectec/src/il/env.ml
+++ b/spectec/src/il/env.ml
@@ -26,6 +26,7 @@ type t =
     defs : def_def Map.t;
     rels : rel_def Map.t;
     grams : gram_def Map.t;
+    eqs : (exp * exp) list;
   }
 
 
@@ -37,6 +38,7 @@ let empty =
     defs = Map.empty;
     rels = Map.empty;
     grams = Map.empty;
+    eqs = [];
   }
 
 let mem map id = Map.mem id.it map
@@ -93,6 +95,13 @@ let rebind_def env id rhs = {env with defs = rebind "definition" env.defs id rhs
 let rebind_rel env id rhs = {env with rels = rebind "relation" env.rels id rhs}
 let rebind_gram env id rhs = {env with grams = rebind "grammar" env.grams id rhs}
 
+let record_eq env e1 e2 = {env with eqs = (e1, e2)::env.eqs}
+let recall_eq env e1 e2 =
+  List.exists (fun (x, y) ->
+    Eq.eq_exp x e1 && Eq.eq_exp y e2 ||
+    Eq.eq_exp x e2 && Eq.eq_exp y e1
+  ) env.eqs
+
 
 (* Extraction *)
 
diff --git a/spectec/src/il/eval.ml b/spectec/src/il/eval.ml
index b6b06512db..1b52956ba2 100644
--- a/spectec/src/il/eval.ml
+++ b/spectec/src/il/eval.ml
@@ -1192,8 +1192,10 @@ and equiv_exp static env e1 e2 =
   ) @@ fun _ ->
   (* TODO(3, rossberg): this does not reduce inner type arguments *)
   match reduce_exp static env e1, reduce_exp static env e2 with
-  | Ok e1', Ok e2' -> Eq.eq_exp e1' e2'
-  | (Ok e1' | Error e1'), (Ok e2' | Error e2') when static -> Eq.eq_exp e1' e2'
+  | Ok e1', Ok e2' ->
+    Eq.eq_exp e1' e2' || Env.recall_eq env e1' e2'
+  | (Ok e1' | Error e1'), (Ok e2' | Error e2') when static ->
+    Eq.eq_exp e1' e2' || Env.recall_eq env e1' e2'
   | Error _, _ ->
     Error.error e1.at "validation"
       "expression failed to evaluate during pattern-matching"
diff --git a/spectec/src/il/valid.ml b/spectec/src/il/valid.ml
index 0075836c21..a2767ff2b3 100644
--- a/spectec/src/il/valid.ml
+++ b/spectec/src/il/valid.ml
@@ -592,7 +592,10 @@ and valid_sym env g : typ =
 (* Premises *)
 
 and valid_prem env prem =
-  Debug.(log_in_at "il.valid_prem" prem.at (fun _ -> il_prem prem));
+  Debug.(log_at "il.valid_prem" prem.at
+    (fun _ -> il_prem prem)
+    (fun _ -> "")
+  ) @@ fun _ ->
   match prem.it with
   | RulePr (x, as_, mixop, e) ->
     let ps, mixop', t, _rules = Env.find_rel env x in
@@ -600,6 +603,11 @@ and valid_prem env prem =
     let s = valid_args env as_ ps Subst.empty prem.at in
     valid_expmix env mixop e (mixop, Subst.subst_typ s t) e.at;
     env
+  | IfPr ({it = CmpE (`EqOp, _t, e1, e2); _} as e) ->
+    valid_exp env e (BoolT $ e.at);
+    let Ok e1' | Error e1' = Eval.reduce_exp env e1 in
+    let Ok e2' | Error e2' = Eval.reduce_exp env e2 in
+    Env.record_eq env e1' e2'
   | IfPr e ->
     valid_exp env e (BoolT $ e.at);
     env
@@ -616,7 +624,9 @@ and valid_prem env prem =
           List.map (fun x -> "`" ^ x ^ "`") |>
           String.concat ", " ) ^
         " do not occur in left-hand side expression");
-    env'
+    let Ok e1' | Error e1' = Eval.reduce_exp env e1 in
+    let Ok e2' | Error e2' = Eval.reduce_exp env e2 in
+    Env.record_eq env' e1' e2'
   | ElsePr ->
     env
   | IterPr (prem', ite) ->
diff --git a/spectec/test-frontend/TEST.md b/spectec/test-frontend/TEST.md
index 15c60d0f10..8172a6aeaf 100644
--- a/spectec/test-frontend/TEST.md
+++ b/spectec/test-frontend/TEST.md
@@ -785,21 +785,22 @@ rec {
 
 ;; ../../../../specification/wasm-latest/1.1-syntax.values.spectec:91.1-91.25
 def $utf8(char*) : byte*
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:52.1-52.44
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:52.1-53.18
   def $utf8{`ch*` : char*}(ch*{ch <- `ch*`}) = $concat_(syntax byte, $utf8([ch])*{ch <- `ch*`})
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:53.1-55.15
+    -- if (|ch*{ch <- `ch*`}| > 1)
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:54.1-56.15
   def $utf8{ch : char, b : byte}([ch]) = [b]
     -- if (ch!`%`_char.0 < 128)
     -- if (`%`_byte(ch!`%`_char.0) = b)
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:56.1-58.46
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:57.1-59.46
   def $utf8{ch : char, b_1 : byte, b_2 : byte}([ch]) = [b_1 b_2]
     -- if ((128 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 2048))
     -- if (ch!`%`_char.0 = (((2 ^ 6) * (((b_1!`%`_byte.0 : nat <:> int) - (192 : nat <:> int)) : int <:> nat)) + $cont(b_2)))
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:59.1-61.64
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:60.1-62.64
   def $utf8{ch : char, b_1 : byte, b_2 : byte, b_3 : byte}([ch]) = [b_1 b_2 b_3]
     -- if (((2048 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 55296)) \/ ((57344 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 65536)))
     -- if (ch!`%`_char.0 = ((((2 ^ 12) * (((b_1!`%`_byte.0 : nat <:> int) - (224 : nat <:> int)) : int <:> nat)) + ((2 ^ 6) * $cont(b_2))) + $cont(b_3)))
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:62.1-64.82
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:63.1-65.82
   def $utf8{ch : char, b_1 : byte, b_2 : byte, b_3 : byte, b_4 : byte}([ch]) = [b_1 b_2 b_3 b_4]
     -- if ((65536 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 69632))
     -- if (ch!`%`_char.0 = (((((2 ^ 18) * (((b_1!`%`_byte.0 : nat <:> int) - (240 : nat <:> int)) : int <:> nat)) + ((2 ^ 12) * $cont(b_2))) + ((2 ^ 6) * $cont(b_3))) + $cont(b_4)))
diff --git a/spectec/test-latex/TEST.md b/spectec/test-latex/TEST.md
index 1253a23f3c..9ca1bfedb4 100644
--- a/spectec/test-latex/TEST.md
+++ b/spectec/test-latex/TEST.md
@@ -11394,7 +11394,7 @@ $$
 
 $$
 \begin{array}[t]{@{}lcl@{}l@{}}
-{\mathrm{utf{\kern-0.1em\scriptstyle 8}}}({{\mathit{ch}}^\ast}) & = & {\bigoplus}\, {{\mathrm{utf{\kern-0.1em\scriptstyle 8}}}({\mathit{ch}})^\ast} \\
+{\mathrm{utf{\kern-0.1em\scriptstyle 8}}}({{\mathit{ch}}^\ast}) & = & {\bigoplus}\, {{\mathrm{utf{\kern-0.1em\scriptstyle 8}}}({\mathit{ch}})^\ast} & \quad \mbox{if}~ {|{{\mathit{ch}}^\ast}|} > 1 \\
 {\mathrm{utf{\kern-0.1em\scriptstyle 8}}}({\mathit{ch}}) & = & b & \quad
 \begin{array}[t]{@{}l@{}}
 \mbox{if}~ {\mathit{ch}} < \mathrm{U{+}80} \\
diff --git a/spectec/test-middlend/TEST.md b/spectec/test-middlend/TEST.md
index 526d41eb0b..2c3c6f95f2 100644
--- a/spectec/test-middlend/TEST.md
+++ b/spectec/test-middlend/TEST.md
@@ -308,21 +308,22 @@ rec {
 
 ;; ../../../../specification/wasm-latest/1.1-syntax.values.spectec:91.1-91.25
 def $utf8(char*) : byte*
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:52.1-52.44
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:52.1-53.18
   def $utf8{`ch*` : char*}(ch*{ch <- `ch*`}) = $concat_(syntax byte, $utf8([ch])*{ch <- `ch*`})
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:53.1-55.15
+    -- if (|ch*{ch <- `ch*`}| > 1)
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:54.1-56.15
   def $utf8{ch : char, b : byte}([ch]) = [b]
     -- if (ch!`%`_char.0 < 128)
     -- if (`%`_byte(ch!`%`_char.0) = b)
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:56.1-58.46
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:57.1-59.46
   def $utf8{ch : char, b_1 : byte, b_2 : byte}([ch]) = [b_1 b_2]
     -- if ((128 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 2048))
     -- if (ch!`%`_char.0 = (((2 ^ 6) * (((b_1!`%`_byte.0 : nat <:> int) - (192 : nat <:> int)) : int <:> nat)) + $cont(b_2)))
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:59.1-61.64
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:60.1-62.64
   def $utf8{ch : char, b_1 : byte, b_2 : byte, b_3 : byte}([ch]) = [b_1 b_2 b_3]
     -- if (((2048 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 55296)) \/ ((57344 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 65536)))
     -- if (ch!`%`_char.0 = ((((2 ^ 12) * (((b_1!`%`_byte.0 : nat <:> int) - (224 : nat <:> int)) : int <:> nat)) + ((2 ^ 6) * $cont(b_2))) + $cont(b_3)))
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:62.1-64.82
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:63.1-65.82
   def $utf8{ch : char, b_1 : byte, b_2 : byte, b_3 : byte, b_4 : byte}([ch]) = [b_1 b_2 b_3 b_4]
     -- if ((65536 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 69632))
     -- if (ch!`%`_char.0 = (((((2 ^ 18) * (((b_1!`%`_byte.0 : nat <:> int) - (240 : nat <:> int)) : int <:> nat)) + ((2 ^ 12) * $cont(b_2))) + ((2 ^ 6) * $cont(b_3))) + $cont(b_4)))
@@ -12151,21 +12152,22 @@ rec {
 
 ;; ../../../../specification/wasm-latest/1.1-syntax.values.spectec:91.1-91.25
 def $utf8(char*) : byte*
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:52.1-52.44
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:52.1-53.18
   def $utf8{`ch*` : char*}(ch*{ch <- `ch*`}) = $concat_(syntax byte, $utf8([ch])*{ch <- `ch*`})
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:53.1-55.15
+    -- if (|ch*{ch <- `ch*`}| > 1)
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:54.1-56.15
   def $utf8{ch : char, b : byte}([ch]) = [b]
     -- if (ch!`%`_char.0 < 128)
     -- if (`%`_byte(ch!`%`_char.0) = b)
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:56.1-58.46
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:57.1-59.46
   def $utf8{ch : char, b_1 : byte, b_2 : byte}([ch]) = [b_1 b_2]
     -- if ((128 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 2048))
     -- if (ch!`%`_char.0 = (((2 ^ 6) * (((b_1!`%`_byte.0 : nat <:> int) - (192 : nat <:> int)) : int <:> nat)) + $cont(b_2)))
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:59.1-61.64
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:60.1-62.64
   def $utf8{ch : char, b_1 : byte, b_2 : byte, b_3 : byte}([ch]) = [b_1 b_2 b_3]
     -- if (((2048 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 55296)) \/ ((57344 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 65536)))
     -- if (ch!`%`_char.0 = ((((2 ^ 12) * (((b_1!`%`_byte.0 : nat <:> int) - (224 : nat <:> int)) : int <:> nat)) + ((2 ^ 6) * $cont(b_2))) + $cont(b_3)))
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:62.1-64.82
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:63.1-65.82
   def $utf8{ch : char, b_1 : byte, b_2 : byte, b_3 : byte, b_4 : byte}([ch]) = [b_1 b_2 b_3 b_4]
     -- if ((65536 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 69632))
     -- if (ch!`%`_char.0 = (((((2 ^ 18) * (((b_1!`%`_byte.0 : nat <:> int) - (240 : nat <:> int)) : int <:> nat)) + ((2 ^ 12) * $cont(b_2))) + ((2 ^ 6) * $cont(b_3))) + $cont(b_4)))
@@ -24003,21 +24005,22 @@ rec {
 
 ;; ../../../../specification/wasm-latest/1.1-syntax.values.spectec:91.1-91.25
 def $utf8(char*) : byte*
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:52.1-52.44
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:52.1-53.18
   def $utf8{`ch*` : char*}(ch*{ch <- `ch*`}) = $concat_(syntax byte, $utf8([ch])*{ch <- `ch*`})
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:53.1-55.15
+    -- if (|ch*{ch <- `ch*`}| > 1)
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:54.1-56.15
   def $utf8{ch : char, b : byte}([ch]) = [b]
     -- if (ch!`%`_char.0 < 128)
     -- if (`%`_byte(ch!`%`_char.0) = b)
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:56.1-58.46
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:57.1-59.46
   def $utf8{ch : char, b_1 : byte, b_2 : byte}([ch]) = [b_1 b_2]
     -- if ((128 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 2048))
     -- if (ch!`%`_char.0 = (((2 ^ 6) * (((b_1!`%`_byte.0 : nat <:> int) - (192 : nat <:> int)) : int <:> nat)) + $cont(b_2)))
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:59.1-61.64
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:60.1-62.64
   def $utf8{ch : char, b_1 : byte, b_2 : byte, b_3 : byte}([ch]) = [b_1 b_2 b_3]
     -- if (((2048 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 55296)) \/ ((57344 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 65536)))
     -- if (ch!`%`_char.0 = ((((2 ^ 12) * (((b_1!`%`_byte.0 : nat <:> int) - (224 : nat <:> int)) : int <:> nat)) + ((2 ^ 6) * $cont(b_2))) + $cont(b_3)))
-  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:62.1-64.82
+  ;; ../../../../specification/wasm-latest/5.1-binary.values.spectec:63.1-65.82
   def $utf8{ch : char, b_1 : byte, b_2 : byte, b_3 : byte, b_4 : byte}([ch]) = [b_1 b_2 b_3 b_4]
     -- if ((65536 <= ch!`%`_char.0) /\ (ch!`%`_char.0 < 69632))
     -- if (ch!`%`_char.0 = (((((2 ^ 18) * (((b_1!`%`_byte.0 : nat <:> int) - (240 : nat <:> int)) : int <:> nat)) + ((2 ^ 12) * $cont(b_2))) + ((2 ^ 6) * $cont(b_3))) + $cont(b_4)))