Schemas And Instances - Learning Module

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Schema Definition

The Blueprint of Your Data Universe

Imagine you're an architect tasked with designing a massive office building. Before a single brick is laid, you create blueprints—detailed specifications that define the structure's layout, dimensions, load-bearing walls, electrical systems, and plumbing. These blueprints don't contain the actual building; they describe what the building will look like and how it will function.\n\nIn the world of database management systems, the schema is precisely this blueprint. It defines the logical structure of your database—tables, columns, data types, constraints, relationships, and rules—without containing any actual data. Understanding schemas is foundational because every query you write, every application you build, and every optimization you perform assumes an understanding of the underlying schema.

What You Will Learn

By the end of this page, you will understand what a database schema is at a deep, conceptual level. You'll learn how schemas are formally defined, their mathematical foundations in set theory and predicate logic, the different types of schemas at various abstraction levels, and how schemas are specified using Data Definition Language (DDL). Most importantly, you'll understand why schemas are the cornerstone upon which all database operations depend.

What is a Database Schema?

A database schema is the formal description of the structure of a database. It defines::\n\n- What data can be stored — The types of entities and their attributes\n- How data is organized — The relationships between entities\n- What constraints apply — Rules that ensure data validity and consistency\n- How data is accessed — Views and access paths\n\nCrucially, a schema is metadata—data about data. It describes the database's structure without containing the actual data values. Just as an architect's blueprint specifies that 'Room 101 will be an office with dimensions 20×15 feet' without placing any furniture there, a schema specifies that 'the Employees table will have columns for ID (integer), Name (varchar), and Salary (decimal)' without storing any employee records.

The Schema-Instance Distinction

Think of a schema like a cookie cutter and an instance like the cookies produced from it. The cookie cutter (schema) defines the shape, but you can produce many cookies (instances) with different dough colors and decorations. The schema is stable; instances change constantly as data is inserted, updated, and deleted.

Formal Definition:\n\nIn relational database theory, a schema can be formally defined as:\n\n> A database schema S is a collection of relation schemas, where each relation schema R(A₁, A₂, ..., Aₙ) consists of a relation name R and a list of attributes A₁ through Aₙ, each associated with a domain (data type) and potentially subject to constraints.\n\nThis formal definition emphasizes several key points:\n\n1. A schema is a collection — Databases typically contain multiple tables, and the schema describes all of them\n2. Each relation has a name — This is the table name in practical terms\n3. Attributes have domains — Every column has a defined data type (integer, varchar, date, etc.)\n4. Constraints are integral — Primary keys, foreign keys, check constraints, and other rules are part of the schema

Mathematical Foundations of Schemas

To truly understand database schemas, we must briefly visit their mathematical roots. The relational model—invented by Edgar F. Codd at IBM in 1970—is grounded in set theory and first-order predicate logic.\n\nSet Theory Basis:\n\nIn set theory, a relation is defined as a subset of the Cartesian product of sets (domains). Given domains D₁, D₂, ..., Dₙ, a relation R is any subset of D₁ × D₂ × ... × Dₙ.\n\nFor example, if:\n- D₁ = {1, 2, 3} (Employee IDs)\n- D₂ = {'Alice', 'Bob', 'Carol'} (Names)\n- D₃ = {50000, 60000, 70000} (Salaries)\n\nThen the Cartesian product D₁ × D₂ × D₃ contains 27 possible tuples. A specific Employee relation might contain only:\n- (1, 'Alice', 60000)\n- (2, 'Bob', 50000)\n- (3, 'Carol', 70000)\n\nThis relation is a subset of all possible combinations—and the schema defines which combinations are valid.

set-theory-relation.txt
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-- Conceptual representation of set-theoretic semantics
 
-- Domains (Sets)
D_EmployeeID = {1, 2, 3, 4, 5, ...}      -- Set of integers
D_Name       = {'Alice', 'Bob', ...}     -- Set of character strings
D_Salary     = {0.00, 0.01, ..., 999999.99}  -- Set of decimal values
 
-- Cartesian Product (All possible tuples)
D_EmployeeID × D_Name × D_Salary = All possible (id, name, salary) combinations
 
-- Relation Schema (Structure definition)
Employee(EmployeeID: D_EmployeeID, Name: D_Name, Salary: D_Salary)
 
-- Relation Instance (Actual subset of Cartesian product)
Employee = {
    (1, 'Alice', 60000),
    (2, 'Bob', 50000),
    (3, 'Carol', 70000)
}
 
-- The schema defines WHICH attributes exist and their domains
-- The instance contains ACTUAL tuples that satisfy the schema

Predicate Logic Connection:\n\nEach relation can be understood as a predicate—a logical statement that is true for certain combinations of values. The schema defines what predicates exist, and the instance specifies which predicates are currently true.\n\nFor the Employee relation:\n- Predicate: Employee(id, name, salary) means 'There exists an employee with ID id, named name, earning salary'\n- Instance: The predicate Employee(1, 'Alice', 60000) is TRUE; Employee(99, 'Zack', 100000) is FALSE (for the current database state)\n\nThis logical foundation is why database schemas are so powerful—they enable formal reasoning about data correctness, query optimization, and constraint verification.

Why Mathematics Matters Here

Understanding the mathematical basis helps you reason about schemas at a deeper level. When you define a constraint like 'Salary > 0', you're defining a logical predicate that every tuple must satisfy. When you create a foreign key, you're establishing a logical implication between relations. This formal grounding is what makes relational databases so reliable and SQL so expressive.

Components of a Database Schema

A complete database schema encompasses multiple components, each serving a distinct purpose in defining the database's structure. Let's examine each component in detail:

Core Schema Components

•Table Definitions (Relation Schemas) — The fundamental building blocks. Each table schema specifies the table name, column names, column data types, and column-level constraints. Example: CREATE TABLE Employees(id INT PRIMARY KEY, name VARCHAR(100) NOT NULL, salary DECIMAL(10,2))
•Attribute Domains — The set of valid values for each column. In practice, this includes data types (INT, VARCHAR, DATE) and additional domain constraints (CHECK constraints, enumerations).
•Primary Key Constraints — Definitions of uniqueness and non-nullability for entity identification. The primary key is the minimal set of attributes that uniquely identifies each tuple.
•Foreign Key Constraints — Referential integrity rules linking tables together. They ensure that relationships between entities are maintained and prevent orphan records.
•Check Constraints — Business rules encoded as logical predicates. Examples: 'salary > 0', 'hire_date <= CURRENT_DATE', 'status IN ("active", "inactive", "suspended")'
•Unique Constraints — Columns or combinations of columns that must be unique but are not the primary key. Example: email address in a Users table.
•Default Values — Predefined values assigned when no explicit value is provided during insertion.
•Indexes — While sometimes considered physical, index definitions are often part of the logical schema as they affect query semantics (unique indexes enforce constraints).
•Views — Virtual tables defined by queries. Views are part of the external schema but are often considered in schema discussions because they define derived data structures.
•Stored Procedures and Functions — Procedural code that operates on schema objects, encapsulating business logic within the database.
•Triggers — Automated responses to data modification events, enforcing complex business rules that can't be expressed as simple constraints.

Schema Components and Their Purposes
Component	Purpose	Example
Table Definition	Define entity structure	CREATE TABLE Orders(...)
Primary Key	Uniquely identify tuples	PRIMARY KEY (order_id)
Foreign Key	Enforce relationships	FOREIGN KEY (customer_id) REFERENCES Customers(id)
Check Constraint	Validate business rules	CHECK (quantity > 0)
Default Value	Provide fallback values	DEFAULT CURRENT_TIMESTAMP
Index	Optimize access & uniqueness	CREATE UNIQUE INDEX idx_email ON Users(email)
View	Provide derived perspectives	CREATE VIEW ActiveOrders AS SELECT ...
Trigger	Automate responses	CREATE TRIGGER audit_log AFTER UPDATE ...

Schema Types in the Three-Level Architecture

In the ANSI-SPARC three-level architecture (which we explored in the previous module), there are actually three distinct types of schemas, each serving a different audience and purpose:\n\n1. External Schema (View Level)\n\nThe external schema defines individual user views of the database. Different users or applications may have different external schemas tailored to their needs. A sales department might see customer and order data; the HR department sees employee and payroll data; a public API might expose only product catalog information.\n\n2. Conceptual Schema (Logical Level)\n\nThe conceptual schema describes the logical structure of the entire database for the community of users. It defines entities, relationships, constraints, and all other logical structures independent of physical storage. This is what most people mean when they say 'the database schema.'\n\n3. Internal Schema (Physical Level)\n\nThe internal schema describes how data is physically stored—file organizations, indexing techniques, storage allocation, and access paths. While users and applications don't interact with this level directly, database administrators must understand it for performance tuning.

Conceptual Schema Focus

•All entity types (tables)
•All attributes (columns)
•All relationships (foreign keys)
•All integrity constraints
•Security and authorization rules
•Derived data definitions (views)

Internal Schema Focus

•Storage record formats
•Record ordering and placement
•Index structures (B+ trees, hash)
•Compression techniques
•Encryption at rest
•Partitioning and clustering

Schema Layers Enable Independence

The separation of schemas at different levels is the foundation of data independence. When you change the internal schema (e.g., add an index or reorganize storage), the conceptual and external schemas remain unchanged. When you modify the conceptual schema (e.g., add a column), properly designed external schemas can remain stable. This layering protects applications from database changes.

Converting Mermaid diagram...

Defining Schemas with Data Definition Language (DDL)

In practice, database schemas are defined using Data Definition Language (DDL)—a subset of SQL specifically designed for schema manipulation. DDL statements create, modify, and delete schema objects.\n\nThe primary DDL commands are:\n- CREATE — Define new schema objects (tables, views, indexes, etc.)\n- ALTER — Modify existing schema objects\n- DROP — Remove schema objects\n- TRUNCATE — Remove all data while preserving structure (borderline DDL/DML)\n\nLet's examine a comprehensive schema definition that demonstrates all major components:

comprehensive-schema.sql
PostgreSQL
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-- ============================================
-- COMPREHENSIVE DATABASE SCHEMA EXAMPLE
-- E-Commerce Database for Learning Platform
-- ============================================
 
-- Create custom domain for positive money values
CREATE DOMAIN money_positive AS DECIMAL(12, 2)
    CHECK (VALUE >= 0);
 
-- Create enumeration type for order status
CREATE TYPE order_status AS ENUM (
    'pending', 'processing', 'shipped', 'delivered', 'cancelled'
);
 
-- ============================================
-- CUSTOMERS TABLE
-- Core entity representing system users
-- ============================================
CREATE TABLE customers (
    customer_id     SERIAL PRIMARY KEY,
    email           VARCHAR(255) NOT NULL UNIQUE,
    password_hash   CHAR(60) NOT NULL,  -- bcrypt hash
    first_name      VARCHAR(100) NOT NULL,
    last_name       VARCHAR(100) NOT NULL,
    phone           VARCHAR(20),
    created_at      TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
    updated_at      TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
    is_active       BOOLEAN NOT NULL DEFAULT TRUE,
    
    -- Check constraint: email format validation
    CONSTRAINT valid_email CHECK (email ~* '^[A-Za-z0-9._%+-]+@[A-Za-z0-9.-]+\.[A-Z|a-z]{2,}$')
);
 
-- Index for email lookups (implicit unique index created)
-- Index for name searches
CREATE INDEX idx_customers_name ON customers(last_name, first_name);
 
-- ============================================
-- ADDRESSES TABLE
-- Customer addresses with one-to-many relationship
-- ============================================
CREATE TABLE addresses (
    address_id      SERIAL PRIMARY KEY,
    customer_id     INTEGER NOT NULL,
    address_type    VARCHAR(20) NOT NULL DEFAULT 'shipping',
    street_line1    VARCHAR(255) NOT NULL,
    street_line2    VARCHAR(255),
    city            VARCHAR(100) NOT NULL,
    state_province  VARCHAR(100) NOT NULL,
    postal_code     VARCHAR(20) NOT NULL,
    country_code    CHAR(2) NOT NULL DEFAULT 'US',
    is_default      BOOLEAN NOT NULL DEFAULT FALSE,
    
    -- Foreign key constraint with cascading delete
    CONSTRAINT fk_addresses_customer 
        FOREIGN KEY (customer_id) 
        REFERENCES customers(customer_id) 
        ON DELETE CASCADE,
    
    -- Check constraint: valid address type
    CONSTRAINT valid_address_type 
        CHECK (address_type IN ('billing', 'shipping', 'both'))
);
 
-- ============================================
-- PRODUCTS TABLE
-- Catalog of items available for purchase
-- ============================================
CREATE TABLE products (
    product_id      SERIAL PRIMARY KEY,
    sku             VARCHAR(50) NOT NULL UNIQUE,
    name            VARCHAR(255) NOT NULL,
    description     TEXT,
    price           money_positive NOT NULL,
    cost            money_positive NOT NULL,
    quantity_in_stock INTEGER NOT NULL DEFAULT 0,
    category_id     INTEGER,
    is_active       BOOLEAN NOT NULL DEFAULT TRUE,
    created_at      TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
    
    -- Business rule: price must exceed cost
    CONSTRAINT price_exceeds_cost CHECK (price >= cost),
    
    -- Business rule: non-negative inventory
    CONSTRAINT non_negative_stock CHECK (quantity_in_stock >= 0)
);
 
-- Full-text search index on product name and description
CREATE INDEX idx_products_search ON products 
    USING GIN (to_tsvector('english', name || ' ' || COALESCE(description, '')));
 
-- ============================================
-- ORDERS TABLE
-- Customer purchase transactions
-- ============================================
CREATE TABLE orders (
    order_id        SERIAL PRIMARY KEY,
    customer_id     INTEGER NOT NULL,
    order_status    order_status NOT NULL DEFAULT 'pending',
    order_date      TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
    shipped_date    TIMESTAMP,
    shipping_address_id INTEGER,
    billing_address_id INTEGER,
    subtotal        money_positive NOT NULL,
    tax_amount      money_positive NOT NULL DEFAULT 0,
    shipping_cost   money_positive NOT NULL DEFAULT 0,
    total_amount    money_positive NOT NULL,
    notes           TEXT,
    
    -- Foreign keys
    CONSTRAINT fk_orders_customer 
        FOREIGN KEY (customer_id) 
        REFERENCES customers(customer_id),
    
    CONSTRAINT fk_orders_shipping_address 
        FOREIGN KEY (shipping_address_id) 
        REFERENCES addresses(address_id),
    
    CONSTRAINT fk_orders_billing_address 
        FOREIGN KEY (billing_address_id) 
        REFERENCES addresses(address_id),
    
    -- Business rule: total must equal sum of components
    CONSTRAINT valid_total 
        CHECK (total_amount = subtotal + tax_amount + shipping_cost),
    
    -- Business rule: shipped_date only when status is shipped or later
    CONSTRAINT valid_shipped_date 
        CHECK (shipped_date IS NULL OR order_status IN ('shipped', 'delivered'))
);
 
-- Indexes for common query patterns
CREATE INDEX idx_orders_customer ON orders(customer_id);
CREATE INDEX idx_orders_date ON orders(order_date DESC);
CREATE INDEX idx_orders_status ON orders(order_status) WHERE order_status NOT IN ('delivered', 'cancelled');
 
-- ============================================
-- ORDER_ITEMS TABLE
-- Line items within each order (junction table)
-- ============================================
CREATE TABLE order_items (
    order_item_id   SERIAL PRIMARY KEY,
    order_id        INTEGER NOT NULL,
    product_id      INTEGER NOT NULL,
    quantity        INTEGER NOT NULL,
    unit_price      money_positive NOT NULL,
    line_total      money_positive NOT NULL,
    
    -- Foreign keys
    CONSTRAINT fk_order_items_order 
        FOREIGN KEY (order_id) 
        REFERENCES orders(order_id) 
        ON DELETE CASCADE,
    
    CONSTRAINT fk_order_items_product 
        FOREIGN KEY (product_id) 
        REFERENCES products(product_id),
    
    -- Business rules
    CONSTRAINT positive_quantity CHECK (quantity > 0),
    CONSTRAINT valid_line_total CHECK (line_total = quantity * unit_price),
    
    -- Prevent duplicate products in same order
    CONSTRAINT unique_order_product UNIQUE (order_id, product_id)
);
 
-- ============================================
-- VIEWS: External Schema Components
-- ============================================
 
-- Customer order summary view
CREATE VIEW customer_order_summary AS
SELECT 
    c.customer_id,
    c.email,
    c.first_name || ' ' || c.last_name AS full_name,
    COUNT(DISTINCT o.order_id) AS total_orders,
    COALESCE(SUM(o.total_amount), 0) AS lifetime_value,
    MAX(o.order_date) AS last_order_date
FROM customers c
LEFT JOIN orders o ON c.customer_id = o.customer_id
GROUP BY c.customer_id, c.email, c.first_name, c.last_name;
 
-- Active inventory view
CREATE VIEW active_inventory AS
SELECT 
    product_id,
    sku,
    name,
    price,
    quantity_in_stock,
    CASE 
        WHEN quantity_in_stock = 0 THEN 'Out of Stock'
        WHEN quantity_in_stock < 10 THEN 'Low Stock'
        ELSE 'In Stock'
    END AS stock_status
FROM products
WHERE is_active = TRUE;
 
-- ============================================
-- TRIGGERS: Automated Business Logic
-- ============================================
 
-- Trigger function to update timestamps
CREATE OR REPLACE FUNCTION update_updated_at()
RETURNS TRIGGER AS $$
BEGIN
    NEW.updated_at = CURRENT_TIMESTAMP;
    RETURN NEW;
END;
$$ LANGUAGE plpgsql;
 
-- Apply trigger to customers table
CREATE TRIGGER trg_customers_updated_at
    BEFORE UPDATE ON customers
    FOR EACH ROW
    EXECUTE FUNCTION update_updated_at();
 
-- Trigger to update inventory on order placement
CREATE OR REPLACE FUNCTION decrement_inventory()
RETURNS TRIGGER AS $$
BEGIN
    UPDATE products 
    SET quantity_in_stock = quantity_in_stock - NEW.quantity
    WHERE product_id = NEW.product_id;
    RETURN NEW;
END;
$$ LANGUAGE plpgsql;
 
CREATE TRIGGER trg_decrement_inventory
    AFTER INSERT ON order_items
    FOR EACH ROW
    EXECUTE FUNCTION decrement_inventory();

Schema Documentation

Notice the extensive comments in the schema definition above. Professional schemas are self-documenting. Each table, constraint, and index should explain its purpose. Your future self (and your team) will thank you when debugging issues at 2 AM.

Schema Naming Conventions and Best Practices

Consistent naming conventions are essential for maintainable schemas. While conventions vary between organizations, here are widely-adopted best practices:

Recommended Naming Conventions
Element	Convention	Examples	Anti-Patterns
Tables	Plural nouns, snake_case or PascalCase	customers, order_items, OrderItems	tbl_Cust, T_ORDERS, customerData
Columns	Singular nouns, snake_case	customer_id, first_name, created_at	CustID, fname, date1
Primary Keys	table_singular_id or just id	customer_id, product_id, id	pk_customers, cust_pk, ID
Foreign Keys	referenced_table_singular_id	customer_id, order_id	fk_1, cust_fk, customerForeignKey
Indexes	idx_table_column(s)	idx_orders_customer_id	index1, fastLookup, i_ord
Constraints	type_table_description	chk_orders_positive_total	constraint1, check_1, c1
Views	Descriptive, action-based	active_customers, pending_orders_summary	v_cust, VIEW_1, customersView
Triggers	trg_table_action_timing	trg_orders_after_insert	trigger1, t_ord, orderTrigger

Universal Best Practices

•Be consistent — Pick a convention and apply it everywhere. Mixed styles create confusion.
•Be descriptive — Names should convey meaning. 'order_date' beats 'dt'; 'is_active' beats 'flag1'.
•Avoid reserved words — Don't name columns 'index', 'order', 'user', or 'date' without quoting.
•Consider SQL compatibility — snake_case is more portable; some databases are case-insensitive.
•Prefix boolean columns — Use 'is_', 'has_', 'can_' to clarify intent (is_active, has_children).
•Suffix timestamp columns — Use '_at' or '_on' for timestamps (created_at, last_login_at).
•Avoid abbreviations — 'customer' is clearer than 'cust'; 'description' beats 'desc'.

Schema Documentation and Data Dictionaries

A schema is only as useful as its documentation. Professional database management requires maintaining data dictionaries—comprehensive catalogs that describe every schema element in human-readable form.\n\nWhat a Data Dictionary Contains:\n\nFor each table:\n- Table name and purpose\n- Business context and ownership\n- Column definitions with types and constraints\n- Relationships to other tables\n- Sample values and acceptable ranges\n- Historical change log\n\nFor each column:\n- Name, data type, and size\n- Whether nullable\n- Default value\n- Business definition and valid values\n- Source of truth (if derived or copied)\n- Privacy classification (PII, confidential, public)

The Cost of Undocumented Schemas

Undocumented schemas become legacy nightmares. New team members spend weeks understanding data. Analysts create incorrect reports based on wrong assumptions. Developers break constraints they didn't know existed. Schema documentation isn't optional—it's essential for sustainable database management.

Database System Catalogs:\n\nModern DBMSs maintain internal system catalogs (metadata repositories) that store schema information. You can query these catalogs to dynamically discover schema structure:\n\n- PostgreSQL: pg_catalog schema (pg_tables, pg_columns, pg_constraints)\n- MySQL: information_schema database\n- SQL Server: sys schema and INFORMATION_SCHEMA views\n- Oracle: ALL_TABLES, ALL_TAB_COLUMNS, USER_* dictionary views\n\nThese catalogs are invaluable for automation, documentation generation, and schema introspection.

query-schema-catalog.sql
PostgreSQL
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-- Query system catalog to list all tables and their columns
-- This is how you programmatically discover schema structure
 
-- List all tables in current schema
SELECT 
    table_name,
    table_type
FROM information_schema.tables
WHERE table_schema = 'public'
ORDER BY table_name;
 
-- Get detailed column information for a specific table
SELECT 
    column_name,
    data_type,
    character_maximum_length,
    is_nullable,
    column_default,
    ordinal_position
FROM information_schema.columns
WHERE table_schema = 'public' 
    AND table_name = 'customers'
ORDER BY ordinal_position;
 
-- List all constraints on a table
SELECT 
    tc.constraint_name,
    tc.constraint_type,
    kcu.column_name,
    ccu.table_name AS foreign_table_name,
    ccu.column_name AS foreign_column_name
FROM information_schema.table_constraints tc
JOIN information_schema.key_column_usage kcu 
    ON tc.constraint_name = kcu.constraint_name
LEFT JOIN information_schema.constraint_column_usage ccu 
    ON tc.constraint_name = ccu.constraint_name
WHERE tc.table_name = 'orders';

Summary: Understanding Database Schemas

We've covered the foundational concept of database schemas comprehensively. Let's consolidate the key takeaways:

Key Takeaways

•A schema is the database blueprint — It defines structure (tables, columns), constraints (rules), and relationships without containing actual data.
•Schemas have mathematical foundations — Set theory and predicate logic underpin the relational model, enabling formal reasoning about data correctness.
•Multiple schema types exist — External (user views), conceptual (logical structure), and internal (physical storage) schemas serve different purposes.
•DDL is the language of schemas — CREATE, ALTER, and DROP statements define and modify schema objects.
•Components include more than tables — Constraints, indexes, views, triggers, and stored procedures are all part of a complete schema.
•Naming conventions matter — Consistent, descriptive naming makes schemas maintainable and self-documenting.
•Documentation is non-negotiable — Data dictionaries and schema documentation prevent technical debt and enable team collaboration.
•System catalogs store metadata — All DBMSs maintain queryable catalogs that describe schema structure programmatically.

What's Next:\n\nNow that we understand what schemas are, we'll explore their counterpart: database instances. While the schema defines what can exist, the instance represents what actually exists at any moment. Understanding this distinction is crucial for grasping how databases operate dynamically while maintaining structural integrity.

Page Complete

You now have a deep understanding of database schemas—the blueprints that define every aspect of how data is structured, constrained, and organized. This knowledge is foundational for database design, query writing, and system administration. Next, we'll examine database instances—the actual data that lives within these carefully defined structures.