Likely correct software

2023-11-28

Introduction

  • Idea
    • We have a definition of correctness
    • We know software is the result of a development process
    • We know software has architectural layers
  • Proposal
    • The software architecture design process should produce likely correct deliverables
    • The software development process should produce likely correct deliverables

The software development process and correctness

  • Software development is a process 1
  • The process can use different methods
    • Better the method, formalism
    • Better the deliverable
    • Better the correctness

Formalism, correctness, cost 1

Method Correctness Cost
Formal Provably correct Expensive
Semi formal Likely correct Affordable
Informal Maybe correct Minimal, but it’s a debt

\[\begin{gather*} \tiny{\text{Formal method, Provably correct, Expensive}}\\ \text{Input }\to\boxed{\xrightarrow[\text{Semantics ✅}]{\text{Syntax ✅}}\text{Works 100%}} \end{gather*}\]

\[\begin{gather*} \tiny{\text{Semi formal method, Likely correct, Affordable}}\\ \text{Input }\to\boxed{\xrightarrow[\text{Semantics ❓}]{\text{Syntax ✅}}\text{Works 100% - edges}} \end{gather*}\]

Likely correct software development process

  • Relies on semi formal methods
  • Produces likely correct deliverables
  • At an affordable cost

How to develop likely correct software?

  • Identify the exact steps
    • Of the software development process
    • With its inputs and outputs
  • For each step
    • Find a semi formal method
    • That will produce a semi formal deliverable
    • Which is likely correct

The software development process

Input Process /
Step		 Deliverables
Problem Understanding Model
Model Design Specification
Specification Implementation Code
Code Verification Software

1

\[\begin{gather*} Problem\xrightarrow[\text{}]{\text{Understanding}}Model \end{gather*}\]

Understanding

  • Input
    • The problem
    • Informal, comes as is
    • A document in plain english
  • Deliverable
    • The mental model of the problem
    • In a structured, standardized document

Methods for understanding

  • The scientific method 1
    • Produces a thesis, dissertation
    • Where the hypothesis is supported, not proven
    • But good enough to be likely correct
  • Design in practice 2
    • It’s like the scientific method
    • Taylored to software development

2

\[\begin{gather*} Model\xrightarrow[\text{}]{\text{Design}}Specification \end{gather*}\]

Design

  • Input
    • The mental model of the problem
    • In a structured, standardized document
  • Deliverable
    • The exact specification of the problem
    • In a structured, standardized document
    • Or, better, in executable english 1

Methods for design

  • Concept-based design 1
    • Concepts are semi formal
    • Concept composition is transactional
    • Concepts translate to executable specifications
  • We couldn’t find other methods
    • Functional programming might be a way
    • Category theory is definitively a way 2

3

\[\begin{gather*} Specification\xrightarrow[\text{}]{\text{Implementation}}Code \end{gather*}\]

Implementation

  • Input
    • The exact specification of the problem
    • In an executable specification format
  • Deliverable
    • Totally correct 1 code
    • “The algorithm terminates”
    • No impossible states 2

Methods for implementation

  • Pattern matching 1 2
    • Built-in in most languages
  • Finite-state machine 3 4
    • Also visualizes the business logic
    • For designers, executives

4

\[\begin{gather*} Code\xrightarrow[\text{}]{\text{Verification}}Software \end{gather*}\]

Verification

  • Input
    • Totally correct code
    • The algorithm terminates
    • No impossible states
  • Deliverable
    • Partially correct code 1
    • “If an answer is returned it’s correct”

Methods for verification

  • 100% code coverage 1
    • All code paths checked
    • Not all possible answers checked
  • Property based testing 2
    • All code paths checked
    • All possible answers checked

A likely correct software development process is

  • Likely correct understanding ✅
    • There are good methods
  • Likely correct design ✅❓
    • A single method so far
    • The most difficult part
  • Likely correct implementation ✅
    • Even provably correct is possible
  • Likely correct verification ✅
    • Even provably correct is possible

A complete example

Likely Correct React Apps

Thank you!

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