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1250 | class AnyDiceInterpreter:
def __init__(self) -> None:
# `_settings` is non-`None` only during a `run()` call -- see `run()`'s
# try/finally. Code paths that need the active settings assert
# non-`None` to satisfy type checkers; calling them outside a run is a
# bug. Same lifecycle pattern as `_quantize_stack` below.
self._settings: Settings | None = None
# ExitStack that owns the nested `quantize_hs` contexts produced by
# `set "anydyce: calculation precision"` directives. Owned by `run()`;
# `_apply_calc_precision` unwinds and re-enters as needed when a `set`
# changes the calc bit_width.
self._quantize_stack: ExitStack | None = None
self._env: dict[str, _Val] = {}
self._outputs: AnyDiceResultsT = []
# Functions are keyed by their pattern *shape* -- a tuple slotting fixed words
# at fixed positions and `None` for each parameter slot regardless of type
# annotation. AnyDice's user-visible "function name" is exactly this shape (e.g.
# `function: add X:n to Y:d` and `function: add X:s to Y:n` are the same
# callable. The latter REPLACES the former on registration). Param type
# annotations are body-evaluation hints, not dispatch keys.
self._funcs: dict[tuple[str | None, ...], FunctionDef] = {}
# Built-in dispatch table mirrors _funcs but maps to (param_types, impl). User
# functions take precedence: _call consults _funcs first and falls back here.
self._builtins: dict[
tuple[str | None, ...], tuple[list[str | None], Callable[..., _Val]]
] = {}
for pattern, param_types, impl in BUILTINS:
shape = tuple(p if isinstance(p, str) else None for p in pattern)
self._builtins[shape] = (list(param_types), impl)
self._depth = 0
def run(
self,
program: Program,
*,
settings: Settings | None = None,
) -> AnyDiceResultsT:
r"""Execute a parsed program and return `(name, distribution)` pairs.
If `settings` is provided, the interpreter uses it for the duration of
the call and mutations from `set` directives are visible to the
caller afterwards (the final value at end-of-run is what the caller
observes -- formatting consumers read e.g. `settings.display_precision`
from it). If omitted, a fresh `Settings()` is used internally and the
caller cannot observe `set`-directive effects.
"""
self._env = {}
self._outputs = []
self._funcs = {}
self._depth = 0
self._settings = settings if settings is not None else Settings()
# Bump Python's recursion limit for the duration of this run. Both
# `dyce.p`'s pool-selection (recurses ~4 Python frames per distinct
# outcome of the underlying H, via `lowest_terms` / `__hash__` in
# the inner loop) and our own interpreter call chain (~7 Python
# frames per AnyDice call) can hit the default ~1000 limit on
# otherwise reasonable programs. Empirically 5000 covers
# pool-selection on dies up to ~d1250 and user-function recursion
# up to ~`set "maximum function depth" to 700`, while staying well
# below the C-stack overflow risk zone (a Python frame is a few
# hundred bytes, default Linux thread stack is 8MB).
prev_limit = sys.getrecursionlimit()
if prev_limit < 5000:
sys.setrecursionlimit(5000)
try:
with ExitStack() as stack:
self._quantize_stack = stack
self._apply_calc_precision(self._settings.calc_bit_width)
for stmt in program.stmts:
self._exec(stmt)
return list(self._outputs)
finally:
if prev_limit < 5000:
sys.setrecursionlimit(prev_limit)
self._settings = None
self._quantize_stack = None
def _apply_calc_precision(self, bit_width: int) -> None:
r"""Unwind any active `quantize_hs` context and enter a new one for
`bit_width`. `bit_width == 0` means "exact" -- no quantization, no
active context. Called from `run()` at entry and from the SetStmt
handler when `"anydyce: calculation precision"` changes."""
assert self._quantize_stack is not None, "called outside run()"
# close() unwinds all registered exits. ExitStack stays reusable, so
# subsequent enter_context() registers the replacement (or no
# replacement, for bit_width=0).
self._quantize_stack.close()
if bit_width > 0:
self._quantize_stack.enter_context(
quantize_hs(bit_width=bit_width, preserve_zero_counts=True)
)
# ---- Statement execution -------------------------------------------------------------
def _exec(self, stmt: Stmt) -> None: # noqa: C901
if isinstance(stmt, OutputStmt):
value = self._eval(stmt.expr)
h = self._coerce_to_h(value)
label = self._eval_name(stmt.name)
if label is None:
label = f"output {len(self._outputs) + 1}"
self._outputs.append((label, h))
elif isinstance(stmt, SetStmt):
assert self._settings is not None, "SetStmt outside run()"
v = self._eval(stmt.value)
if isinstance(v, (str, int)):
self._settings.set(stmt.key, v)
# Adjusts the active `quantize_hs` context for the rest of the run
if stmt.key == "anydyce: calculation precision":
self._apply_calc_precision(self._settings.calc_bit_width)
else: # pragma: no cover
raise TypeError(
f"set value must resolve to string or number, got {type(v).__name__}"
)
elif isinstance(stmt, FunctionDef):
# Redefinition with the same shape replaces. Param types do not affect
# identity.
self._funcs[_pattern_shape(stmt.pattern)] = stmt
elif isinstance(stmt, VarAssign):
self._env[stmt.name] = self._eval(stmt.expr)
elif isinstance(stmt, IfStmt):
self._exec_if(stmt)
elif isinstance(stmt, LoopStmt):
self._exec_loop(stmt)
elif isinstance(stmt, ResultStmt):
# `result:` is grammatically restricted to function bodies, but the body can
# nest the statement inside `if` / `loop` blocks. Raising an exception
# unwinds through any nesting back to the function-call machinery, which
# catches it.
raise _ResultReturn(self._eval(stmt.expr))
else: # pragma: no cover
raise NotImplementedError(f"unhandled statement: {type(stmt).__name__}")
def _exec_if(self, stmt: IfStmt) -> None:
for branch in stmt.branches:
if self._is_truthy(self._eval(branch.condition)):
for body_stmt in branch.body:
self._exec(body_stmt)
return
if stmt.else_branch is not None:
for body_stmt in stmt.else_branch.body:
self._exec(body_stmt)
def _exec_loop(self, stmt: LoopStmt) -> None:
over = self._eval(stmt.over)
if not isinstance(over, tuple):
raise TypeError(f"loop over must be a sequence, got {type(over).__name__}")
# AnyDice does not introduce a child scope for loop bodies. The loop variable is
# bound in the enclosing environment and any assignments in the body persist
# after the loop.
for value in over:
self._env[stmt.var] = value
for body_stmt in stmt.body:
self._exec(body_stmt)
def _is_truthy(self, v: _Val) -> bool:
# AnyDice's `if` accepts ONLY numbers. Sequences are NOT sum-coerced in
# condition position (verified against AnyDice via program 42aac, which
# errors on `if {} { ... }` with "Boolean values can only be numbers").
# Dice and strings are also rejected.
if isinstance(v, int):
return v != 0
else:
raise TypeError(f"cannot use {type(v).__name__} as boolean condition")
# ---- Expression evaluation -----------------------------------------------------------
def _eval(self, node: Expr) -> _Val: # noqa: C901
if isinstance(node, EmptySeq):
return ()
elif isinstance(node, Number):
return node.value
elif isinstance(node, SeqExpr):
return self._eval_seq(node.elems)
elif isinstance(node, DiceUnary):
faces = self._eval(node.faces)
# Unary `d` on an already-die-like value (H or P) is identity.
# Critical for preserving pool positional info through `dDIE` when
# DIE = NdX is a pool: collapsing via `_make_die` (which would
# call `P.h()`) loses the N-die structure that downstream
# `[highest K of dDIE]`-style builtins need to operate over.
# Verified necessary by program 178 (`[highest H of dDIE]` where
# DIE = 4d100; AnyDice's `d` on a pool is a no-op).
return faces if isinstance(faces, (H, P)) else self._make_die(faces)
elif isinstance(node, DiceBinOp):
n = self._eval(node.n)
if isinstance(n, tuple):
n = sum(n)
elif isinstance(n, P):
n = n.h()
if isinstance(n, int):
faces = self._eval(node.faces)
if n == 1 and isinstance(faces, P):
# 1d(<pool>) is treated as a no-op
return faces
return self._roll_n(n, self._make_die(faces))
elif isinstance(n, H):
# AnyDice expands a die-as-count over its outcomes: for each
# outcome k, evaluate `k d <faces>` and combine the per-outcome
# distributions weighted by k's probability. Inner distributions
# have different totals (1d6 vs 2d6 vs ...) so we must LCM-
# normalize before merging or the relative weighting will be
# wrong.
return self._expand_dice_count(
n, self._make_die(self._eval(node.faces))
)
else:
raise TypeError(f"dice count must be a number, got {type(n).__name__}")
elif isinstance(node, StringExpr):
return self._eval_string(node.parts)
elif isinstance(node, Var):
if node.name not in self._env:
raise NameError(f"undefined variable: {node.name!r}")
return self._env[node.name]
elif isinstance(node, BinOp):
left = self._eval(node.left)
right = self._eval(node.right)
if node.op == "@":
return self._apply_at(left, right)
return self._apply_binop(node.op, left, right)
elif isinstance(node, HashOp):
return self._apply_hash(self._eval(node.expr))
elif isinstance(node, NegOp):
return self._apply_neg(self._eval(node.expr))
elif isinstance(node, NotOp):
return self._apply_not(self._eval(node.expr))
elif isinstance(node, PosOp):
return self._eval(node.expr)
elif isinstance(node, Call):
return self._call(node)
else: # pragma: no cover
raise NotImplementedError(f"unhandled expression: {type(node).__name__}")
# ---- Unary operators -----------------------------------------------------------------
def _apply_neg(self, v: _Val) -> int | H[int] | P[int]:
if isinstance(v, tuple):
return -sum(v)
elif isinstance(v, (int, H)):
return -v
elif isinstance(v, P):
return P(*(-h for h in v))
else: # pragma: no cover
raise TypeError(f"cannot negate {type(v).__name__}")
def _apply_not(self, v: _Val) -> int | H[int]:
if isinstance(v, tuple):
v = sum(v)
elif isinstance(v, P):
v = v.h()
if isinstance(v, int):
return int(not v)
elif isinstance(v, H):
return v.apply(lambda x: int(not x))
else: # pragma: no cover
raise TypeError(f"cannot apply ! to {type(v).__name__}")
def _apply_hash(self, v: _Val) -> int:
if isinstance(v, int):
return len(str(abs(v))) if v != 0 else 1
elif isinstance(v, tuple):
return len(v)
elif isinstance(v, P):
return len(v) # this could be _EmptyPoolOfOne
elif isinstance(v, H):
# A bare die is a 1-position pool. Empty H -> 0. Verified via 42af3.
return 1 if v else 0
else: # pragma: no cover
raise TypeError(f"cannot apply # to {type(v).__name__}")
# ---- Binary operators ----------------------------------------------------------------
def _apply_binop(self, op: str, left: _Val, right: _Val) -> int | H[int] | P[int]:
if op in _ARITH_OPS:
return self._apply_arith(op, left, right)
elif op in _CMP_OPS:
return self._apply_cmp(op, left, right)
else: # pragma: no cover
raise NotImplementedError(f"unhandled operator: {op!r}")
def _apply_arith(self, op: str, left: _Val, right: _Val) -> int | H[int] | P[int]:
l_empty = isinstance(left, (H, P)) and not left
r_empty = isinstance(right, (H, P)) and not right
if l_empty and r_empty:
return dempty
# Sequences sum-coerce for boolean ops
if isinstance(left, tuple):
left = sum(left)
if isinstance(right, tuple):
right = sum(right)
if op in _EMPTY_DIE_SKIPS_ARITH:
# AnyDice anomaly: d{} - <thing> propagates <thing> (acts as a no-op). We
# match AnyDice's actual outputs (except for a bug where AnyDice is
# internally inconsistent when d{} is the lhs parameter).
if l_empty:
if isinstance(right, P):
return right
else:
left = 0
l_empty = False
elif r_empty:
if isinstance(left, P):
return left
else:
right = 0
r_empty = False
left = left.h() if isinstance(left, P) else left
right = right.h() if isinstance(right, P) else right
return dempty if l_empty or r_empty else self._h_binop(op, left, right)
def _apply_cmp(self, op: str, left: _Val, right: _Val) -> int | H[int]: # noqa: C901
if isinstance(left, P):
left = left.h()
if isinstance(right, P):
right = right.h()
# Empty die: Comparisons always propagate H({}).
if (isinstance(left, H) and not left) or (isinstance(right, H) and not right):
return H({})
if isinstance(left, tuple) and isinstance(right, tuple):
# Lex tuple compare (per AnyDice docs, "compared number by number, left to
# right"). Tuples support Python's native lex comparison directly.
return int(_CMP_RAW[op](left, right))
if isinstance(left, tuple):
if isinstance(right, int):
# seq vs number: Count elements satisfying op(elem, num).
return sum(_OP_FUNCS[op](e, right) for e in left)
elif isinstance(right, H):
# seq vs die: sum-coerce seq.
left = sum(left)
else: # pragma: no cover
raise TypeError(f"unexpected right operand type {type(right).__name__}")
if isinstance(right, tuple):
if isinstance(left, H):
# die vs seq: Sum-coerce seq.
right = sum(right)
elif isinstance(left, int):
# number vs seq: Count elements satisfying op(num, elem).
return sum(_OP_FUNCS[op](left, e) for e in right)
else: # pragma: no cover
raise TypeError(f"unexpected left operand type {type(left).__name__}")
return self._h_binop(op, left, right)
def _h_binop(self, op: str, left: _Val, right: _Val) -> int | H[int]:
if isinstance(left, int) and isinstance(right, int):
return _OP_FUNCS[op](left, right)
if not isinstance(left, (int, H)): # pragma: no cover
raise TypeError(f"expected a number or die, got {type(left).__name__}")
if not isinstance(right, (int, H)): # pragma: no cover
raise TypeError(f"expected a number or die, got {type(right).__name__}")
left_h = left if isinstance(left, H) else H({left: 1})
right_h = right if isinstance(right, H) else H({right: 1})
result: dict[int, int] = {}
op_func = _OP_FUNCS_H_ITER[op]
for lo, lw in left_h.items():
for ro, rw in right_h.items():
outcome = op_func(lo, ro)
result[outcome] = result.get(outcome, 0) + lw * rw
return H(result)
# ---- @ operator ----------------------------------------------------------------------
def _apply_at(self, left: _Val, right: _Val) -> int | H[int]:
if isinstance(left, (H, P)):
raise TypeError("@ left operand must be a number or sequence, got die")
# Right-side empty die propagates emptiness
if isinstance(right, int):
return self._at_num(left, right)
elif isinstance(right, tuple):
return self._at_seq(left, right)
elif isinstance(right, P):
return self._at_pool(left, right)
elif isinstance(right, H):
# AnyDice treats a non-empty H as a 1-element pool for `@`. Empty H
# propagates as H({}); non-empty H wraps as P(H) and reuses the pool
# path so `1@die` returns the die and `N@die` (N != 1) returns 0.
if not right:
return H({})
return self._at_pool(left, P(right))
else: # pragma: no cover
raise TypeError(
f"@ right operand has unexpected type {type(right).__name__}"
)
def _at_pool(self, left: _Val, pool: PoolT) -> H[int]:
assert self._settings is not None, "_at_pool called outside run()"
if isinstance(left, int):
size = len(pool)
# Left is out of range
if not 1 <= left <= size:
return dzero
# 1-based position. highest-first: pos 1 = highest = pool.h(-1).
# lowest-first: pos 1 = lowest = pool.h(0).
elif self._settings.highest_first():
return pool.h(-left)
else:
return pool.h(left - 1)
elif isinstance(left, tuple):
# Multi-position semantic: each element of the seq is a separate
# position. The positions come from the SAME pool roll, so they're
# correlated; dyce's `P.h(*selectors)` sums them jointly. Out-of-
# range positions are silently dropped (they contribute 0 to the
# sum). Verified against AnyDice via 42ad5.
size = len(pool)
highest_first = self._settings.highest_first()
selectors: list[int] = []
for p in left:
p_int = int(p)
if 1 <= p_int <= size:
selectors.append(-p_int if highest_first else p_int - 1)
if not selectors:
return dzero
return pool.h(*selectors)
else:
raise TypeError(
f"@ left operand must be a number or sequence, got {type(left).__name__}"
)
def _at_num(self, left: _Val, num: int) -> int:
if isinstance(left, int):
return self._digit_at(left, num)
elif isinstance(left, tuple):
# Each element of the seq is a separate position. Results sum.
return sum(self._digit_at(int(p), num) for p in left)
else:
raise TypeError(
f"@ left operand must be a number or sequence, got {type(left).__name__}"
)
def _at_seq(self, left: _Val, seq: SeqT) -> int:
if isinstance(left, tuple):
# Multi-position semantic: each element of the seq is a separate
# position; results are summed (verified against AnyDice via 42ad5).
return sum(self._at_seq(int(p), seq) for p in left)
if not isinstance(left, int):
raise TypeError(
f"@ left operand must be a number or sequence, got {type(left).__name__}"
)
elif left < 1 or left > len(seq):
return 0
else:
# The seq tuple is in position-order order already (highest-first or
# lowest-first)
return seq[left - 1]
def _digit_at(self, pos: int, num: int) -> int:
assert self._settings is not None, "_digit_at called outside run()"
if pos < 1:
return 0
sign = -1 if num < 0 else 1
digits = str(abs(num))
n = len(digits)
if pos > n:
return 0
d = digits[pos - 1] if self._settings.highest_first() else digits[n - pos]
return sign * int(d)
# ---- Dice helpers --------------------------------------------------------------------
def _make_die(self, faces: _Val) -> H[int]:
if isinstance(faces, int):
# AnyDice convention: d0 always shows 0.
return dzero if faces == 0 else H(faces)
elif isinstance(faces, tuple):
return H(Counter(faces)) if faces else H({})
elif isinstance(faces, P):
return faces.h()
elif isinstance(faces, H):
return faces
else:
raise TypeError(f"cannot use {type(faces).__name__} as die faces")
def _roll_n(self, n: int, die: H[int]) -> H[int] | PoolT:
# Strip zero-count entries before constructing a pool. Most of the time, we
# preserve them as keys (so `#{H}` reads the right support), but pool selection
# arithmetic in dyce.p assumes positive counts and divides by gcd(0, 0) when fed
# zeros.
die = H({o: c for o, c in die.items() if c > 0})
if not die:
# Empty die regardless of n
return H({})
elif n == 0:
return dzero
elif n < 0:
# AnyDice convention: `(-N)dX = -(NdX)` -- roll |N| dice and negate the
# sum. Verified via 6585 (`1d6 - (-1d6)` yields 2d6's distribution).
# Returns an H since negation collapses the pool's positional info,
# which the negative-count case can't preserve anyway.
return (-n) @ P(-die)
else:
# Use a Pool so that @ can select positions. Arithmetic/output sums via .h().
return n @ P(die)
def _expand_dice_count(
self, n_die: H[int], face_die: H[int]
) -> H[int] | _EmptyPoolOfOne:
# For each outcome k of n_die with weight w_k, compute kd<face_die> and combine.
# Inner distributions can have different totals (e.g. 1d6 has total 6 vs 2d6's
# 36). aggregate_weighted LCM-normalizes them before merging to preserve the
# relative probabilities of each outer-outcome branch.
#
# Erm, that is, *except* when either n_die or face_die is the empty die. How big
# is the die with no faces? To answer, we have to leave the world of reality,
# entering a realm not only of sight and sound, but lacking of mind. That's the
# signpost up ahead--your next stop, the AnyDice Twilight Clone. (3-5 days to
# get a basic syntax and interpreter working, and 5-10 times that trying to
# figure out and possibly reproduce all of the unprincipled idiosyncrasies. But
# who's counting?)
if not n_die or not face_die:
return _EmptyPoolOfOne()
def _gen() -> Iterator[tuple[H[int], int]]:
for k, w_k in n_die.items():
sub = self._roll_n(k, face_die)
yield (sub.h() if isinstance(sub, P) else sub), w_k
return aggregate_weighted(_gen()) # ty: ignore[invalid-return-type]
# ---- Coercion ------------------------------------------------------------------------
def _coerce_to_h(self, value: _Val) -> H[int]:
if isinstance(value, int):
return H({value: 1})
elif isinstance(value, tuple):
return H(Counter(value)) if value else H({})
elif isinstance(value, P):
return value.h()
elif isinstance(value, H):
return value
else:
raise TypeError(f"cannot coerce {type(value).__name__} to die")
def _eval_name(self, name: Expr | None) -> str | None:
if name is None:
return None
v = self._eval(name)
if isinstance(v, str):
return v
else:
raise TypeError(
f"output name must resolve to string, got {type(v).__name__}"
)
def _eval_string(self, parts: list[StrLit | StrVar]) -> str:
fragments: list[str] = []
for part in parts:
if isinstance(part, StrLit):
fragments.append(part.text)
elif isinstance(part, StrVar):
if part.name not in self._env:
raise NameError(f"undefined variable: {part.name!r}")
fragments.append(self._stringify(self._env[part.name]))
return "".join(fragments)
def _stringify(self, v: _Val) -> str:
# Used for string interpolation. We don't try to reverse-engineer AnyDice's
# source-text rendering ("2d6", "d{1..6}", etc.) for arbitrary values. Our
# evaluated form has lost that history. Instead we render opaquely with just
# enough shape to disambiguate types, plus a special case for empties (useful as
# a debugging signal).
# int -> decimal
# () -> "{}"
# non-empty tuple -> "{?}"
# H({}) -> "d{}"
# non-empty H -> "d{?}"
# P of size N -> "Nd{?}"
if isinstance(v, int):
return str(v)
if isinstance(v, tuple):
return "{}" if not v else "{?}"
if isinstance(v, H):
return "d{}" if not v else "d{?}"
if isinstance(v, P):
return f"{len(v)}d{{?}}"
raise TypeError(f"cannot interpolate {type(v).__name__} into a string")
# ---- Sequence evaluation -------------------------------------------------------------
def _eval_seq(self, elems: list[SeqElem]) -> SeqT:
values: list[int] = []
for elem in elems:
if isinstance(elem, ValueElem):
self._extend_seq_value(values, self._eval(elem.expr), repeat=1)
elif isinstance(elem, ValueRepeatElem):
repeat = self._eval(elem.repeat)
if isinstance(repeat, tuple):
repeat = sum(repeat)
if not isinstance(repeat, int):
raise TypeError("sequence repeat count must be a number")
self._extend_seq_value(values, self._eval(elem.expr), repeat=repeat)
elif isinstance(elem, RangeElem):
start = self._eval_int(elem.start, "range bounds")
stop = self._eval_int(elem.stop, "range bounds")
# AnyDice: Only ascending ranges yield values. Descending yields empty.
if start <= stop:
values.extend(range(start, stop + 1))
elif isinstance(elem, RangeRepeatElem):
start = self._eval_int(elem.start, "range bounds")
stop = self._eval_int(elem.stop, "range bounds")
repeat = self._eval_int(elem.repeat, "range repeat count")
if start <= stop:
# `{a..b:N}` concatenates the whole [a..b] range N times, *not* each
# element repeated N times
values.extend(list(range(start, stop + 1)) * repeat)
else:
raise NotImplementedError(
f"unhandled sequence element: {type(elem).__name__}"
)
# Sequences preserve write order. The "position order" setting affects digit
# selection on numbers and position selection on pools, not sequence indexing.
return tuple(values)
def _extend_seq_value(self, values: list[int], v: _Val, *, repeat: int) -> None:
if isinstance(v, int):
values.extend([v] * repeat)
return
if isinstance(v, tuple):
# Sub-sequences flatten into the outer sequence (concatenation), not
# sum-coerce. AnyDice idiom: {NEW, val} appends val to NEW. Bug
# discovered via 663d's `set element` function.
values.extend(list(v) * repeat)
return
if isinstance(v, P):
v = v.h()
if isinstance(v, H):
# AnyDice repeats the distinct-outcomes block as a unit, not each
# outcome individually: `{d4:2}` yields (1, 2, 3, 4, 1, 2, 3, 4),
# not (1, 1, 2, 2, 3, 3, 4, 4). Verified via 42971/42974/42975.
# H already iterates outcomes in ascending order (sorted on
# construction), so we extend directly without materializing.
for _ in range(repeat):
values.extend(v)
return
raise TypeError(
f"sequence element must be a number, sequence, or die, got {type(v).__name__}"
)
def _eval_int(self, expr: Expr, what: str) -> int:
v = self._eval(expr)
if isinstance(v, tuple):
v = sum(v)
if isinstance(v, int):
return v
raise TypeError(f"{what} must be a number")
# ---- Function calls ------------------------------------------------------------------
def _call(self, call: Call) -> _Val:
assert self._settings is not None, "_call called outside run()"
# Recursion-depth guard: Each call exceeding the configured maximum returns
# H({}) without executing the body. The unwinding result is then governed by
# how each operator treats H({}) (e.g. + treats it as 0; / propagates).
if self._depth >= self._settings.max_depth:
return H({})
shape = _call_shape(call.parts)
args: list[_Val] = [
self._eval(part) for part in call.parts if not isinstance(part, str)
]
# User-defined functions shadow builtins by lookup order.
entry: FunctionDef | tuple[list[str | None], Callable[..., _Val]] | None = (
self._funcs.get(shape) or self._builtins.get(shape)
)
if entry is None:
raise NameError(f"undefined function for call: {call.parts!r}")
return self._invoke(entry, args)
def _bind_and_expand( # noqa: C901
self,
param_types: list[str | None],
args: list[_Val],
*,
err_label: Callable[[int], str],
) -> tuple[_BoundT, _ExpansionT] | None:
r"""Coerce args per their param types, building the (bound, expansion) pair.
Returns `(bound, expansion)` where `bound` carries each arg in its final
per-param shape and `expansion` lists the per-param iteration items for
any `:n`/`:s` arg that needs to expand the body across outcomes.
Returns `None` to signal an early-empty short-circuit: an empty H bound
to an `:n` or `:s` param means the caller should return `H({})` without
executing the body.
Param-type semantics (shared between user-defined and builtin entry):
* `None`: pass arg through with no coercion (AnyDice bare-param).
* `:n`: sum-coerce sequences, collapse P -> H; scalar binds directly,
H expands per-outcome.
* `:d`: int/tuple wraps as a 1-outcome H; H/P passes through (no
empty short-circuit -- the body decides).
* `:s`: int wraps as `(int,)`, tuple binds directly, P expands per-roll
under AnyDice's tripartite rule (single-die pool -> ascending
H-outcome order; multi-die under highest-first -> roll-tuples
sorted by reversed form lex-descending; multi-die under lowest-
first -> roll-tuples sorted lex-ascending; corpus 0xbcc and
probes -0x2a / -0x2b / -0x2c), H expands as singleton-per-outcome.
*err_label(i)* returns the human-readable label for param `i`, used in
TypeError messages -- e.g. `"function param FOO"` or `"builtin param 0"`.
"""
assert self._settings is not None, "_bind_and_expand called outside run()"
bound: _BoundT = [0] * len(param_types)
expansion: _ExpansionT = []
for i, (ptype, arg) in enumerate(zip(param_types, args, strict=True)):
if ptype is None:
# AnyDice's bare/untyped params pass the argument through without
# coercion or expansion. The body sees whatever was passed --
# int as int, seq as seq, die as die, pool as pool. Verified
# against AnyDice via probes (42ace and the [f {1,2,3}]/#X
# round-trip).
bound[i] = arg
elif ptype == "n":
if isinstance(arg, P):
arg = arg.h() # noqa: PLW2901
if isinstance(arg, tuple):
# AnyDice sum-coerces a seq arg to `:n`, then wraps it as
# a 1-outcome die at that sum so the call still routes
# through the expansion-aggregation path. That way a
# body that returns a tuple gets per-iter sum-coerced
# (1 iter), even though the seq arg itself doesn't
# multiply iterations. An empty seq is `H({sum(()): 1})`
# = `H({0: 1})`, NOT `H({})` -- AnyDice runs the body
# once with N=0 rather than eliminating the call.
# Verified via tmp-probes -0x40 (weighted-seq body), -0x41
# (scalar body), and -0x42 (empty-seq edge case).
arg = H({sum(arg): 1}) # noqa: PLW2901
if isinstance(arg, int):
bound[i] = arg
elif isinstance(arg, H):
if not arg:
# An empty die argument to an n-typed param yields H({})
return None
expansion.append((i, [(o, w) for o, w in arg.items()]))
else:
raise TypeError(
f"{err_label(i)}: expected number, got {type(arg).__name__}"
)
elif ptype == "d":
# `:d` is lossless on pools: the body's `@` and other pool-aware
# ops must see the actual pool. Arithmetic and comparison ops
# already collapse P -> H at the operator site, so keeping P in
# the env doesn't break those.
#
# Note we DO NOT short-circuit on empty H/P here -- the body
# runs once regardless, and the body's conditionals decide
# whether each outcome eliminates (e.g. `if X { result: REROLL }`
# with REROLL bound to d{} only eliminates the X-matching
# branches, not the whole call).
if isinstance(arg, int):
arg = H({arg: 1}) # noqa: PLW2901
elif isinstance(arg, tuple):
# AnyDice sum-coerces a seq to an int, then wraps as a 1-outcome die
# (NOT distinct outcomes)
arg = H({sum(arg): 1}) # noqa: PLW2901
if not isinstance(arg, (H, P)):
raise TypeError(
f"{err_label(i)}: expected die, got {type(arg).__name__}"
)
bound[i] = arg
elif ptype == "s":
if isinstance(arg, int):
bound[i] = (arg,)
elif isinstance(arg, tuple):
bound[i] = arg
elif isinstance(arg, P):
if not arg.h():
return None
if len(arg) == 1:
expansion.append((i, [((o,), w) for o, w in arg.h().items()]))
elif self._settings.highest_first():
rolls = sorted(
arg.rolls_with_counts(),
key=lambda rc: rc[0][::-1],
reverse=True,
)
expansion.append((i, [(r[::-1], c) for r, c in rolls]))
else:
rolls = sorted(arg.rolls_with_counts())
expansion.append((i, [(r, c) for r, c in rolls]))
elif isinstance(arg, H):
if not arg:
return None
# A bare die (vs a pool) is treated as a 1-element seq. The body
# still expands once per outcome with X = (outcome,).
expansion.append((i, [((o,), w) for o, w in arg.items()]))
else:
raise TypeError(
f"{err_label(i)}: expected sequence, got {type(arg).__name__}"
)
else:
raise NotImplementedError(f"unknown param type: {ptype!r}")
return bound, expansion
def _invoke(
self,
entry: FunctionDef | tuple[list[str | None], Callable[..., _Val]],
args: list[_Val],
) -> _Val:
# Polymorphic on entry type. User-defined functions (`FunctionDef`)
# tree-walk an AST body inside a managed local env with first-
# occurrence-wins duplicate-name handling. Builtins
# (`(param_types, impl)`) call a Python callable per expansion combo
# with the bound args. Both paths share the per-param coercion via
# `_bind_and_expand` and the LCM-aggregate via `_aggregate_iters`.
if isinstance(entry, FunctionDef):
params = [p for p in entry.pattern if isinstance(p, Param)]
param_types = [p.type for p in params]
err_label = lambda i: f"function param {params[i].name}" # noqa: E731
bind = self._bind_and_expand(param_types, args, err_label=err_label)
if bind is None:
return H({})
bound, expansion = bind
return self._invoke_user(entry, params, bound, expansion)
else:
param_types, impl = entry
err_label = lambda i: f"builtin param {i}" # noqa: E731
bind = self._bind_and_expand(param_types, args, err_label=err_label)
if bind is None:
return H({})
bound, expansion = bind
return self._invoke_builtin(impl, bound, expansion)
def _invoke_user(
self,
func: FunctionDef,
params: list[Param],
bound: _BoundT,
expansion: _ExpansionT,
) -> _Val:
# No-expansion fast path: invoke the body once with `bound` installed
# in the env. Truncate the return when it's an H -- important for deep-
# recursion programs whose recursive calls are all-passthrough (e.g.
# `function: f N:n D:d { ... [f N/2 D] ... }` -- both args bypass
# expansion, so the body's bigint-growing operations would otherwise
# propagate untruncated).
if not expansion:
return self._invoke_with_bound(func, params, bound)
# Cartesian product over expanded iterations. Per-iteration return
# values may have differing internal totals (a body branch returning
# a die has sum>1; a branch returning a scalar has sum=1). AnyDice
# normalizes those internal totals to a common LCM before combining
# so each iteration contributes its outer weight, not its outer
# weight scaled by its inner total. Same pattern as
# `_expand_dice_count`.
#
# The function's local env is forked ONCE at the top of the call.
# Within that single local env, the body runs once per outcome combo.
# Two distinct semantics across iterations:
# - Parameters reset to their entry-bound values at the start of
# each iteration. Verified via 5fec (`SEQUENCE:s` parameter, body
# does `SEQUENCE: [remove X from SEQUENCE]`; AnyDice's output
# matches independent draw-without-replacement semantics, which
# requires each X-iteration to see the original SEQUENCE).
# - Non-parameter variables persist mutations across iterations.
# Verified via program -7 (`[weird d6]` produces the cumulative
# sequence d{1, 3, 6, 10, 15, 21}, where REROLL is a non-param
# accumulator that visibly carries across V-iterations).
# Duplicate-named params: AnyDice's rule is FIRST-OCCURRENCE WINS
# (positional, regardless of `:n`/`:d`/`:s` annotation). Subsequent
# same-named params are bound but their values are discarded -- the
# body sees only the first binding. Verified empirically:
# function: dup A:n and A:d { result: A } output [dup 7 and 1d6]
# -> H({7: 1})
# function: dup A:n and A:d { if A=7 {result: 1dA} result: 999 }
# output [dup 7 and 1d6] -> H({1:1,...,7:1}) i.e. 1dA = 1d7.
# Surfaced by corpus program 26018 (signature has `D:n` and `D:d`).
first_idx_for_name: dict[str, int] = {}
for i, param in enumerate(params):
first_idx_for_name.setdefault(param.name, i)
saved_env = self._env
self._env = dict(saved_env)
self._depth += 1
def _per_iter(combo: tuple[tuple[_Val, int], ...]) -> _Val:
# Reset ALL params to their entry-bound values per iter.
# Non-param env vars persist their mutations from the
# previous iter. Skip duplicate-named param positions so
# only the first-occurrence binding takes effect.
for i, param in enumerate(params):
if first_idx_for_name[param.name] == i:
self._env[param.name] = bound[i]
# Override expanding params with this iteration's combo,
# again only at the first-occurrence position so a
# duplicate that happens to expand doesn't clobber the
# earlier binding.
for j, (idx, _) in enumerate(expansion):
value, _w = combo[j]
if first_idx_for_name[params[idx].name] == idx:
self._env[params[idx].name] = value
return self._execute_body(func)
try:
return self._aggregate_iters(
expansion, reverse_combos=True, per_iter=_per_iter
)
finally:
self._depth -= 1
self._env = saved_env
def _invoke_builtin(
self,
impl: Callable[..., _Val],
bound: _BoundT,
expansion: _ExpansionT,
) -> _Val:
assert self._settings is not None, "_invoke_builtin called outside run()"
# No-expansion fast path: just call the impl with the bound args.
if not expansion:
return impl(self._settings, *bound)
# Expansion path: aggregate impl results across the Cartesian product.
# `reverse_combos=True` mirrors the user-defined enumeration order.
# Stateless builtin impls produce aggregates that are independent of
# iteration order, so True is observably equivalent to False here.
# The `_depth` bracket is structurally a no-op for builtins (impls
# don't recursively re-enter `_call`), but kept for symmetry with the
# user-defined path so future stateful builtins, if any, would behave
# consistently.
self._depth += 1
try:
def _per_iter(combo: tuple[tuple[_Val, int], ...]) -> _Val:
for j, (idx, _) in enumerate(expansion):
value, _w = combo[j]
bound[idx] = value
return impl(self._settings, *bound)
return self._aggregate_iters(
expansion, reverse_combos=True, per_iter=_per_iter
)
finally:
self._depth -= 1
def _aggregate_iters(
self,
expansion: _ExpansionT,
*,
reverse_combos: bool,
per_iter: Callable[[tuple[tuple[_Val, int], ...]], _Val],
) -> H[int]:
r"""LCM-aggregate per-iteration results across the expansion's
Cartesian product, returning a truncated H.
Each combination of expansion items is passed to *per_iter*, which
mutates whatever ambient state it needs (env, bound list, etc.) and
returns the body result for that combination. The per-combination
weight (product of the expansion's item weights) is computed here.
*reverse_combos* controls iteration order:
* `True`: iterate with the *reversed* expansion order so the first
expansion entry varies fastest (AnyDice's little-endian rule;
required for any user-defined function body that may observe
iteration order via non-param accumulators).
* `False`: iterate the natural Cartesian-product order. Observably
equivalent to True for any *per_iter* whose return depends only
on the combination's values (e.g. stateless builtin impls), but
distinct for user-defined bodies that read mutated non-param
env vars.
"""
from itertools import product
if reverse_combos:
items_list = [items for _, items in reversed(expansion)]
else:
items_list = [items for _, items in expansion]
def _gen() -> Iterator[tuple[H[int], int]]:
for combo in product(*items_list):
if reverse_combos:
combo = combo[::-1] # noqa: PLW2901
weight = 1
for _, w in combo:
weight *= w
r = per_iter(combo)
# When a body iteration returns a sequence, AnyDice sum-coerces
# it to a single number rather than distributing seq elements
# as separate outcomes. (Verified against AnyDice via 405c6's
# `[roll 1d6 1d6]` which produces an H over A+B+C, not over
# {A+B, C} elements.)
if isinstance(r, tuple):
r = sum(r)
yield self._coerce_to_h(r), weight
return aggregate_weighted(_gen()) # ty: ignore[invalid-return-type]
def _execute_body(self, func: FunctionDef) -> _Val:
r"""Run `func`'s body in the current env, returning the `result:` value
or `H({})` if the body falls through. Caller is responsible for env
save/restore and depth tracking. Used directly by `_invoke`'s
expansion path so iterations share the function's local env."""
try:
for stmt in func.body:
self._exec(stmt)
except _ResultReturn as r:
return r.value
return H({})
def _invoke_with_bound(
self, func: FunctionDef, params: list[Param], bound: _BoundT
) -> _Val:
saved_env = self._env
self._env = dict(saved_env)
# First-occurrence wins for duplicate-named params (see `_invoke`'s
# expansion path for the full rationale + AnyDice verification).
seen: set[str] = set()
for param, val in zip(params, bound, strict=True):
if param.name not in seen:
self._env[param.name] = val
seen.add(param.name)
self._depth += 1
try:
return self._execute_body(func)
finally:
self._depth -= 1
self._env = saved_env
|