# Copyright 2019 Ingmar Dasseville, Pierre Carbonnelle
#
# This file is part of Interactive_Consultant.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
Classes to parse an IDP-Z3 theory.
"""
from __future__ import annotations
from copy import copy, deepcopy
from datetime import date
from enum import Enum
from itertools import groupby
from os import path
from re import match
from sys import intern
from textx import metamodel_from_file
from typing import Dict, List, Union, Optional
from .Assignments import Assignments
from .Expression import (Annotations, ASTNode, Constructor, CONSTRUCTOR, Accessor,
Symbol, SYMBOL, SymbolExpr, Expression, AIfExpr, IF, AQuantification,
Type, TYPE, Quantee, ARImplication, AEquivalence,
AImplication, ADisjunction, AConjunction,
AComparison, ASumMinus, AMultDiv, APower, AUnary,
AAggregate, AppliedSymbol, UnappliedSymbol,
Number, Brackets, Date, Extension,
Variable, TRUEC, FALSEC, TRUE, FALSE, EQUALS, AND, OR, EQUIV)
from .utils import (RESERVED_SYMBOLS, OrderedSet, NEWL, BOOL, INT, REAL, DATE, CONCEPT,
GOAL_SYMBOL, EXPAND, RELEVANT, ABS, IDPZ3Error, MAX_QUANTIFIER_EXPANSION,
Semantics as S)
[docs]def str_to_IDP(atom: Expression, val_string: str) -> Expression:
"""cast a string value for 'atom into an Expr object, or None
used to convert Z3 models or json data from GUI
Args:
atom (Expression): the atom whose value must be converted
val_string (str): the string representation of the value
Returns:
Expression: the value cast as Expression, or None if unknown
"""
val_string = val_string.replace('True', 'true').replace('False', 'false')
if val_string == str(atom) or val_string+"()" == str(atom):
return None # Z3 means the value is unknown
assert atom.type, "Internal error"
type_string = atom.type
typ = atom.decl.out.decl if hasattr(atom, 'decl') else None
#TODO assert typ is None or typ.name == type_string, f"{atom}: {typ.name} != {type_string}"
return str_to_IDP2(type_string, typ, val_string)
[docs]def str_to_IDP2(type_string: str,
typ: TypeDeclaration|None,
val_string: str
) -> Expression:
"""recursive function to decode a val_string of type type_string and type
Args:
type_string (str):
typ (TypeDeclaration): type declaration of the value string
val_string (str): value_string
Raises:
IDPZ3Error: if wrong value
Returns:
Expression: the internal representation of the value
"""
if type_string == BOOL:
out = (TRUE if val_string == 'true' else
FALSE if val_string == 'false' else
None)
if out is None:
raise IDPZ3Error(f"wrong boolean value: {val_string}")
elif type_string == DATE:
d = (date.fromordinal(eval(val_string)) if not val_string.startswith('#') else
date.fromisoformat(val_string[1:]))
out = Date(iso=f"#{d.isoformat()}")
elif (hasattr(typ.base_type, 'map')
and val_string in typ.base_type.map): # constructor
out = typ.base_type.map[val_string]
elif 1 < len(val_string.split('(')): # e.g., pos(0,0)
assert hasattr(typ, 'interpretation'), "Internal error"
# find constructor name and its arguments in val_string
stack, args = [], []
for i, c in enumerate(val_string):
if c == '(':
name = val_string[:i].strip() if len(stack) == 0 else name
stack.append(i+1)
elif c == ',' and len(stack) == 1:
start = stack.pop()
args.append(val_string[start: i])
stack.append(i+2)
elif c == ')':
start = stack.pop()
if len(stack) == 0:
args.append(val_string[start: i]) # TODO construct the AppliedSymbol here, rather than later
# find the constructor
constructor = None
for c in typ.interpretation.enumeration.constructors:
if c.name == name:
constructor = c
assert constructor is not None, f"wrong constructor name '{name}' for {type_string}"
new_args = []
for a, acc in zip(args, constructor.args):
new_args.append(str_to_IDP2(acc.decl.out.name, acc.decl.out.decl, a))
out = AppliedSymbol.construct(constructor, new_args)
elif type_string == REAL: # Z3 adds a '?' when the real number is rounded
out = Number(number= val_string if '/' in val_string else
str(float(eval(val_string.replace('?', '')))))
else: # an Int
out = Number(number=str(eval(val_string)))
return out
[docs]class ViewType(Enum):
HIDDEN = "hidden"
NORMAL = "normal"
EXPANDED = "expanded"
[docs]class IDP(ASTNode):
"""The class of AST nodes representing an IDP-Z3 program.
"""
""" do not display this info in the API
Attributes:
code (str): source code of the IDP program
vocabularies (Dict[str, Vocabulary]): list of vocabulary blocks, by name
theories (Dict[str, TheoryBlock]): list of theory blocks, by name
structures (Dict[str, Structure]): list of structure blocks, by name
procedures (Dict[str, Procedure]): list of procedure blocks, by name
display (Display, Optional): display block, if any
"""
[docs] def __init__(self, **kwargs):
# log("parsing done")
self.code = None
self.vocabularies = self.dedup_nodes(kwargs, 'vocabularies')
self.theories = self.dedup_nodes(kwargs, 'theories')
self.structures = self.dedup_nodes(kwargs, 'structures')
displays = kwargs.pop('displays')
self.procedures = self.dedup_nodes(kwargs, 'procedures')
assert len(displays) <= 1, "Too many display blocks"
self.display = displays[0] if len(displays) == 1 else None
for voc in self.vocabularies.values():
voc.annotate(self)
for t in self.theories.values():
t.annotate(self)
for struct in self.structures.values():
struct.annotate(self)
# determine default vocabulary, theory, before annotating display
self.vocabulary = next(iter(self.vocabularies.values()))
self.theory = next(iter(self.theories .values()))
if self.display is None:
self.display = Display(constraints=[], interpretations=[])
[docs] @classmethod
def from_file(cls, file:str) -> "IDP":
"""parse an IDP program from file
Args:
file (str): path to the source file
Returns:
IDP: the result of parsing the IDP program
"""
assert path.exists(file), f"Can't find {file}"
with open(file, "r") as source:
code = source.read()
return cls.from_str(code)
[docs] @classmethod
def from_str(cls, code:str) -> "IDP":
"""parse an IDP program
Args:
code (str): source code to be parsed
Returns:
IDP: the result of parsing the IDP program
"""
out = idpparser.model_from_str(code)
out.code = code
return out
[docs] @classmethod
def parse(cls, file_or_string: str) -> "IDP":
"""DEPRECATED: parse an IDP program
Args:
file_or_string (str): path to the source file, or the source code itself
Returns:
IDP: the result of parsing the IDP program
"""
print("IDP.parse() is deprecated. Use `from_file` or `from_str` instead")
code = file_or_string
if path.exists(file_or_string):
with open(file_or_string, "r") as source:
code = source.read()
out = idpparser.model_from_str(code)
out.code = code
return out
[docs] def get_blocks(self, blocks: List[str]) -> List[ASTNode]:
"""returns the AST nodes for the blocks whose names are given
Args:
blocks (List[str]): list of names of the blocks to retrieve
Returns:
List[Union[Vocabulary, TheoryBlock, Structure, Procedure, Display]]:
list of AST nodes
"""
names = blocks.split(",") if type(blocks) is str else blocks
out = []
for name in names:
name = name.strip() # remove spaces
out.append(self.vocabularies[name] if name in self.vocabularies else
self.theories[name] if name in self.theories else
self.structures[name] if name in self.structures else
self.procedures[name] if name in self.procedures else
self.display if name == "Display" else
"")
return out
def execute(self) -> None:
pass # monkey patched
################################ Vocabulary ##############################
[docs]class Vocabulary(ASTNode):
"""The class of AST nodes representing a vocabulary block.
"""
[docs] def __init__(self, **kwargs):
self.name = kwargs.pop('name')
self.declarations = kwargs.pop('declarations')
self.idp = None # parent object
self.symbol_decls: Dict[str, Declaration] = {}
self.name = 'V' if not self.name else self.name
self.voc = self
# expand multi-symbol declarations
temp = []
for decl in self.declarations:
if not isinstance(decl, SymbolDeclaration):
decl.private = decl.name.startswith('_')
temp.append(decl)
else:
for symbol in decl.symbols:
new = copy(decl) # shallow copy !
new.name = intern(symbol.name)
new.private = new.name.startswith('_')
new.symbols = None
temp.append(new)
self.declarations = temp
# define built-in types: Bool, Int, Real, Symbols
self.declarations = [
TypeDeclaration(
name=BOOL, constructors=[TRUEC, FALSEC]),
TypeDeclaration(name=INT, enumeration=IntRange()),
TypeDeclaration(name=REAL, enumeration=RealRange()),
TypeDeclaration(name=DATE, enumeration=DateRange()),
TypeDeclaration(
name=CONCEPT,
constructors=[]),
SymbolDeclaration(annotations='', name=SYMBOL(GOAL_SYMBOL),
sorts=[TYPE(CONCEPT, ins=[],
out=TYPE(BOOL))],
out=TYPE(BOOL)),
SymbolDeclaration(annotations='', name=SYMBOL(RELEVANT),
sorts=[TYPE(CONCEPT, ins=[],
out=TYPE(BOOL))],
out=TYPE(BOOL)),
SymbolDeclaration(annotations='', name=SYMBOL(ABS),
sorts=[TYPE(INT)],
out=TYPE(INT)),
] + self.declarations
def __str__(self):
return (f"vocabulary {{{NEWL}"
f" {f'{NEWL} '.join(str(i) for i in self.declarations)}"
f"{NEWL}}}{NEWL}").replace(" \n", "")
[docs] def add_voc_to_block(self, block):
"""adds the enumerations in a vocabulary to a theory or structure block
Args:
block (Theory): the block to be updated
"""
for s in self.declarations:
block.check(s.name not in block.declarations,
f"Duplicate declaration of {self.name} "
f"in vocabulary and block {block.name}")
block.declarations[s.name] = s
if (type(s) == TypeDeclaration
and s.interpretation
and self.name != BOOL):
block.check(s.name not in block.interpretations,
f"Duplicate enumeration of {self.name} "
f"in vocabulary and block {block.name}")
block.interpretations[s.name] = s.interpretation
[docs]class Import(ASTNode):
[docs] def __init__(self, **kwargs):
self.name = kwargs.pop('name')
def __str__(self):
return f"Import {self.name}"
[docs]class TypeDeclaration(ASTNode):
"""AST node to represent `type <symbol> := <enumeration>`
Args:
name (string): name of the type
arity (int): the number of arguments
sorts (List[Symbol]): the types of the arguments
out (Symbol): the Boolean Symbol
type (string): Z3 type of an element of the type; same as `name`
base_type : self
constructors ([Constructor]): list of constructors in the enumeration
interpretation (SymbolInterpretation): the symbol interpretation
map (Dict[string, Expression]): a mapping from code to Expression in range
voc (Vocabulary): the vocabulary block that contains it
"""
[docs] def __init__(self, **kwargs):
self.name = kwargs.pop('name')
self.constructors = ([] if 'constructors' not in kwargs else
kwargs.pop('constructors'))
enumeration = (None if 'enumeration' not in kwargs else
kwargs.pop('enumeration'))
self.arity = 1
self.sorts = [SYMBOL(self.name)]
self.out = SYMBOL(BOOL)
self.type = (self.name if type(enumeration) != Ranges else
enumeration.type) # INT or REAL or DATE
self.base_type = self
self.map = {} # {String: constructor}
self.interpretation = (None if enumeration is None else
SymbolInterpretation(name=SYMBOL(self.name), sign='≜',
enumeration=enumeration, default=None))
def __str__(self):
if self.name in RESERVED_SYMBOLS:
return ''
enumeration = self.enumeration if hasattr(self, 'enumeration') and self.enumeration else ""
constructors = enumeration.constructors if enumeration else None
constructed = ("" if not bool(constructors) or all(0 == len(c.sorts) for c in constructors)
else "constructed from ")
enumeration = (f"{constructed}{{{', '.join(str(c) for c in constructors)}}}" if constructors else
f"{self.interpretation}" if self.interpretation else
f"{enumeration}")
return (f"type {self.name} {'' if not enumeration else ':= ' + enumeration}")
[docs] def contains_element(self, term: Expression,
interpretations: Dict[str, "SymbolInterpretation"],
extensions: Dict[str, Extension]
) -> Expression:
"""returns an Expression that is TRUE when `term` is in the type
"""
if self.name == CONCEPT:
comparisons = [EQUALS([term, UnappliedSymbol.construct(c)])
for c in self.constructors]
return OR(comparisons)
else:
(superset, filter) = extensions[self.name]
if superset is not None:
# superset.sort(key=lambda t: str(t))
comparisons = [EQUALS([term, t[0]]) for t in superset]
out = (OR(comparisons) if filter is None else
AND([filter([term]), OR(comparisons)]))
elif filter is not None:
out = filter([term])
else:
out = TRUE
return out
[docs]class SymbolDeclaration(ASTNode):
"""The class of AST nodes representing an entry in the vocabulary,
declaring one or more symbols.
Multi-symbols declaration are replaced by single-symbol declarations
before the annotate() stage.
Attributes:
annotations : the annotations given by the expert.
`annotations['reading']` is the annotation
giving the intended meaning of the expression (in English).
symbols ([Symbol]): the symbols being defined, before expansion
name (string): the identifier of the symbol, after expansion of the node
arity (int): the number of arguments
sorts (List[Symbol]): the types of the arguments
out (Symbol): the type of the symbol
type (string): name of the Z3 type of an instance of the symbol
base_type (TypeDeclaration): base type of the unary predicate (None otherwise)
instances (Dict[string, Expression]):
a mapping from the code of a symbol applied to a tuple of
arguments to its parsed AST
range (List[Expression]): the list of possible values
private (Bool): True if the symbol name starts with '_' (for use in IC)
unit (str):
the unit of the symbol, such as m (meters)
heading (str):
the heading that the symbol should belong to
optimizable (bool):
whether this symbol should get optimize buttons in the IC
needs_interpretation (bool):
whether its interpretation must be sent to Z3
voc (Vocabulary): the vocabulary block that contains it
"""
[docs] def __init__(self, **kwargs):
self.annotations = kwargs.pop('annotations')
if 'symbols' in kwargs:
self.symbols = kwargs.pop('symbols')
self.name = None
else:
self.symbols = None
if 'name' in kwargs:
self.name = intern(kwargs.pop('name').name)
else:
self.name = intern(kwargs.pop('strname'))
self.sorts = kwargs.pop('sorts')
self.out = kwargs.pop('out')
if self.out is None:
self.out = SYMBOL(BOOL)
self.arity = len(self.sorts)
self.annotations = self.annotations.annotations if self.annotations else {}
self.private = None
self.unit: str = None
self.heading: str = None
self.optimizable: bool = True
self.needs_interpretation = False
self.type = None # a string
self.base_type = None
self.range = None # all possible values. Used in get_range and IO.py
self.instances = None # {string: AppliedSymbol} not starting with '_'
self.block: Optional[Block] = None # vocabulary where it is declared
self.view = ViewType.NORMAL # "hidden" | "normal" | "expanded" whether the symbol box should show atoms that contain that symbol, by default
@classmethod
def make(cls, strname, arity, sorts, out):
o = cls(strname=strname, arity=arity, sorts=sorts, out=out, annotations={})
return o
def __str__(self):
if self.name in RESERVED_SYMBOLS:
return ''
args = '⨯'.join(map(str, self.sorts)) if 0 < len(self.sorts) else ''
return (f"{self.name}: "
f"{ '('+args+')' if args else '()'}"
f" → {self.out.name}")
def __repr__(self):
return str(self)
[docs] def has_in_domain(self, args: List[Expression],
interpretations: Dict[str, "SymbolInterpretation"],
extensions: Dict[str, Extension]
) -> Expression:
"""Returns an expression that is TRUE when `args` are in the domain of the symbol.
Arguments:
args (List[Expression]): the list of arguments to be checked, e.g. `[1, 2]`
Returns:
Expression: whether `(1,2)` is in the domain of the symbol
"""
assert len(self.sorts) == len(args), \
f"Incorrect arity of {str(args)} for {self.name}"
return AND([typ.has_element(term, interpretations, extensions)
for typ, term in zip(self.sorts, args)])
[docs] def has_in_range(self, value: Expression,
interpretations: Dict[str, "SymbolInterpretation"],
extensions: Dict[str, Extension]
) -> Expression:
"""Returns an expression that says whether `value` is in the range of the symbol.
"""
return self.out.has_element(value, interpretations, extensions)
[docs] def contains_element(self, term: Expression,
interpretations: Dict[str, "SymbolInterpretation"],
extensions: Dict[str, Extension]
) -> Expression:
"""returns an Expression that is TRUE when `term` satisfies the predicate
"""
assert self.type == BOOL, "Internal error"
(superset, filter) = extensions[self.name]
if superset is not None:
# superset.sort(key=lambda t: str(t))
comparisons = [EQUALS([term, t[0]]) for t in superset]
out = (OR(comparisons) if filter is None else
AND([filter([term]), OR(comparisons)]))
elif filter is not None:
out = filter([term])
else:
out = TRUE
return out
[docs]class VarDeclaration(ASTNode):
""" represents a declaration of variable (IEP 24)
Attributes:
name (str): name of the variable
subtype (Type): type of the variable
"""
[docs] def __init__(self, **kwargs):
self.name = kwargs.pop('name').name
self.subtype = kwargs.pop('subtype')
def __str__(self):
return f"var {self.name} ∈ {self.subtype}"
Declaration = Union[TypeDeclaration, SymbolDeclaration]
################################ TheoryBlock ###############################
[docs]class TheoryBlock(ASTNode):
""" The class of AST nodes representing a theory block.
"""
[docs] def __init__(self, **kwargs):
self.name = kwargs.pop('name')
self.vocab_name = kwargs.pop('vocab_name')
constraints = kwargs.pop('constraints')
self.definitions = kwargs.pop('definitions')
self.interpretations = self.dedup_nodes(kwargs, 'interpretations')
self.name = "T" if not self.name else self.name
self.vocab_name = 'V' if not self.vocab_name else self.vocab_name
self.declarations = {}
self.def_constraints = {} # {(Declaration, Definition): List[Expression]}
self.assignments = Assignments()
self.constraints = OrderedSet()
for c in constraints:
c.block = self
if c.annotations is not None:
c.expr.annotations = c.annotations.annotations
self.constraints.append(c.expr)
for definition in self.definitions:
for rule in definition.rules:
rule.block = self
def __str__(self):
return self.name
[docs]class Definition(ASTNode):
""" The class of AST nodes representing an inductive definition.
id (num): unique identifier for each definition
rules ([Rule]):
set of rules for the definition, e.g., `!x: p(x) <- q(x)`
renamed (Dict[Declaration, List[Rule]]):
normalized rule for each defined symbol (except for the value in the head),
e.g., `!$p!1$: p($p!1$) <- q($p!1$)`
canonicals (Dict[Declaration, List[Rule]]):
normalized rule for each defined symbol,
e.g., `!$p!1$: p($p!1$) <- q($p!1$)`
clarks (Dict[Declaration, Transformed Rule]):
normalized rule for each defined symbol (used to be Clark completion)
e.g., `!$p!1$: p($p!1$) <=> q($p!1$)`
def_vars (Dict[String, Dict[String, Variable]]):
Fresh variables for arguments and result
level_symbols (Dict[SymbolDeclaration, Symbol]):
map of recursively defined symbols to level mapping symbols
cache (Dict[SymbolDeclaration, str, Expression]):
cache of instantiation of the definition
inst_def_level (int): depth of recursion during instantiation
"""
definition_id = 0 # intentional static variable so that no two definitions get the same ID
[docs] def __init__(self, parent, annotations, mode, rules):
Definition.definition_id += 1
self.id = Definition.definition_id
self.mode = (S.WELLFOUNDED if mode is None or 'well-founded' in mode else
S.COMPLETION if 'completion' in mode else
S.KRIPKEKLEENE if 'Kripke-Kleene' in mode else
S.COINDUCTION if 'co-induction' in mode else
S.RECDATA if 'recursive' in mode else
mode)
assert type(self.mode) == S, f"Unsupported mode: {mode}"
self.annotations = annotations.annotations if annotations else {}
self.rules = rules
self.renamed = {}
self.clarks = {} # {SymbolDeclaration: Transformed Rule}
self.canonicals = {}
self.def_vars = {} # {String: {String: Variable}}
self.level_symbols = {} # {SymbolDeclaration: Symbol}
self.cache = {} # {decl, str: Expression}
self.inst_def_level = 0
def __str__(self):
return "Definition " +str(self.id)+" of " + ",".join([k.name for k in self.canonicals.keys()])
def __repr__(self):
out = []
for rule in self.clarks.values():
out.append(repr(rule))
return NEWL.join(out)
def __eq__(self, another):
return self.id == another.id
def __hash__(self):
return hash(self.id)
def get_def_constraints(self,
problem,
for_explain: bool = False
) -> Dict[SymbolDeclaration, Definition, List[Expression]]:
pass # monkey-patched
def instantiate_definition(self, decl, new_args, theory):
pass # monkey-patched
[docs]class Rule(ASTNode):
[docs] def __init__(self, **kwargs):
self.annotations = kwargs.pop('annotations')
self.quantees = kwargs.pop('quantees')
self.definiendum = kwargs.pop('definiendum')
self.out = kwargs.pop('out')
self.body = kwargs.pop('body')
self.has_finite_domain = None # Bool
self.block = None # theory where it occurs
self.annotations = (self.annotations.annotations if self.annotations else
{'reading': str(self)})
if self.out is not None:
self.definiendum.sub_exprs.append(self.out)
if self.body is None:
self.body = TRUE
self.original = None
def __repr__(self):
quant = ('' if not self.quantees else
f"∀ {','.join(str(q) for q in self.quantees)}: ")
return (f"{quant}{self.definiendum} "
f"{(' = ' + str(self.out)) if self.out else ''}"
f"← {str(self.body)}")
def __deepcopy__(self, memo):
out = copy(self)
out.definiendum = deepcopy(self.definiendum)
out.definiendum.sub_exprs = [deepcopy(e) for e in self.definiendum.sub_exprs]
out.out = deepcopy(self.out)
out.body = deepcopy(self.body)
return out
def instantiate_definition(self, new_args, theory):
pass # monkey-patched
# Expressions : see Expression.py
################################ Structure ###############################
[docs]class Structure(ASTNode):
"""
The class of AST nodes representing an structure block.
"""
[docs] def __init__(self, **kwargs):
"""
The textx parser creates the Structure object. All information used in
this method directly comes from text.
"""
self.name = kwargs.pop('name')
self.vocab_name = kwargs.pop('vocab_name')
self.interpretations = self.dedup_nodes(kwargs, 'interpretations')
self.name = 'S' if not self.name else self.name
self.vocab_name = 'V' if not self.vocab_name else self.vocab_name
self.voc = None
self.declarations = {}
self.assignments = Assignments()
def __str__(self):
return self.name
[docs]class SymbolInterpretation(ASTNode):
"""
AST node representing `<symbol> := { <identifiers*> } else <default>.`
Attributes:
name (string): name of the symbol being enumerated.
symbol (Symbol): symbol being enumerated
enumeration ([Enumeration]): enumeration.
default (Expression): default value (for function enumeration).
is_type_enumeration (Bool): True if the enumeration is for a type symbol.
"""
[docs] def __init__(self, **kwargs):
self.name = kwargs.pop('name').name
self.sign = kwargs.pop('sign')
self.enumeration = kwargs.pop('enumeration')
self.default = kwargs.pop('default')
if not self.enumeration:
self.enumeration = Enumeration(tuples=[])
self.sign = ('⊇' if self.sign == '>>' else
'≜' if self.sign == ':=' else self.sign)
self.check(self.sign == '≜' or
(type(self.enumeration) == FunctionEnum and self.default is None),
"'⊇' can only be used with a functional enumeration ('→') without else clause")
self.symbol = None
self.is_type_enumeration = None
def __repr__(self):
return f"{self.name} {self.sign} {self.enumeration}"
[docs] def interpret_application(self, rank, applied, args, tuples=None):
"""returns an expression equivalent to `self.symbol` applied to `args`,
simplified by the interpretation of `self.symbol`.
This is a recursive function.
Example: assume `f>>{(1,2)->A, (1, 3)->B, (2,1)->C}` and `args=[g(1),2)]`.
The returned expression is:
```
if g(1) = 1 then A
else if g(1)=2 then f(g(1),2)
else f(g(1),2)
```
Args:
rank (Int): iteration number (from 0)
applied (AppliedSymbol): template to create new AppliedSymbol
(ex: `g(1),a()`, before interpretation)
args (List(Expression)): interpreted arguments applied to the symbol (ex: `g(1),2`)
tuples (OrderedSet[TupleIDP], optional): relevant tuples for this iteration.
Initialized with `[[1,2,A], [1,3,B], [2,1,C]]`
Returns:
Expression: Grounded interpretation of self.symbol applied to args
"""
if tuples == None: # first call
tuples = self.enumeration.sorted_tuples
key = ",".join(a.code for a in args)
if key in self.enumeration.lookup:
return self.enumeration.lookup[key]
elif self.enumeration.parent.sign != '≜':
return applied._change(sub_exprs=args)
return self.enumeration.parent.default
"""
if rank == self.symbol.decl.arity: # valid tuple -> return a value
if not type(self.enumeration) == FunctionEnum:
return TRUE if tuples else self.default
else:
self.check(len(tuples) <= 1,
f"Duplicate values in structure "
f"for {str(self.name)}{str(tuples[0])}")
return (self.default if not tuples else # enumeration of constant
tuples[0].args[rank])
else: # constructs If-then-else recursively
out = (self.default if self.default is not None else
applied._change(sub_exprs=args))
groups = groupby(tuples, key=lambda t: str(t.args[rank]))
if args[rank].value is not None:
for val, tuples2 in groups: # try to resolve
if str(args[rank]) == val:
out = self.interpret_application(rank+1,
applied, args, list(tuples2))
else:
for val, tuples2 in groups:
tuples = list(tuples2)
out = IF(
EQUALS([args[rank], tuples[0].args[rank]]),
self.interpret_application(rank+1,
applied, args, tuples),
out)
return out
"""
[docs]class Enumeration(ASTNode):
"""Represents an enumeration of tuples of expressions.
Used for predicates, or types without n-ary constructors.
Attributes:
tuples (OrderedSet[TupleIDP]): OrderedSet of TupleIDP of Expression
sorted_tuples: a sorted list of tuples
lookup: dictionary from arguments to values
constructors (List[Constructor], optional): List of Constructor
"""
[docs] def __init__(self, **kwargs):
self.tuples = kwargs.pop('tuples')
self.sorted_tuples = sorted(self.tuples, key=lambda t: t.code) # do not change dropdown order
self.tuples = OrderedSet(self.tuples)
self.lookup = {}
if all(len(c.args) == 1 and type(c.args[0]) == UnappliedSymbol
for c in self.tuples):
self.constructors = [CONSTRUCTOR(c.args[0].name)
for c in self.tuples]
else:
self.constructors = None
def __repr__(self):
return (f'{{{", ".join([repr(t) for t in self.tuples])}}}' if self.tuples else
f'{{{", ".join([repr(t) for t in self.constructors])}}}')
[docs] def contains(self, args, function, arity=None, rank=0, tuples=None,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Expression:
""" returns an Expression that says whether Tuple args is in the enumeration """
if arity is None:
arity = len(args)
if rank == arity: # valid tuple
return TRUE
if tuples is None:
tuples = self.sorted_tuples
# constructs If-then-else recursively
groups = groupby(tuples, key=lambda t: str(t.args[rank]))
if args[rank].is_value():
for val, tuples2 in groups: # try to resolve
if str(args[rank]) == val:
return self.contains(args, function, arity, rank+1, list(tuples2),
interpretations=interpretations, extensions=extensions)
return FALSE
else:
if rank + 1 == arity: # use OR
out = [ EQUALS([args[rank], t.args[rank]])
for t in tuples]
out = OR(out)
out.enumerated = ', '.join(str(c) for c in tuples)
return out
out = FALSE
for val, tuples2 in groups:
tuples = list(tuples2)
out = IF(EQUALS([args[rank], tuples[0].args[rank]]),
self.contains(args, function, arity, rank+1, tuples,
interpretations=interpretations, extensions=extensions),
out)
return out
[docs] def extensionE(self,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Extension:
"""computes the extension of an enumeration, i.e., a set of tuples and a filter
Args:
interpretations (Dict[str, "SymbolInterpretation"], optional): _description_. Defaults to None.
extensions (Dict[str, Extension], optional): _description_. Defaults to None.
Returns:
Extension: _description_
"""
ranges = [c.range for c in self.constructors]
return ([[t] for r in ranges for t in r], None)
[docs]class FunctionEnum(Enumeration):
[docs] def extensionE(self,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Extension:
self.check(False,
f"Can't use function enumeration for type declaration or quantification")
[docs]class CSVEnumeration(Enumeration):
pass
[docs]class ConstructedFrom(Enumeration):
"""Represents a 'constructed from' enumeration of constructors
Attributes:
tuples (OrderedSet[TupleIDP]): OrderedSet of tuples of Expression
constructors (List[Constructor]): List of Constructor
accessors (Dict[str, Int]): index of the accessor in the constructors
"""
[docs] def __init__(self, **kwargs):
self.constructed = kwargs.pop('constructed')
self.constructors = kwargs.pop('constructors')
self.tuples = None
self.accessors = dict()
[docs] def contains(self, args, function, arity=None, rank=0, tuples=None,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Expression:
"""returns True if args belong to the type enumeration"""
# args must satisfy the tester of one of the constructors
assert len(args) == 1, f"Incorrect arity in {self.parent.name}{args}"
if type(args[0].decl) == Constructor: # try to simplify it
self.check(self.parent.name == args[0].decl.type,
f"Incorrect type of {args[0]} for {self.parent.name}")
self.check(len(args[0].sub_exprs) == len(args[0].decl.sorts),
f"Incorrect arity")
return AND([t.decl.out.has_element(e, interpretations, extensions)
for e,t in zip(args[0].sub_exprs, args[0].decl.sorts)])
out = [AppliedSymbol.construct(constructor.tester, args)
for constructor in self.constructors]
return OR(out)
[docs] def extensionE(self,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Extension:
def filter(args):
if type(args[0]) != Variable and type(args[0].decl) == Constructor: # try to simplify it
self.check(self.parent.name == args[0].decl.type,
f"Incorrect type of {args[0]} for {self.parent.name}")
self.check(len(args[0].sub_exprs) == len(args[0].decl.sorts),
f"Incorrect arity")
return AND([t.decl.out.has_element(e, interpretations, extensions)
for e,t in zip(args[0].sub_exprs, args[0].decl.sorts)])
out = [AppliedSymbol.construct(constructor.tester, args)
for constructor in self.constructors]
return OR(out) # return of filter()
return (([t.args for t in self.tuples], None) if self.tuples else
(None, filter))
[docs]class TupleIDP(ASTNode):
[docs] def __init__(self, **kwargs):
self.args = kwargs.pop('args')
self.code = intern(",".join([str(a) for a in self.args]))
def __str__(self):
return self.code
def __repr__(self):
return f"({self.code})" if 1 < len(self.args) else self.code
[docs]class FunctionTuple(TupleIDP):
[docs] def __init__(self, **kwargs):
self.args = kwargs.pop('args')
if not isinstance(self.args, list):
self.args = [self.args]
self.value = kwargs.pop('value')
self.args.append(self.value)
self.code = intern(",".join([str(a) for a in self.args]))
[docs]class CSVTuple(TupleIDP):
pass
[docs]class Ranges(Enumeration):
[docs] def __init__(self, **kwargs):
self.elements = kwargs.pop('elements')
tuples = []
self.type = None
if self.elements:
self.type = self.elements[0].fromI.type
for x in self.elements:
if x.fromI.type != self.type:
if self.type in [INT, REAL] and x.fromI.type in [INT, REAL]:
self.type = REAL # convert to REAL
tuples = [TupleIDP(args=[n.args[0].real()])
for n in tuples]
else:
self.check(False,
f"incorrect value {x.fromI} for {self.type}")
if x.toI is None:
tuples.append(TupleIDP(args=[x.fromI]))
elif self.type == INT and x.fromI.type == INT and x.toI.type == INT:
for i in range(x.fromI.py_value, x.toI.py_value + 1):
tuples.append(TupleIDP(args=[Number(number=str(i))]))
elif self.type == REAL and x.fromI.type == INT and x.toI.type == INT:
for i in range(x.fromI.py_value, x.toI.py_value + 1):
tuples.append(TupleIDP(args=[Number(number=str(float(i)))]))
elif self.type == REAL:
self.check(False, f"Can't have a range over real: {x.fromI}..{x.toI}")
elif self.type == DATE and x.fromI.type == DATE and x.toI.type == DATE:
for i in range(x.fromI.py_value, x.toI.py_value + 1):
d = Date(iso=f"#{date.fromordinal(i).isoformat()}")
tuples.append(TupleIDP(args=[d]))
else:
self.check(False, f"Incorrect value {x.toI} for {self.type}")
Enumeration.__init__(self, tuples=tuples)
[docs] def contains(self, args, function, arity=None, rank=0, tuples=None,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Expression:
var = args[0]
if not self.elements:
return TRUE
if self.tuples and len(self.tuples) < MAX_QUANTIFIER_EXPANSION:
es = [EQUALS([var, c.args[0]]) for c in self.tuples]
e = OR(es)
return e
sub_exprs = []
for x in self.elements:
if x.toI is None:
e = EQUALS([var, x.fromI])
else:
e = AComparison.make('≤', [x.fromI, var, x.toI])
sub_exprs.append(e)
return OR(sub_exprs)
[docs] def extensionE(self,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Extension:
if not self.elements:
return(None, None)
if self.tuples is not None: # and len(self.tuples) < MAX_QUANTIFIER_EXPANSION:
return ([t.args for t in self.tuples], None)
def filter(args):
sub_exprs = []
for x in self.elements:
if x.toI is None:
e = EQUALS([args[0], x.fromI])
else:
e = AComparison.make('≤', [x.fromI, args[0], x.toI])
sub_exprs.append(e)
return OR(sub_exprs)
return(None, filter)
[docs]class RangeElement(ASTNode):
[docs] def __init__(self, **kwargs):
self.fromI = kwargs.pop('fromI')
self.toI = kwargs.pop('toI')
[docs]class IntRange(Ranges):
[docs] def __init__(self):
Ranges.__init__(self, elements=[])
self.type = INT
self.tuples = None
[docs] def extensionE(self,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Extension:
return (None, None)
[docs]class RealRange(Ranges):
[docs] def __init__(self):
Ranges.__init__(self, elements=[])
self.type = REAL
self.tuples = None
[docs] def extensionE(self,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Extension:
return (None, None)
[docs]class DateRange(Ranges):
[docs] def __init__(self):
Ranges.__init__(self, elements=[])
self.type = DATE
self.tuples = None
[docs] def extensionE(self,
interpretations: Dict[str, "SymbolInterpretation"]=None,
extensions: Dict[str, Extension]=None
) -> Extension:
return (None, None)
################################ Display ###############################
[docs]class Display(ASTNode):
[docs] def __init__(self, **kwargs):
self.constraints = kwargs.pop('constraints')
self.interpretations = self.dedup_nodes(kwargs, 'interpretations')
self.moveSymbols = False
self.optionalPropagation = False
self.manualPropagation = False
self.optionalRelevance = False
self.manualRelevance = False
self.name = "display"
[docs] def run(self, idp):
"""apply the display block to the idp theory"""
def base_symbols(name, concepts):
"""Verify that concepts is a list of concepts. Returns the list of symbols"""
symbols = []
# All concepts should be concepts, except for the first
# argument of 'unit' and 'heading'.
for i, symbol in enumerate(concepts):
if name in ['unit', 'heading'] and i == 0:
continue
self.check(symbol.name.startswith('`'),
f"arg '{symbol.name}' of {name}'"
f" must begin with a tick '`'")
self.check(symbol.name[1:] in self.voc.symbol_decls,
f"argument '{symbol.name}' of '{name}'"
f" must be a concept")
symbols.append(self.voc.symbol_decls[symbol.name[1:]])
return symbols
for k, interpretation in self.interpretations.items():
symbols = base_symbols(interpretation.name,
[t.args[0] for t in interpretation.enumeration.tuples])
if interpretation.name == EXPAND:
for symbol in symbols:
self.voc.symbol_decls[symbol.name].view = ViewType.EXPANDED
elif interpretation.name == GOAL_SYMBOL:
idp.theory.interpretations[k] = interpretation
else:
raise IDPZ3Error(f"Unknown enumeration in display: {interpretation}")
for constraint in self.constraints:
if type(constraint) == AppliedSymbol:
self.check(type(constraint.symbol) == Symbol,
f"Invalid syntax: {constraint}") # SymbolExpr $()
name = constraint.symbol.name
symbols = base_symbols(name, constraint.sub_exprs)
if name == 'hide': # e.g. hide(Length, Angle)
for symbol in symbols:
self.voc.symbol_decls[symbol.name].view = ViewType.HIDDEN
elif name in [GOAL_SYMBOL, EXPAND]: # e.g. goal_symbol(`tax_amount`)
self.check(False, f"Please use an enumeration for {name}")
elif name == 'unit': # e.g. unit('m', `length):
for symbol in symbols:
symbol.unit = str(constraint.sub_exprs[0])
elif name == 'heading':
# e.g. heading('Shape', `type).
for symbol in symbols:
symbol.heading = str(constraint.sub_exprs[0])
elif name == 'noOptimization': # e.g., noOptimization(`temp)
for symbol in symbols:
symbol.optimizable = False
elif name == "moveSymbols":
self.moveSymbols = True
elif name == "optionalPropagation":
self.optionalPropagation = True
elif name == "manualPropagation":
self.manualPropagation = True
elif name == "optionalRelevance":
self.optionalRelevance = True
elif name == "manualRelevance":
self.manualRelevance = True
else:
raise IDPZ3Error(f"Unknown display axiom:"
f" {constraint}")
elif type(constraint) == AComparison: # e.g. view = normal
self.check(constraint.is_assignment(), "Internal error")
self.check(type(constraint.sub_exprs[0].symbol) == Symbol,
f"Invalid syntax: {constraint}")
if constraint.sub_exprs[0].symbol.name == 'view':
if constraint.sub_exprs[1].name == 'expanded':
for s in self.voc.symbol_decls.values():
if type(s) == SymbolDeclaration and s.view == ViewType.NORMAL:
s.view = ViewType.EXPANDED # don't change hidden symbols
else:
self.check(constraint.sub_exprs[1].name == 'normal',
f"Unknown display axiom: {constraint}")
else:
raise IDPZ3Error(f"Unknown display axiom: {constraint}")
################################ Main ##################################
[docs]class Procedure(ASTNode):
[docs] def __init__(self, **kwargs):
self.name = kwargs.pop('name')
self.args = kwargs.pop('args')
self.pystatements = kwargs.pop('pystatements')
def __str__(self):
return f"{NEWL.join(str(s) for s in self.pystatements)}"
[docs]class Call1(ASTNode):
[docs] def __init__(self, **kwargs):
self.name = kwargs.pop('name')
self.par = kwargs.pop('par') if 'par' in kwargs else None
self.args = kwargs.pop('args')
self.kwargs = kwargs.pop('kwargs')
self.post = kwargs.pop('post')
def __str__(self):
kwargs = ("" if len(self.kwargs)==0 else
f"{',' if self.args else ''}{','.join(str(a) for a in self.kwargs)}")
args = ("" if not self.par else
f"({','.join(str(a) for a in self.args)}{kwargs})")
return ( f"{self.name}{args}"
f"{'' if self.post is None else '.'+str(self.post)}")
[docs]class String(ASTNode):
[docs] def __init__(self, **kwargs):
self.literal = kwargs.pop('literal')
def __str__(self):
return f'{self.literal}'
[docs]class PyList(ASTNode):
[docs] def __init__(self, **kwargs):
self.elements = kwargs.pop('elements')
def __str__(self):
return f"[{','.join(str(e) for e in self.elements)}]"
[docs]class PyAssignment(ASTNode):
[docs] def __init__(self, **kwargs):
self.var = kwargs.pop('var')
self.val = kwargs.pop('val')
def __str__(self):
return f'{self.var} = {self.val}'
########################################################################
Block = Union[Vocabulary, TheoryBlock, Structure, Display]
dslFile = path.join(path.dirname(__file__), 'Idp.tx')
idpparser = metamodel_from_file(dslFile, memoization=True,
classes=[IDP, Annotations,
Vocabulary, Import, VarDeclaration,
TypeDeclaration, Accessor, Type,
SymbolDeclaration, Symbol,
SymbolExpr,
TheoryBlock, Definition, Rule, AIfExpr,
AQuantification, Quantee, ARImplication,
AEquivalence, AImplication,
ADisjunction, AConjunction,
AComparison, ASumMinus, AMultDiv,
APower, AUnary, AAggregate,
AppliedSymbol, UnappliedSymbol,
Number, Brackets, Date, Variable,
Structure, SymbolInterpretation,
Enumeration, FunctionEnum, CSVEnumeration,
TupleIDP, FunctionTuple, CSVTuple,
ConstructedFrom, Constructor, Ranges,
RangeElement, Display,
Procedure, Call1, String,
PyList, PyAssignment])