diff --git a/pyk/src/pyk/kore/rule.py b/pyk/src/pyk/kore/rule.py
new file mode 100644
index 00000000000..680d91082f7
--- /dev/null
+++ b/pyk/src/pyk/kore/rule.py
@@ -0,0 +1,300 @@
+"""Parse KORE axioms into rewrite rules.
+
+Based on the [LLVM Backend's implementation](https://github.com/runtimeverification/llvm-backend/blob/d5eab4b0f0e610bc60843ebb482f79c043b92702/lib/ast/pattern_matching.cpp).
+"""
+
+from __future__ import annotations
+
+from abc import ABC
+from dataclasses import dataclass
+from typing import TYPE_CHECKING, final
+
+from .prelude import inj
+from .syntax import And, App, Axiom, Ceil, Equals, EVar, Implies, In, Not, Rewrites, SortVar, String, Top
+
+if TYPE_CHECKING:
+    from typing import Final
+
+    from .syntax import Definition, Pattern
+
+    Attrs = dict[str, tuple[Pattern, ...]]
+
+
+# There's a simplification rule with irregular form in the prelude module INJ.
+# This rule is skipped in Rule.extract_all.
+_S1, _S2, _S3, _R = (SortVar(name) for name in ['S1', 'S2', 'S3', 'R'])
+_T: Final = EVar('T', _S1)
+# axiom {S1, S2, S3, R} \equals{S3, R}(inj{S2, S3}(inj{S1, S2}(T:S1)), inj{S1, S3}(T:S1)) [simplification{}()]
+_INJ_AXIOM: Final = Axiom(
+    vars=(_S1, _S2, _S3, _R),
+    pattern=Equals(_S3, _R, inj(_S2, _S3, inj(_S1, _S2, _T)), inj(_S1, _S3, _T)),
+    attrs=(App('simplification'),),
+)
+
+# The following attributes mark axioms that are not rule axioms.
+# Such axioms are skipped in Rule.extract_all.
+_SKIPPED_ATTRS: Final = (
+    'assoc',
+    'constructor',
+    'functional',
+    'idem',
+    'symbol-overload',
+    'subsort',
+    'unit',
+)
+
+
+class Rule(ABC):
+    lhs: Pattern
+    rhs: Pattern
+    req: Pattern | None
+    ens: Pattern | None
+    priority: int
+
+    @staticmethod
+    def from_axiom(axiom: Axiom) -> Rule:
+        if isinstance(axiom.pattern, Rewrites):
+            return RewriteRule.from_axiom(axiom)
+
+        if 'simplification' in axiom.attrs_by_key:
+            return SimpliRule.from_axiom(axiom)
+
+        return FunctionRule.from_axiom(axiom)
+
+    @staticmethod
+    def extract_all(defn: Definition) -> list[Rule]:
+        return [Rule.from_axiom(axiom) for axiom in defn.axioms if Rule._is_rule(axiom)]
+
+    @staticmethod
+    def _is_rule(axiom: Axiom) -> bool:
+        if axiom == _INJ_AXIOM:
+            return False
+
+        if any(attr in axiom.attrs_by_key for attr in _SKIPPED_ATTRS):
+            return False
+
+        match axiom.pattern:
+            case Implies(right=Equals(left=Ceil())):
+                # Ceil rule
+                return False
+
+        return True
+
+
+@final
+@dataclass
+class RewriteRule(Rule):
+    lhs: App
+    rhs: App
+    req: Pattern | None
+    ens: Pattern | None
+    ctx: EVar | None
+    priority: int
+    uid: str
+    label: str | None
+
+    @staticmethod
+    def from_axiom(axiom: Axiom) -> RewriteRule:
+        lhs, req, ctx = RewriteRule._extract_lhs(axiom)
+        rhs, ens = RewriteRule._extract_rhs(axiom)
+        priority = _extract_priority(axiom)
+        uid = _extract_uid(axiom)
+        label = _extract_label(axiom)
+        return RewriteRule(
+            lhs=lhs,
+            rhs=rhs,
+            req=req,
+            ens=ens,
+            ctx=ctx,
+            priority=priority,
+            uid=uid,
+            label=label,
+        )
+
+    @staticmethod
+    def _extract_lhs(axiom: Axiom) -> tuple[App, Pattern | None, EVar | None]:
+        req: Pattern | None = None
+        # Cases 0-5 of get_left_hand_side
+        # Cases 5-10 of get_requires
+        match axiom.pattern:
+            case Rewrites(left=And(ops=(Top(), lhs))):
+                pass
+            case Rewrites(left=And(ops=(Equals(left=req), lhs))):
+                pass
+            case Rewrites(left=And(ops=(lhs, Top()))):
+                pass
+            case Rewrites(left=And(ops=(lhs, Equals(left=req)))):
+                pass
+            case Rewrites(left=And(ops=(Not(), And(ops=(Top(), lhs))))):
+                pass
+            case Rewrites(left=And(ops=(Not(), And(ops=(Equals(left=req), lhs))))):
+                pass
+            case _:
+                raise ValueError(f'Cannot extract LHS from axiom: {axiom.text}')
+
+        ctx: EVar | None = None
+        match lhs:
+            case App("Lbl'-LT-'generatedTop'-GT-'") as app:
+                pass
+            case And(_, (App("Lbl'-LT-'generatedTop'-GT-'") as app, EVar("Var'Hash'Configuration") as ctx)):
+                pass
+
+        return app, req, ctx
+
+    @staticmethod
+    def _extract_rhs(axiom: Axiom) -> tuple[App, Pattern | None]:
+        # Case 2 of get_right_hand_side:
+        # 2: rhs(\rewrites(_, \and(X, Y))) = get_builtin(\and(X, Y))
+        # Below is a special case without get_builtin
+        match axiom.pattern:
+            case Rewrites(right=And(ops=(App("Lbl'-LT-'generatedTop'-GT-'") as rhs, Top() | Equals() as _ens))):
+                pass
+            case _:
+                raise ValueError(f'Cannot extract RHS from axiom: {axiom.text}')
+        ens = _extract_ensures(_ens)
+        return rhs, ens
+
+
+@final
+@dataclass
+class FunctionRule(Rule):
+    lhs: App
+    rhs: Pattern
+    req: Pattern | None
+    ens: Pattern | None
+    priority: int
+
+    @staticmethod
+    def from_axiom(axiom: Axiom) -> FunctionRule:
+        args, req = FunctionRule._extract_args(axiom)
+        app, rhs, ens = FunctionRule._extract_rhs(axiom)
+        lhs = app.let(args=args)
+        priority = _extract_priority(axiom)
+        return FunctionRule(
+            lhs=lhs,
+            rhs=rhs,
+            req=req,
+            ens=ens,
+            priority=priority,
+        )
+
+    @staticmethod
+    def _extract_args(axiom: Axiom) -> tuple[tuple[Pattern, ...], Pattern | None]:
+        req: Pattern | None = None
+        # Cases 7-10 of get_left_hand_side
+        # Cases 0-3 of get_requires
+        match axiom.pattern:
+            case Implies(left=And(ops=(Top(), pat))):
+                return FunctionRule._get_patterns(pat), req
+            case Implies(left=And(ops=(Equals(left=req), pat))):
+                return FunctionRule._get_patterns(pat), req
+            case Implies(left=And(ops=(Not(), And(ops=(Top(), pat))))):
+                return FunctionRule._get_patterns(pat), req
+            case Implies(left=And(ops=(Not(), And(ops=(Equals(left=req), pat))))):
+                return FunctionRule._get_patterns(pat), req
+            case _:
+                raise ValueError(f'Cannot extract LHS from axiom: {axiom.text}')
+
+    @staticmethod
+    def _get_patterns(pattern: Pattern) -> tuple[Pattern, ...]:
+        # get_patterns(\top()) = []
+        # get_patterns(\and(\in(_, X), Y)) = X : get_patterns(Y)
+        match pattern:
+            case Top():
+                return ()
+            case And(ops=(In(right=x), y)):
+                return (x,) + FunctionRule._get_patterns(y)
+            case _:
+                raise AssertionError()
+
+    @staticmethod
+    def _extract_rhs(axiom: Axiom) -> tuple[App, Pattern, Pattern | None]:
+        # Case 0 of get_right_hand_side
+        match axiom.pattern:
+            case Implies(right=Equals(left=App() as app, right=And(ops=(rhs, Top() | Equals() as _ens)))):
+                pass
+            case _:
+                raise ValueError(f'Cannot extract RHS from axiom: {axiom.text}')
+        ens = _extract_ensures(_ens)
+        return app, rhs, ens
+
+
+@final
+@dataclass
+class SimpliRule(Rule):
+    lhs: Pattern
+    rhs: Pattern
+    req: Pattern | None
+    ens: Pattern | None
+    priority: int
+
+    @staticmethod
+    def from_axiom(axiom: Axiom) -> SimpliRule:
+        lhs, rhs, req, ens = SimpliRule._extract(axiom)
+        priority = _extract_priority(axiom)
+        return SimpliRule(
+            lhs=lhs,
+            rhs=rhs,
+            req=req,
+            ens=ens,
+            priority=priority,
+        )
+
+    @staticmethod
+    def _extract(axiom: Axiom) -> tuple[Pattern, Pattern, Pattern | None, Pattern | None]:
+        req: Pattern | None = None
+        # Cases 11-12 of get_left_hand_side
+        # Case 0 of get_right_hand_side
+        match axiom.pattern:
+            case Implies(left=Top(), right=Equals(left=lhs, right=And(ops=(rhs, Top() | Equals() as _ens)))):
+                pass
+            case Implies(left=Equals(left=req), right=Equals(left=lhs, right=And(ops=(rhs, Top() | Equals() as _ens)))):
+                pass
+            case Implies(right=Equals(left=Ceil())):
+                raise ValueError(f'Axiom is a ceil rule: {axiom.text}')
+            case _:
+                raise ValueError(f'Cannot extract simplification rule from axiom: {axiom.text}')
+        ens = _extract_ensures(_ens)
+        return lhs, rhs, req, ens
+
+
+def _extract_ensures(ens: Top | Equals | None) -> Pattern | None:
+    match ens:
+        case Top():
+            return None
+        case Equals(left=res):
+            return res
+        case _:
+            raise AssertionError()
+
+
+def _extract_uid(axiom: Axiom) -> str:
+    attrs = axiom.attrs_by_key
+    match attrs["UNIQUE'Unds'ID"]:
+        case App(args=(String(uid),)):
+            return uid
+        case _:
+            raise ValueError(f'Cannot extract uid from axiom: {axiom.text}')
+
+
+def _extract_label(axiom: Axiom) -> str | None:
+    attrs = axiom.attrs_by_key
+    match attrs.get('label'):
+        case App(args=(String(label),)):
+            return label
+        case None:
+            return None
+        case _:
+            raise ValueError(f'Cannot extract label from axiom: {axiom.text}')
+
+
+def _extract_priority(axiom: Axiom) -> int:
+    attrs = axiom.attrs_by_key
+    match attrs.get('priority'):
+        case App(args=(String(p),)):
+            assert 'owise' not in attrs
+            return int(p)
+        case None:
+            return 200 if 'owise' in attrs else 50
+        case _:
+            raise ValueError(f'Cannot extract priority from axiom: {axiom.text}')
diff --git a/pyk/src/pyk/kore/syntax.py b/pyk/src/pyk/kore/syntax.py
index 6727fa99531..f49abba1932 100644
--- a/pyk/src/pyk/kore/syntax.py
+++ b/pyk/src/pyk/kore/syntax.py
@@ -11,7 +11,7 @@
 from typing import TYPE_CHECKING, final
 
 from ..dequote import enquoted
-from ..utils import check_type
+from ..utils import FrozenDict, check_type
 
 if TYPE_CHECKING:
     from collections.abc import Callable, Iterator, Mapping
@@ -1792,6 +1792,10 @@ def let_attrs(self: WA, attrs: Iterable[App]) -> WA: ...
     def map_attrs(self: WA, f: Callable[[tuple[App, ...]], Iterable[App]]) -> WA:
         return self.let_attrs(f(self.attrs))
 
+    @cached_property
+    def attrs_by_key(self) -> FrozenDict[str, App]:
+        return FrozenDict({attr.symbol: attr for attr in self.attrs})
+
 
 class Sentence(Kore, WithAttrs): ...
 
diff --git a/pyk/src/tests/integration/kore/test_rule.py b/pyk/src/tests/integration/kore/test_rule.py
new file mode 100644
index 00000000000..5f723146d89
--- /dev/null
+++ b/pyk/src/tests/integration/kore/test_rule.py
@@ -0,0 +1,36 @@
+from __future__ import annotations
+
+from collections import Counter
+from typing import TYPE_CHECKING
+
+import pytest
+
+from pyk.kore.parser import KoreParser
+from pyk.kore.rule import Rule
+
+from ..utils import K_FILES
+
+if TYPE_CHECKING:
+    from pyk.kore.syntax import Definition
+    from pyk.testing import Kompiler
+
+
+@pytest.fixture(scope='module')
+def definition(kompile: Kompiler) -> Definition:
+    main_file = K_FILES / 'imp.k'
+    definition_dir = kompile(main_file=main_file)
+    kore_file = definition_dir / 'definition.kore'
+    kore_text = kore_file.read_text()
+    definition = KoreParser(kore_text).definition()
+    return definition
+
+
+def test_extract_all(definition: Definition) -> None:
+    # When
+    rules = Rule.extract_all(definition)
+
+    # Then
+    cnt = Counter(type(rule).__name__ for rule in rules)
+    assert cnt['RewriteRule']
+    assert cnt['FunctionRule']
+    assert cnt['SimpliRule']