JSON-Lang/types_.py

from emis_funky_funktions import *
from typing import *

from dataclasses import dataclass, field
from functools import reduce

MonoType: TypeAlias = 'FunctionTy | HoleTy | IntTy | VarTy'
Substitution: TypeAlias = 'tuple[MonoType, VarTy]'

@dataclass(frozen=True)
class UnificationError:
	ty1: MonoType
	ty2: MonoType

@dataclass(frozen=True)
class VarTy:
	id: int
	name: str = field(compare=False)

	def subst(self, replacement: MonoType, var: 'VarTy') -> MonoType:
		if var.id == self.id:
			return replacement
		else:
			return self

	def unify(self, other: MonoType) -> Result[Sequence[Substitution], UnificationError]:
		match other:
			case VarTy(id, str) if id == self.id:
				return Ok(tuple())
			case _:
				return Ok(((other, self),))
		raise Exception('Unreachable')

	def free_vars(self) -> FrozenSet['VarTy']:
		return fset(self)

	def __repr__(self) -> str:
		return self.name

@dataclass(frozen=True)
class FunctionTy:
	arg_type: MonoType
	ret_type: MonoType

	def subst(self, replacement: MonoType, var: VarTy) -> MonoType:
		return FunctionTy(
			self.arg_type.subst(replacement, var),
			self.ret_type.subst(replacement, var)
		)

	def unify(self, other: MonoType) -> Result[Sequence[Substitution], UnificationError]:
		match other:
			case VarTy(id, str) as var:
				return Ok(((self, var),))
			case FunctionTy(other_arg, other_ret):
				return self.arg_type.unify(other_arg) << (lambda arg_substs:
					subst_all_monotype(self.ret_type, arg_substs)
						.unify(
							subst_all_monotype(other_ret, arg_substs)) << (lambda ret_substs:
								Ok((*arg_substs, *ret_substs))))
			case _:
				return Err(UnificationError(self, other))

	def free_vars(self) -> FrozenSet[VarTy]:
		return self.arg_type.free_vars() | self.ret_type.free_vars()

	def __repr__(self) -> str:
		return f'({self.arg_type}) -> {self.ret_type}'

@dataclass(frozen=True)
class HoleTy:

	def subst(self, replacement: MonoType, var: VarTy) -> MonoType:
		return self

	def unify(self, other: MonoType) -> Result[Sequence[Substitution], UnificationError]:
		match other:
			case VarTy(id, str) as var:
				return Ok(((self, var),))
			case HoleTy():
				return Ok(tuple())
			case _:
				return Err(UnificationError(self, other))

	def free_vars(self) -> FrozenSet[VarTy]:
		return FSet()

	def __repr__(self) -> str:
		return '[]'

@dataclass(frozen=True)
class IntTy:

	def subst(self, replacement: MonoType, var: VarTy) -> MonoType:
		return self

	def unify(self, other: MonoType) -> Result[Sequence[Substitution], UnificationError]:
		match other:
			case VarTy(id, str) as var:
				return Ok(((self, var),))
			case IntTy():
				return Ok(tuple())
			case _:
				return Err(UnificationError(self, other))

	def free_vars(self) -> FrozenSet[VarTy]:
		return FSet()

	def __repr__(self) -> str:
		return 'int'

@dataclass(frozen=True)
class PolyType:
	quantified_variables: Collection[VarTy]
	monotype: MonoType

	def subst(self, replacement: MonoType, var: VarTy) -> 'PolyType':
		if var in self.quantified_variables:
			return self
		else:
			return PolyType(
				self.quantified_variables,
				self.monotype.subst(replacement, var)
			)

	def instantiate(self, ctx: 'Context', name: str) -> MonoType:
		match self.quantified_variables:
			case []:
				return self.monotype
			case [alpha, *rest]:
				return PolyType(
					rest,
					self.monotype.subst(ctx.new_type_var(name), alpha)
				).instantiate(ctx, name)
		raise Exception('Unreachable')

	def free_vars(self) -> FrozenSet[VarTy]:
		return self.monotype.free_vars() - FSet(self.quantified_variables)

	def __repr__(self) -> str:
		if len(self.quantified_variables):
			qv = ' '.join(qv.name for qv in self.quantified_variables)
			return f'forall {qv}. {self.monotype}'
		else:
			return repr(self.monotype)

UNIQUE_VAR_COUNTER:int = 0

@dataclass(frozen=True)
class Context:
	variable_types: Mapping[str, PolyType]

	def with_(self, var_name: str, var_type: PolyType) -> 'Context':
		return Context({var_name: var_type, **self.variable_types})

	def with_mono(self, var_name: str, var_type: MonoType) -> 'Context':
		return Context({var_name: PolyType([], var_type), **self.variable_types})

	def with_many_mono(self, bindings: Sequence[tuple[str, MonoType]]) -> 'Context':
		match bindings:
			case []:
				return self
			case [(var_name, var_type), *rest]:
				return self.with_mono(var_name, var_type).with_many_mono(rest)
		raise Exception('Unreachable')

	def subst(self, replacement: MonoType, var: VarTy) -> 'Context':
		return Context({
			name: val
			for (name, val) in self.variable_types.items()
		})

	def subst_all(self, subst: Sequence[Tuple[MonoType, VarTy]]) -> 'Context':
		return reduce(lambda a, s: a.subst(*s), subst, self)

	def new_type_var(self, name_prefix = 'T') -> VarTy:
		global UNIQUE_VAR_COUNTER
		UNIQUE_VAR_COUNTER += 1
		return VarTy(UNIQUE_VAR_COUNTER, f'{name_prefix}${UNIQUE_VAR_COUNTER}')

	def instantiate(self, name: str) -> Option[MonoType]:
		if name in self.variable_types:
			return Some(self.variable_types[name].instantiate(self, name))
		else:
			return None

	def free_vars(self) -> FrozenSet[VarTy]:
		return FSet(fv for ty in self.variable_types.values() for fv in ty.free_vars())

	def generalize(self, mt: MonoType) -> PolyType:
		variable_mappings = [(VarTy(fv.id, 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'[i]), fv) for (i, fv) in enumerate(mt.free_vars())]
		return PolyType([new_var for (new_var, _) in variable_mappings], subst_all_monotype(mt, variable_mappings))

	def __contains__(self, name: str) -> bool:
		return name in self.variable_types

	def __getitem__(self, i: str) -> PolyType:
		return self.variable_types[i]

BUILTINS_CONTEXT: Context = (
	Context({})
		.with_mono('+', FunctionTy(IntTy(), FunctionTy(IntTy(), IntTy())))
		.with_mono('S', FunctionTy(IntTy(), IntTy()))
)

def subst_all_monotype(m: MonoType, substs: Sequence[Tuple[MonoType, VarTy]]) -> MonoType:
		return reduce(lambda a, s: a.subst(*s), substs, m)