https://github.com/lukstafi/curious-ocaml

A curious book about OCaml: logic (types), algebra (values), computation (rewrite semantics), functions (lambda calculus), constraints, monads, expression.
https://github.com/lukstafi/curious-ocaml

computer-science functional-programming ocaml

Last synced: 6 months ago
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A curious book about OCaml: logic (types), algebra (values), computation (rewrite semantics), functions (lambda calculus), constraints, monads, expression.

• Host: GitHub
• URL: https://github.com/lukstafi/curious-ocaml
• Owner: lukstafi
• License: gpl-3.0
• Created: 2023-01-29T06:55:17.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2023-11-13T15:33:30.000Z (almost 2 years ago)
• Last Synced: 2024-05-01T13:58:31.793Z (over 1 year ago)
• Topics: computer-science, functional-programming, ocaml
• Language: Tcl
• Homepage: https://lukstafi.github.io/curious-ocaml/
• Size: 14.8 MB
• Stars: 24
• Watchers: 2
• Forks: 0
• Open Issues: 3
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
---

title: Curious OCaml

author: Lukasz Stafiniak

header-includes:

  - 

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---

# Curious OCaml

## From logic rules to programming constructs

What logical connectives do you know?

|$\top$ | $\bot$ | $\wedge$ | $\vee$ | $\rightarrow$

|---|---|---|---|---

|   |   | $a \wedge b$ | $a \vee b$ | $a \rightarrow b$

| truth | falsehood | conjunction | disjunction | implication

| "trivial" | "impossible" | $a$ and $b$ | $a$ or $b$ | $a$ gives $b$

|   | shouldn't get | got both | got at least one | given $a$, we get $b$

How can we define them? Think in terms of _derivation trees_:

$$

\frac{

\frac{\frac{\,}{\text{a premise}} \; \frac{\,}{\text{another premise}}}{\frac{\,}{\text{some fact}}} \;

\frac{\frac{\,}{\text{a premise}} \; \frac{\,}{\text{another premise}}}{\frac{\,}{\text{another fact}}}}

{\text{final conclusion}}

$$

To define the connectives, we provide rules for using them: for example, a rule $\frac{a \; b}{c}$

matches parts of the tree that have two premises, represented by variables $a$

and $b$, and have any conclusion, represented by variable $c$.

### Rules for Logical Connectives

Introduction rules say how to produce a connective. Elimination rules say how to use it.

Text in parentheses is comments. Letters are variables: stand for anything.

Try to use only the connective you define in its definition.

TODO