dotall

Universal quantifier for collections

Part of the Truth pillar, dotall checks if all items in a collection satisfy a condition.

Overview

dotall implements the universal quantifier (∀) from mathematical logic, returning True if every item in a collection matches a specified value at a given path.

Basic Usage

from truth.dotall import all_match

users = [
    {"name": "Alice", "verified": True},
    {"name": "Bob", "verified": True},
    {"name": "Charlie", "verified": True}
]

# Check if all users are verified
all_verified = all_match(users, "verified", True)  # True

# Add an unverified user
users.append({"name": "David", "verified": False})
all_verified = all_match(users, "verified", True)  # False

Nested Paths

Works with nested data structures:

data = [
    {"user": {"status": {"active": True}}},
    {"user": {"status": {"active": True}}},
    {"user": {"status": {"active": True}}}
]

# Check if all users are active
all_active = all_match(data, "user.status.active", True)  # True

Edge Cases

Empty Collections (Vacuous Truth)

Returns True for empty collections (vacuous truth in logic):

empty = []
result = all_match(empty, "any.path", "value")  # True
# "All items in an empty set satisfy any condition"

Missing Paths

Items with missing paths are treated as non-matching:

data = [
    {"name": "Alice", "age": 30},
    {"name": "Bob"}  # Missing age
]

# Bob doesn't have age field
all_age_30 = all_match(data, "age", 30)  # False

Mathematical Properties

  • Vacuous truth: Empty collections always return True
  • Universal quantification: ∀x ∈ collection : predicate(x)
  • Dual of dotany: all and any form a duality in boolean logic
  • De Morgan's laws: not(all(p)) ≡ any(not(p))

Integration with dotquery

dotall is used internally by dotquery for collection queries:

from truth.dotquery import Query

# These are equivalent:
q = Query("all users.verified equals true")
# vs
from truth.dotall import all_match
result = all_match(users, "verified", True)

Real-World Examples

Data Validation

# Ensure all products have required fields
products = [
    {"name": "Widget", "price": 9.99, "sku": "W001"},
    {"name": "Gadget", "price": 19.99, "sku": "G001"}
]

# All products must have positive prices
valid = all_match(products, "price", lambda x: x > 0)

Permission Checking

# Check if all team members have access
team = [
    {"name": "Alice", "permissions": ["read", "write"]},
    {"name": "Bob", "permissions": ["read", "write"]}
]

# All must have write permission
can_edit = all_match(team, "permissions", lambda p: "write" in p)