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The language in this module is deliberately small and domain-neutral. A
program is an expression tree, not host code: it has no recursion, function
calls, or open-ended loop construct. Repetition is limited to finite input
lists and is guarded by host-supplied limits.
Exact rationals use the canonical JSON record ``{"num": n, "den": d}``, where
``n`` and ``d`` are integers, ``d`` is positive, and the fraction is reduced.
Arithmetic operations always return that representation. Plain JSON integers
remain useful for list indexes and may also be used as exact numeric operands.
The ``unique`` operation identifies values by canonical JSON bytes and preserves
the first occurrence in the finite source list.
"""
from __future__ import annotations
from dataclasses import dataclass
from fractions import Fraction
import copy
import hashlib
import json
import math
from typing import Any, Mapping
PROGRAM_SCHEMA = "TOMAGI-FORMAL-PROGRAM-1.0"
RESULT_SCHEMA = "TOMAGI-FORMAL-RESULT-1.0"
OPERATIONS = frozenset({
"lit", "rat", "ref", "list", "record", "let",
"get", "has", "keys", "values", "put", "merge", "len", "is_string", "concat", "append",
"add", "sub", "mul", "div", "neg", "abs", "floor", "integer_abs", "bit_length",
"eq", "ne", "lt", "le", "gt", "ge", "not", "and", "or",
"if", "assert", "hash",
"pairs", "unique", "map", "filter", "sort", "group", "fold",
})
class FormalError(ValueError):
"""Base class for formal-program validation and evaluation failures."""
class FormalValidationError(FormalError):
"""The program or a JSON value is outside the formal data model."""
class FormalEvaluationError(FormalError):
"""A well-formed operation cannot be evaluated for the supplied values."""
class FormalBudgetExceeded(FormalEvaluationError):
"""Evaluation exceeded a host-defined finite resource limit."""
class FormalAssertionError(FormalEvaluationError):
"""A formal ``assert`` expression evaluated to false."""
@dataclass(frozen=True)
class Limits:
"""Host-side limits; a literal program cannot relax these values."""
max_steps: int = 100_000
max_depth: int = 128
max_collection_items: int = 10_000
max_value_nodes: int = 100_000
max_canonical_bytes: int = 4_000_000
def __post_init__(self) -> None:
for name in (
"max_steps",
"max_depth",
"max_collection_items",
"max_value_nodes",
"max_canonical_bytes",
):
value = getattr(self, name)
if isinstance(value, bool) or not isinstance(value, int) or value <= 0:
raise FormalValidationError(f"{name} must be a positive integer")
def _is_int(value: Any) -> bool:
return isinstance(value, int) and not isinstance(value, bool)
def _is_rational(value: Any) -> bool:
return (
isinstance(value, dict)
and set(value) == {"num", "den"}
and _is_int(value.get("num"))
and _is_int(value.get("den"))
)
def _looks_rational(value: Any) -> bool:
return isinstance(value, dict) and set(value) == {"num", "den"}
def _validate_rational(value: Mapping[str, Any], path: str) -> None:
num = value["num"]
den = value["den"]
if not _is_int(num) or not _is_int(den):
raise FormalValidationError(f"{path}: rational numerator and denominator must be integers")
if den <= 0:
raise FormalValidationError(f"{path}: rational denominator must be positive")
if math.gcd(abs(num), den) != 1:
raise FormalValidationError(f"{path}: rational must be reduced")
if num == 0 and den != 1:
raise FormalValidationError(f"{path}: zero rational must have denominator 1")
def rational(num: int, den: int = 1) -> dict[str, int]:
"""Return a reduced exact-rational JSON record."""
if not _is_int(num) or not _is_int(den):
raise FormalValidationError("rational numerator and denominator must be integers")
if den == 0:
raise FormalEvaluationError("division by zero")
fraction = Fraction(num, den)
return {"num": fraction.numerator, "den": fraction.denominator}
def _validate_json(value: Any, limits: Limits, *, path: str = "$", depth: int = 0,
counter: list[int] | None = None) -> None:
if counter is None:
counter = [0]
counter[0] += 1
if counter[0] > limits.max_value_nodes:
raise FormalBudgetExceeded(
f"JSON value exceeds max_value_nodes={limits.max_value_nodes}"
)
if depth > limits.max_depth:
raise FormalBudgetExceeded(f"JSON value exceeds max_depth={limits.max_depth}")
if value is None or isinstance(value, (bool, str)) or _is_int(value):
return
if isinstance(value, float):
raise FormalValidationError(f"{path}: floating-point values are forbidden")
if isinstance(value, list):
if len(value) > limits.max_collection_items:
raise FormalBudgetExceeded(
f"{path}: list exceeds max_collection_items={limits.max_collection_items}"
)
for index, item in enumerate(value):
_validate_json(item, limits, path=f"{path}[{index}]", depth=depth + 1,
counter=counter)
return
if isinstance(value, dict):
if len(value) > limits.max_collection_items:
raise FormalBudgetExceeded(
f"{path}: record exceeds max_collection_items={limits.max_collection_items}"
)
for key in value:
if not isinstance(key, str):
raise FormalValidationError(f"{path}: record keys must be strings")
if _looks_rational(value):
_validate_rational(value, path)
for key in sorted(value):
_validate_json(value[key], limits, path=f"{path}.{key}", depth=depth + 1,
counter=counter)
return
raise FormalValidationError(
f"{path}: value of type {type(value).__name__} is not JSON-native"
)
def canonical_bytes(value: Any, *, limits: Limits | None = None) -> bytes:
"""Validate and serialize a formal value to deterministic canonical JSON."""
active = limits or Limits()
_validate_json(value, active)
data = json.dumps(
value, sort_keys=True, ensure_ascii=False, separators=(",", ":"), allow_nan=False
).encode("utf-8")
if len(data) > active.max_canonical_bytes:
raise FormalBudgetExceeded(
f"canonical value exceeds max_canonical_bytes={active.max_canonical_bytes}"
)
return data
def content_address(value: Any, *, limits: Limits | None = None) -> str:
"""Return the canonical SHA-256 address of a formal JSON value."""
return "sha256:" + hashlib.sha256(canonical_bytes(value, limits=limits)).hexdigest()
def program_content_hash(program: Mapping[str, Any], *, limits: Limits | None = None) -> str:
"""Hash a program record while excluding its self-address field."""
if not isinstance(program, Mapping):
raise FormalValidationError("program must be a record")
body = {key: copy.deepcopy(value) for key, value in program.items()
if key != "content_hash"}
return content_address(body, limits=limits)
def attach_program_hash(program: Mapping[str, Any], *, limits: Limits | None = None) -> dict[str, Any]:
"""Return a detached program record with its canonical content address."""
out = copy.deepcopy(dict(program))
out["content_hash"] = program_content_hash(out, limits=limits)
return out
def verify_program_hash(program: Mapping[str, Any], *, limits: Limits | None = None) -> bool:
"""Return whether a program carries its exact canonical content address."""
claimed = program.get("content_hash") if isinstance(program, Mapping) else None
return isinstance(claimed, str) and claimed == program_content_hash(program, limits=limits)
def make_program(expression: Mapping[str, Any], *, program_id: str | None = None,
limits: Limits | None = None) -> dict[str, Any]:
"""Construct and content-address a formal program record."""
active = limits or Limits()
canonical_bytes(expression, limits=active)
_validate_expression_syntax(expression, active)
record: dict[str, Any] = {"schema": PROGRAM_SCHEMA, "expression": copy.deepcopy(expression)}
if program_id is not None:
if not isinstance(program_id, str) or not program_id:
raise FormalValidationError("program_id must be a non-empty string")
record["id"] = program_id
return attach_program_hash(record, limits=active)
def _as_fraction(value: Any, context: str) -> Fraction:
if _is_int(value):
return Fraction(value, 1)
if _is_rational(value):
_validate_rational(value, context)
return Fraction(value["num"], value["den"])
raise FormalEvaluationError(f"{context} requires an exact integer or rational")
def _from_fraction(value: Fraction) -> dict[str, int]:
return {"num": value.numerator, "den": value.denominator}
def _require_bool(value: Any, context: str) -> bool:
if not isinstance(value, bool):
raise FormalEvaluationError(f"{context} requires a boolean")
return value
def _total_key(value: Any) -> tuple[Any, ...]:
"""A deterministic total order over validated formal JSON values."""
if value is None:
return (0,)
if isinstance(value, bool):
return (1, int(value))
if _is_int(value):
fraction = Fraction(value, 1)
return (2, fraction)
if _is_rational(value):
fraction = _as_fraction(value, "sort key")
return (2, fraction)
if isinstance(value, str):
return (3, value)
if isinstance(value, list):
return (4, tuple(_total_key(item) for item in value))
if isinstance(value, dict):
return (5, tuple((key, _total_key(value[key])) for key in sorted(value)))
raise FormalEvaluationError("sort key is not a formal JSON value")
def _strict_fields(expression: Mapping[str, Any], required: set[str],
optional: set[str] | None = None) -> None:
permitted = required | (optional or set()) | {"op"}
missing = sorted(required - set(expression))
extra = sorted(set(expression) - permitted)
if missing:
raise FormalValidationError(f"operation {expression.get('op')!r} missing fields: {missing}")
if extra:
raise FormalValidationError(f"operation {expression.get('op')!r} has unknown fields: {extra}")
def _binding_name(value: Any, field: str) -> str:
if not isinstance(value, str) or not value:
raise FormalValidationError(f"{field} must be a non-empty binding name")
return value
def _validate_expression_syntax(expression: Any, limits: Limits, depth: int = 0) -> None:
"""Validate the complete expression tree, including unreachable branches."""
if depth > limits.max_depth:
raise FormalBudgetExceeded(f"expression exceeds max_depth={limits.max_depth}")
if not isinstance(expression, dict):
raise FormalValidationError("every expression must be an operation record")
operation = expression.get("op")
if not isinstance(operation, str):
raise FormalValidationError("expression op must be a string")
if operation not in OPERATIONS:
hint = " (unbounded loops are not supported)" if operation in {"while", "loop"} else ""
raise FormalValidationError(f"unknown formal operation {operation!r}{hint}")
children: list[Any] = []
if operation == "lit":
_strict_fields(expression, {"value"})
elif operation == "rat":
_strict_fields(expression, {"num", "den"})
children = [expression["num"], expression["den"]]
elif operation == "ref":
_strict_fields(expression, {"name"})
_binding_name(expression["name"], "ref name")
elif operation == "list":
_strict_fields(expression, {"items"})
if not isinstance(expression["items"], list):
raise FormalValidationError("list items must be an expression list")
children = list(expression["items"])
elif operation == "record":
_strict_fields(expression, {"fields"})
fields = expression["fields"]
if not isinstance(fields, dict) or any(not isinstance(key, str) for key in fields):
raise FormalValidationError("record fields must be a string-keyed expression record")
children = [fields[key] for key in sorted(fields)]
elif operation == "let":
_strict_fields(expression, {"bindings", "body"})
bindings = expression["bindings"]
if not isinstance(bindings, list):
raise FormalValidationError("let bindings must be an ordered list")
names: set[str] = set()
for binding in bindings:
if not isinstance(binding, dict) or set(binding) != {"name", "value"}:
raise FormalValidationError("each let binding requires only name and value")
name = _binding_name(binding["name"], "let binding name")
if name in names:
raise FormalValidationError(f"duplicate let binding {name!r}")
names.add(name)
children.append(binding["value"])
children.append(expression["body"])
elif operation in {"get", "has"}:
_strict_fields(expression, {"target", "key"})
children = [expression["target"], expression["key"]]
elif operation in {"keys", "values"}:
_strict_fields(expression, {"target"})
children = [expression["target"]]
elif operation in {"len", "is_string", "neg", "abs", "floor", "integer_abs", "bit_length", "not", "hash"}:
_strict_fields(expression, {"value"})
children = [expression["value"]]
elif operation in {
"add", "sub", "mul", "div", "eq", "ne", "lt", "le", "gt", "ge",
"concat", "merge",
}:
_strict_fields(expression, {"left", "right"})
children = [expression["left"], expression["right"]]
elif operation == "put":
_strict_fields(expression, {"target", "key", "value"})
children = [expression["target"], expression["key"], expression["value"]]
elif operation == "append":
_strict_fields(expression, {"source", "value"})
children = [expression["source"], expression["value"]]
elif operation in {"and", "or"}:
_strict_fields(expression, {"values"})
if not isinstance(expression["values"], list):
raise FormalValidationError(f"{operation} values must be an expression list")
children = list(expression["values"])
elif operation == "if":
_strict_fields(expression, {"condition", "then", "else"})
children = [expression["condition"], expression["then"], expression["else"]]
elif operation == "assert":
_strict_fields(expression, {"condition", "value"}, {"message"})
if "message" in expression and not isinstance(expression["message"], str):
raise FormalValidationError("assert message must be a string")
children = [expression["condition"], expression["value"]]
elif operation in {"pairs", "unique"}:
_strict_fields(expression, {"source"})
children = [expression["source"]]
elif operation in {"map", "filter", "sort", "group"}:
body_field = {"map": "body", "filter": "predicate"}.get(operation, "key")
optional = {"index", "descending"} if operation == "sort" else {"index"}
_strict_fields(expression, {"source", "item", body_field}, optional)
item = _binding_name(expression["item"], "item")
index = expression.get("index")
if index is not None:
index = _binding_name(index, "index")
if index == item:
raise FormalValidationError("item and index bindings must be distinct")
if operation == "sort" and not isinstance(expression.get("descending", False), bool):
raise FormalValidationError("sort descending must be a boolean")
children = [expression["source"], expression[body_field]]
elif operation == "fold":
_strict_fields(
expression, {"source", "item", "accumulator", "initial", "body"}, {"index"}
)
item = _binding_name(expression["item"], "item")
accumulator = _binding_name(expression["accumulator"], "accumulator")
index = expression.get("index")
if index is not None:
index = _binding_name(index, "index")
names = [name for name in (item, accumulator, index) if name is not None]
if len(names) != len(set(names)):
raise FormalValidationError("fold binding names must be distinct")
children = [expression["source"], expression["initial"], expression["body"]]
for child in children:
_validate_expression_syntax(child, limits, depth + 1)
class _Evaluator:
def __init__(self, limits: Limits):
self.limits = limits
self.steps = 0
# Formal values are immutable by language contract. Retaining each
# validated compound object makes an identity cache safe against id
# reuse while avoiding quadratic re-validation of large shared values.
self._validated_objects: dict[int, Any] = {}
def _check_result(self, value: Any) -> None:
"""Bound every recursive result before its parent consumes it.
Scalars are cheap and are checked directly. Lists/records are checked
once per immutable object identity; the cache retains the object so a
Python id cannot be reused during evaluation. This preserves the
CODEX repair invariant without repeatedly serializing the same large
registry or candidate collection through nested ``ref``/``get`` nodes.
"""
if value is None or isinstance(value, (bool, str)) or _is_int(value):
_validate_json(value, self.limits)
canonical_bytes(value, limits=self.limits)
return
identity = id(value)
prior = self._validated_objects.get(identity)
if prior is value:
return
_validate_json(value, self.limits)
canonical_bytes(value, limits=self.limits)
self._validated_objects[identity] = value
def _charge(self, amount: int = 1) -> None:
if amount < 0 or self.steps + amount > self.limits.max_steps:
raise FormalBudgetExceeded(
f"evaluation exceeds max_steps={self.limits.max_steps}"
)
self.steps += amount
def _finite_source(self, value: Any, operation: str) -> list[Any]:
if not isinstance(value, list):
raise FormalEvaluationError(f"{operation} requires a list source")
if len(value) > self.limits.max_collection_items:
raise FormalBudgetExceeded(
f"{operation} source exceeds max_collection_items="
f"{self.limits.max_collection_items}"
)
return value
@staticmethod
def _binder(expression: Mapping[str, Any], field: str) -> str:
name = expression[field]
if not isinstance(name, str) or not name:
raise FormalValidationError(f"{field} must be a non-empty binding name")
return name
def _child_scope(self, scope: Mapping[str, Any], values: Mapping[str, Any]) -> dict[str, Any]:
out = dict(scope)
out.update(values)
return out
def eval(self, expression: Any, scope: Mapping[str, Any], depth: int = 0) -> Any:
value = self._eval_unchecked(expression, scope, depth)
# Every recursive result is bounded before its parent can consume it.
# This includes fold accumulators and map/filter/group intermediates.
self._check_result(value)
return value
def _eval_unchecked(self, expression: Any, scope: Mapping[str, Any], depth: int = 0) -> Any:
self._charge()
if depth > self.limits.max_depth:
raise FormalBudgetExceeded(
f"expression exceeds max_depth={self.limits.max_depth}"
)
if not isinstance(expression, dict):
raise FormalValidationError("every expression must be an operation record")
operation = expression.get("op")
if not isinstance(operation, str):
raise FormalValidationError("expression op must be a string")
child_depth = depth + 1
if operation == "lit":
_strict_fields(expression, {"value"})
value = copy.deepcopy(expression["value"])
_validate_json(value, self.limits)
return value
if operation == "rat":
_strict_fields(expression, {"num", "den"})
num = self.eval(expression["num"], scope, child_depth)
den = self.eval(expression["den"], scope, child_depth)
if not _is_int(num) or not _is_int(den):
raise FormalEvaluationError("rat numerator and denominator must evaluate to integers")
return rational(num, den)
if operation == "ref":
_strict_fields(expression, {"name"})
name = expression["name"]
if not isinstance(name, str) or not name:
raise FormalValidationError("ref name must be a non-empty string")
if name not in scope:
raise FormalEvaluationError(f"unknown reference {name!r}")
return scope[name]
if operation == "list":
_strict_fields(expression, {"items"})
items = expression["items"]
if not isinstance(items, list):
raise FormalValidationError("list items must be an expression list")
if len(items) > self.limits.max_collection_items:
raise FormalBudgetExceeded("list constructor exceeds max_collection_items")
return [self.eval(item, scope, child_depth) for item in items]
if operation == "record":
_strict_fields(expression, {"fields"})
fields = expression["fields"]
if not isinstance(fields, dict) or any(not isinstance(key, str) for key in fields):
raise FormalValidationError("record fields must be a string-keyed expression record")
if len(fields) > self.limits.max_collection_items:
raise FormalBudgetExceeded("record constructor exceeds max_collection_items")
value = {key: self.eval(fields[key], scope, child_depth) for key in sorted(fields)}
_validate_json(value, self.limits)
return value
if operation == "let":
_strict_fields(expression, {"bindings", "body"})
bindings = expression["bindings"]
if not isinstance(bindings, list):
raise FormalValidationError("let bindings must be an ordered list")
if len(bindings) > self.limits.max_collection_items:
raise FormalBudgetExceeded("let bindings exceed max_collection_items")
nested = dict(scope)
names: set[str] = set()
for binding in bindings:
if not isinstance(binding, dict) or set(binding) != {"name", "value"}:
raise FormalValidationError("each let binding requires only name and value")
name = binding["name"]
if not isinstance(name, str) or not name:
raise FormalValidationError("let binding name must be a non-empty string")
if name in names:
raise FormalValidationError(f"duplicate let binding {name!r}")
nested[name] = self.eval(binding["value"], nested, child_depth)
names.add(name)
return self.eval(expression["body"], nested, child_depth)
if operation == "get":
_strict_fields(expression, {"target", "key"})
target = self.eval(expression["target"], scope, child_depth)
key = self.eval(expression["key"], scope, child_depth)
if isinstance(target, list):
if not _is_int(key) or key < 0 or key >= len(target):
raise FormalEvaluationError("list key must be an in-range non-negative integer")
return target[key]
if isinstance(target, dict):
if not isinstance(key, str) or key not in target:
raise FormalEvaluationError("record key must name an existing field")
return target[key]
raise FormalEvaluationError("get target must be a list or record")
if operation == "has":
_strict_fields(expression, {"target", "key"})
target = self.eval(expression["target"], scope, child_depth)
key = self.eval(expression["key"], scope, child_depth)
if isinstance(target, list):
return _is_int(key) and 0 <= key < len(target)
if isinstance(target, dict):
return isinstance(key, str) and key in target
raise FormalEvaluationError("has target must be a list or record")
if operation == "keys":
_strict_fields(expression, {"target"})
target = self.eval(expression["target"], scope, child_depth)
if not isinstance(target, dict):
raise FormalEvaluationError("keys target must be a record")
return sorted(target)
if operation == "values":
_strict_fields(expression, {"target"})
target = self.eval(expression["target"], scope, child_depth)
if not isinstance(target, dict):
raise FormalEvaluationError("values target must be a record")
return [target[key] for key in sorted(target)]
if operation == "put":
_strict_fields(expression, {"target", "key", "value"})
target = self.eval(expression["target"], scope, child_depth)
key = self.eval(expression["key"], scope, child_depth)
if not isinstance(target, dict) or not isinstance(key, str):
raise FormalEvaluationError("put requires a record and string key")
out = dict(target)
out[key] = self.eval(expression["value"], scope, child_depth)
_validate_json(out, self.limits)
return out
if operation == "merge":
_strict_fields(expression, {"left", "right"})
left = self.eval(expression["left"], scope, child_depth)
right = self.eval(expression["right"], scope, child_depth)
if not isinstance(left, dict) or not isinstance(right, dict):
raise FormalEvaluationError("merge requires two records")
out = dict(left)
for key in sorted(right):
out[key] = right[key]
_validate_json(out, self.limits)
return out
if operation == "len":
_strict_fields(expression, {"value"})
value = self.eval(expression["value"], scope, child_depth)
if not isinstance(value, (list, dict, str)):
raise FormalEvaluationError("len requires a list, record, or string")
return len(value)
if operation == "is_string":
_strict_fields(expression, {"value"})
return isinstance(self.eval(expression["value"], scope, child_depth), str)
if operation == "concat":
_strict_fields(expression, {"left", "right"})
left = self._finite_source(self.eval(expression["left"], scope, child_depth), "concat")
right = self._finite_source(self.eval(expression["right"], scope, child_depth), "concat")
if len(left) + len(right) > self.limits.max_collection_items:
raise FormalBudgetExceeded("concat result exceeds max_collection_items")
self._charge(len(left) + len(right))
return list(left) + list(right)
if operation == "append":
_strict_fields(expression, {"source", "value"})
source = self._finite_source(self.eval(expression["source"], scope, child_depth), "append")
if len(source) + 1 > self.limits.max_collection_items:
raise FormalBudgetExceeded("append result exceeds max_collection_items")
return list(source) + [self.eval(expression["value"], scope, child_depth)]
if operation in {"add", "sub", "mul", "div"}:
_strict_fields(expression, {"left", "right"})
left = _as_fraction(self.eval(expression["left"], scope, child_depth), operation)
right = _as_fraction(self.eval(expression["right"], scope, child_depth), operation)
if operation == "add":
result = left + right
elif operation == "sub":
result = left - right
elif operation == "mul":
result = left * right
else:
if right == 0:
raise FormalEvaluationError("division by zero")
result = left / right
return _from_fraction(result)
if operation in {"neg", "abs"}:
_strict_fields(expression, {"value"})
value = _as_fraction(self.eval(expression["value"], scope, child_depth), operation)
return _from_fraction(-value if operation == "neg" else abs(value))
if operation == "floor":
_strict_fields(expression, {"value"})
value = _as_fraction(self.eval(expression["value"], scope, child_depth), operation)
return value.numerator // value.denominator
if operation == "integer_abs":
_strict_fields(expression, {"value"})
value = self.eval(expression["value"], scope, child_depth)
if not _is_int(value):
raise FormalEvaluationError("integer_abs requires an integer")
return abs(value)
if operation == "bit_length":
_strict_fields(expression, {"value"})
value = self.eval(expression["value"], scope, child_depth)
if not _is_int(value) or value < 0:
raise FormalEvaluationError("bit_length requires a non-negative integer")
return value.bit_length()
if operation in {"eq", "ne", "lt", "le", "gt", "ge"}:
_strict_fields(expression, {"left", "right"})
left = self.eval(expression["left"], scope, child_depth)
right = self.eval(expression["right"], scope, child_depth)
numeric = (_is_int(left) or _is_rational(left)) and (
_is_int(right) or _is_rational(right)
)
if operation in {"eq", "ne"}:
# Python considers ``True == 1`` and applies that coercion
# recursively inside lists and dictionaries. Formal JSON does
# not: booleans and exact numbers are distinct value types.
# Canonical bytes provide type-strict structural equality for
# every non-numeric formal value while retaining rational
# numeric equality in the branch above.
equal = (
_as_fraction(left, operation) == _as_fraction(right, operation)
if numeric
else canonical_bytes(left, limits=self.limits)
== canonical_bytes(right, limits=self.limits)
)
return equal if operation == "eq" else not equal
if not numeric:
raise FormalEvaluationError(f"{operation} requires exact numeric operands")
a = _as_fraction(left, operation)
b = _as_fraction(right, operation)
return {"lt": a < b, "le": a <= b, "gt": a > b, "ge": a >= b}[operation]
if operation == "not":
_strict_fields(expression, {"value"})
return not _require_bool(self.eval(expression["value"], scope, child_depth), "not")
if operation in {"and", "or"}:
_strict_fields(expression, {"values"})
values = expression["values"]
if not isinstance(values, list):
raise FormalValidationError(f"{operation} values must be an expression list")
if len(values) > self.limits.max_collection_items:
raise FormalBudgetExceeded(f"{operation} values exceed max_collection_items")
identity = operation == "and"
for child in values:
value = _require_bool(self.eval(child, scope, child_depth), operation)
if value != identity:
return value
return identity
if operation == "if":
_strict_fields(expression, {"condition", "then", "else"})
condition = _require_bool(
self.eval(expression["condition"], scope, child_depth), "if"
)
branch = "then" if condition else "else"
return self.eval(expression[branch], scope, child_depth)
if operation == "assert":
_strict_fields(expression, {"condition", "value"}, {"message"})
message = expression.get("message", "formal assertion failed")
if not isinstance(message, str):
raise FormalValidationError("assert message must be a string")
condition = _require_bool(
self.eval(expression["condition"], scope, child_depth), "assert"
)
if not condition:
raise FormalAssertionError(message)
return self.eval(expression["value"], scope, child_depth)
if operation == "hash":
_strict_fields(expression, {"value"})
value = self.eval(expression["value"], scope, child_depth)
return content_address(value, limits=self.limits)
if operation == "pairs":
_strict_fields(expression, {"source"})
source = self._finite_source(
self.eval(expression["source"], scope, child_depth), "pairs"
)
count = len(source) * (len(source) - 1) // 2
if count > self.limits.max_collection_items:
raise FormalBudgetExceeded("pairs result exceeds max_collection_items")
self._charge(count)
return [
{
"left": source[left],
"left_index": left,
"right": source[right],
"right_index": right,
}
for left in range(len(source))
for right in range(left + 1, len(source))
]
if operation == "unique":
_strict_fields(expression, {"source"})
source = self._finite_source(
self.eval(expression["source"], scope, child_depth), "unique"
)
seen: set[bytes] = set()
output: list[Any] = []
for item in source:
self._charge()
identity = canonical_bytes(item, limits=self.limits)
if identity not in seen:
seen.add(identity)
output.append(item)
return output
if operation in {"map", "filter", "sort", "group"}:
required = {"source", "item", "body"} if operation == "map" else {
"source", "item", "predicate"
} if operation == "filter" else {"source", "item", "key"}
_strict_fields(expression, required, {"index", "descending"} if operation == "sort"
else {"index"})
source = self._finite_source(
self.eval(expression["source"], scope, child_depth), operation
)
item_name = self._binder(expression, "item")
index_name = expression.get("index")
if index_name is not None and (not isinstance(index_name, str) or not index_name):
raise FormalValidationError("index must be a non-empty binding name")
if index_name == item_name:
raise FormalValidationError("item and index bindings must be distinct")
decorated: list[tuple[Any, Any]] = []
output: list[Any] = []
for index, item in enumerate(source):
self._charge()
values = {item_name: item}
if index_name is not None:
values[index_name] = index
nested = self._child_scope(scope, values)
if operation == "map":
output.append(self.eval(expression["body"], nested, child_depth))
elif operation == "filter":
keep = _require_bool(
self.eval(expression["predicate"], nested, child_depth), "filter"
)
if keep:
output.append(item)
else:
key = self.eval(expression["key"], nested, child_depth)
_validate_json(key, self.limits)
decorated.append((key, item))
if operation in {"map", "filter"}:
if len(output) > self.limits.max_collection_items:
raise FormalBudgetExceeded(f"{operation} result exceeds max_collection_items")
return output
if operation == "sort":
descending = expression.get("descending", False)
if not isinstance(descending, bool):
raise FormalValidationError("sort descending must be a boolean")
decorated.sort(key=lambda pair: _total_key(pair[0]), reverse=descending)
return [item for _, item in decorated]
groups: dict[bytes, tuple[Any, list[Any]]] = {}
for key, item in decorated:
encoded = canonical_bytes(key, limits=self.limits)
if encoded not in groups:
groups[encoded] = (key, [])
groups[encoded][1].append(item)
ordered = sorted(groups.values(), key=lambda group: _total_key(group[0]))
return [{"key": key, "items": items} for key, items in ordered]
if operation == "fold":
_strict_fields(
expression,
{"source", "item", "accumulator", "initial", "body"},
{"index"},
)
source = self._finite_source(
self.eval(expression["source"], scope, child_depth), "fold"
)
item_name = self._binder(expression, "item")
accumulator_name = self._binder(expression, "accumulator")
index_name = expression.get("index")
names = [name for name in (item_name, accumulator_name, index_name) if name is not None]
if len(names) != len(set(names)):
raise FormalValidationError("fold binding names must be distinct")
if index_name is not None and (not isinstance(index_name, str) or not index_name):
raise FormalValidationError("index must be a non-empty binding name")
accumulator = self.eval(expression["initial"], scope, child_depth)
for index, item in enumerate(source):
self._charge()
values = {item_name: item, accumulator_name: accumulator}
if index_name is not None:
values[index_name] = index
accumulator = self.eval(
expression["body"], self._child_scope(scope, values), child_depth
)
return accumulator
hint = " (unbounded loops are not supported)" if operation in {"while", "loop"} else ""
raise FormalValidationError(f"unknown formal operation {operation!r}{hint}")
def evaluate_with_steps(expression: Mapping[str, Any],
bindings: Mapping[str, Any] | None = None, *,
limits: Limits | None = None) -> dict[str, Any]:
"""Evaluate an expression and return its detached value and exact step count."""
active = limits or Limits()
scope = copy.deepcopy(dict(bindings or {}))
if any(not isinstance(name, str) or not name for name in scope):
raise FormalValidationError("binding names must be non-empty strings")
canonical_bytes(scope, limits=active)
canonical_bytes(expression, limits=active)
_validate_expression_syntax(expression, active)
evaluator = _Evaluator(active)
value = evaluator.eval(expression, scope)
_validate_json(value, active)
canonical_bytes(value, limits=active)
return {"value": copy.deepcopy(value), "steps": evaluator.steps}
def evaluate(expression: Mapping[str, Any], bindings: Mapping[str, Any] | None = None,
*, limits: Limits | None = None) -> Any:
"""Evaluate an expression and return a detached JSON-native value."""
return evaluate_with_steps(expression, bindings, limits=limits)["value"]
def run_program(program: Mapping[str, Any], inputs: Mapping[str, Any] | None = None,
*, limits: Limits | None = None) -> dict[str, Any]:
"""Verify and run a content-addressed program, returning an addressed result.
The integration boundary is intentionally JSON-only: ``program`` and
``inputs`` are records, and the returned result is a canonical record with
its own ``content_hash``.
"""
active = limits or Limits()
if not isinstance(program, Mapping):
raise FormalValidationError("program must be a record")
allowed = {"schema", "id", "expression", "content_hash"}
missing = {"schema", "expression", "content_hash"} - set(program)
extra = set(program) - allowed
if missing:
raise FormalValidationError(f"program missing fields: {sorted(missing)}")
if extra:
raise FormalValidationError(f"program has unknown fields: {sorted(extra)}")
if program["schema"] != PROGRAM_SCHEMA:
raise FormalValidationError(f"unsupported program schema {program['schema']!r}")
if "id" in program and (not isinstance(program["id"], str) or not program["id"]):
raise FormalValidationError("program id must be a non-empty string")
_validate_json(dict(program), active)
if not verify_program_hash(program, limits=active):
raise FormalValidationError("program content hash mismatch")
_validate_expression_syntax(program["expression"], active)
scope = copy.deepcopy(dict(inputs or {}))
if any(not isinstance(name, str) or not name for name in scope):
raise FormalValidationError("input names must be non-empty strings")
canonical_bytes(scope, limits=active)
evaluator = _Evaluator(active)
value = evaluator.eval(program["expression"], scope)
_validate_json(value, active)
canonical_bytes(value, limits=active)
record = {
"schema": RESULT_SCHEMA,
"program_hash": program["content_hash"],
"inputs_hash": content_address(scope, limits=active),
"steps": evaluator.steps,
"value": copy.deepcopy(value),
}
record["content_hash"] = content_address(record, limits=active)
return record
__all__ = [
"PROGRAM_SCHEMA",
"RESULT_SCHEMA",
"OPERATIONS",
"FormalAssertionError",
"FormalBudgetExceeded",
"FormalError",
"FormalEvaluationError",
"FormalValidationError",
"Limits",
"attach_program_hash",
"canonical_bytes",
"content_address",
"evaluate",
"evaluate_with_steps",
"make_program",
"program_content_hash",
"rational",
"run_program",
"verify_program_hash",
]
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