diff --git a/libyul/Dialect.h b/libyul/Dialect.h
index 3d261fdee..4a1aff0fc 100644
--- a/libyul/Dialect.h
+++ b/libyul/Dialect.h
@@ -58,8 +58,8 @@ struct Dialect: boost::noncopyable
 	/// @returns the builtin function of the given name or a nullptr if it is not a builtin function.
 	virtual BuiltinFunction const* builtin(YulString /*_name*/) const { return nullptr; }
 
-	virtual BuiltinFunction const* discardFunction() const { return nullptr; }
-	virtual BuiltinFunction const* equalityFunction() const { return nullptr; }
+	virtual BuiltinFunction const* discardFunction(YulString /* _type */) const { return nullptr; }
+	virtual BuiltinFunction const* equalityFunction(YulString /* _type */) const { return nullptr; }
 	virtual BuiltinFunction const* booleanNegationFunction() const { return nullptr; }
 
 	/// Check whether the given type is legal for the given literal value.
diff --git a/libyul/backends/evm/EVMDialect.cpp b/libyul/backends/evm/EVMDialect.cpp
index 39fc65632..27a2b85e3 100644
--- a/libyul/backends/evm/EVMDialect.cpp
+++ b/libyul/backends/evm/EVMDialect.cpp
@@ -290,6 +290,28 @@ EVMDialectTyped::EVMDialectTyped(langutil::EVMVersion _evmVersion, bool _objectA
 	m_functions["u256_to_bool"_yulstring].returns = {"bool"_yulstring};
 }
 
+BuiltinFunctionForEVM const* EVMDialectTyped::discardFunction(YulString _type) const
+{
+	if (_type == "bool"_yulstring)
+		return builtin("popbool"_yulstring);
+	else
+	{
+		yulAssert(_type == defaultType, "");
+		return builtin("pop"_yulstring);
+	}
+}
+
+BuiltinFunctionForEVM const* EVMDialectTyped::equalityFunction(YulString _type) const
+{
+	if (_type == "bool"_yulstring)
+		return nullptr;
+	else
+	{
+		yulAssert(_type == defaultType, "");
+		return builtin("eq"_yulstring);
+	}
+}
+
 EVMDialectTyped const& EVMDialectTyped::instance(langutil::EVMVersion _version)
 {
 	static map<langutil::EVMVersion, unique_ptr<EVMDialectTyped const>> dialects;
diff --git a/libyul/backends/evm/EVMDialect.h b/libyul/backends/evm/EVMDialect.h
index 40842fa57..2141ab98f 100644
--- a/libyul/backends/evm/EVMDialect.h
+++ b/libyul/backends/evm/EVMDialect.h
@@ -68,8 +68,8 @@ struct EVMDialect: public Dialect
 	/// @returns the builtin function of the given name or a nullptr if it is not a builtin function.
 	BuiltinFunctionForEVM const* builtin(YulString _name) const override;
 
-	BuiltinFunctionForEVM const* discardFunction() const override { return builtin("pop"_yulstring); }
-	BuiltinFunctionForEVM const* equalityFunction() const override { return builtin("eq"_yulstring); }
+	BuiltinFunctionForEVM const* discardFunction(YulString /*_type*/) const override { return builtin("pop"_yulstring); }
+	BuiltinFunctionForEVM const* equalityFunction(YulString /*_type*/) const override { return builtin("eq"_yulstring); }
 	BuiltinFunctionForEVM const* booleanNegationFunction() const override { return builtin("iszero"_yulstring); }
 
 	static EVMDialect const& strictAssemblyForEVM(langutil::EVMVersion _version);
@@ -102,6 +102,10 @@ struct EVMDialectTyped: public EVMDialect
 	/// Constructor, should only be used internally. Use the factory function below.
 	EVMDialectTyped(langutil::EVMVersion _evmVersion, bool _objectAccess);
 
+	BuiltinFunctionForEVM const* discardFunction(YulString _type) const override;
+	BuiltinFunctionForEVM const* equalityFunction(YulString _type) const override;
+	BuiltinFunctionForEVM const* booleanNegationFunction() const override { return builtin("not"_yulstring); }
+
 	static EVMDialectTyped const& instance(langutil::EVMVersion _version);
 };
 
diff --git a/libyul/backends/wasm/WasmDialect.cpp b/libyul/backends/wasm/WasmDialect.cpp
index 947326306..7f2149adc 100644
--- a/libyul/backends/wasm/WasmDialect.cpp
+++ b/libyul/backends/wasm/WasmDialect.cpp
@@ -91,8 +91,9 @@ WasmDialect::WasmDialect()
 	m_functions["i64.load"_yulstring].sideEffects.sideEffectFreeIfNoMSize = true;
 
 	// Drop is actually overloaded for all types, but Yul does not support that.
-	// We could introduce "i32.drop".
+	// Because of that, we introduce "i32.drop".
 	addFunction("drop", {i64}, {});
+	addFunction("i32.drop", {i32}, {});
 
 	addFunction("nop", {}, {});
 	addFunction("unreachable", {}, {}, false);
@@ -114,6 +115,22 @@ BuiltinFunction const* WasmDialect::builtin(YulString _name) const
 		return nullptr;
 }
 
+BuiltinFunction const* WasmDialect::discardFunction(YulString _type) const
+{
+	if (_type == "i32"_yulstring)
+		return builtin("i32.drop"_yulstring);
+	yulAssert(_type == "i64"_yulstring, "");
+	return builtin("drop"_yulstring);
+}
+
+BuiltinFunction const* WasmDialect::equalityFunction(YulString _type) const
+{
+	if (_type == "i32"_yulstring)
+		return builtin("i32.eq"_yulstring);
+	yulAssert(_type == "i64"_yulstring, "");
+	return builtin("i64.eq"_yulstring);
+}
+
 WasmDialect const& WasmDialect::instance()
 {
 	static std::unique_ptr<WasmDialect> dialect;
diff --git a/libyul/backends/wasm/WasmDialect.h b/libyul/backends/wasm/WasmDialect.h
index cf1a76d9d..1de65dfdc 100644
--- a/libyul/backends/wasm/WasmDialect.h
+++ b/libyul/backends/wasm/WasmDialect.h
@@ -35,19 +35,19 @@ struct Object;
 /**
  * Yul dialect for Wasm as a backend.
  *
- * Builtin functions are a subset of the wasm instructions, always implicitly assuming
- * unsigned 64 bit types.
+ * Builtin functions are a subset of the wasm instructions.
+ *
+ * There is a builtin function `i32.drop` that takes an i32, while `drop` takes i64.
  *
- * !This is subject to changes!
  */
 struct WasmDialect: public Dialect
 {
 	WasmDialect();
 
 	BuiltinFunction const* builtin(YulString _name) const override;
-	BuiltinFunction const* discardFunction() const override { return builtin("drop"_yulstring); }
-	BuiltinFunction const* equalityFunction() const override { return builtin("i64.eq"_yulstring); }
-	BuiltinFunction const* booleanNegationFunction() const override { return builtin("i64.eqz"_yulstring); }
+	BuiltinFunction const* discardFunction(YulString _type) const override;
+	BuiltinFunction const* equalityFunction(YulString _type) const override;
+	BuiltinFunction const* booleanNegationFunction() const override { return builtin("i32.eqz"_yulstring); }
 
 	std::set<YulString> fixedFunctionNames() const override { return {"main"_yulstring}; }