An implementation of "A Categorical Programming Language"

This package is an implementation of "A Categorical Programming Language" (CPL for short)[1][2] written in Haskell.

🚀 Try CPL in your browser: WebAssembly Demo (no installation required!)

CPL is a functional programming language based on category theory. Data types are declared in a categorical manner by adjunctions. Data types that can be handled include the terminal object, the initial object, the binary product functor, the binary coproduct functor, the exponential functor, the natural number object, the functor for finite lists, and the functor for infinite lists. Each data type is declared with its basic operations or morphisms. Programs consist of these morphisms, and execution of programs is the reduction of elements (i.e. special morphisms) to their canonical form.

📦 Install

Option 1: Use WebAssembly Version (No Installation) 🌐

Try CPL directly in your browser: https://msakai.github.io/cpl/

No installation required! Works on Chrome, Firefox, Safari, and Edge.

Option 2: Build from Source 🔧

Supported GHC versions: >=9.2

Standard Build (Native)

De-Compress the archive and enter its top directory. Then type:

$ cabal configure
$ cabal build
$ cabal install

If you want to compile without haskeline, add -f-Haskeline to the configure command.

Alternatively, you can use Stack:

$ stack build
$ stack exec cpl

To disable haskeline with Stack, use the --flag option:

$ stack build --flag CPL:-Haskeline

WebAssembly Build

See web/README.md for detailed instructions on building and testing the WebAssembly version.

📖 Usage

If you are new to CPL, we recommend starting with the Tutorial below. For a concise reference of the language syntax, see chapter 5 of [1].

Quick Start ⚡

Once you have CPL running (either in browser or terminal), try these commands:

cpl> edit
| right object 1 with !
| end object;
right object 1 defined
cpl> edit
| right object prod(a,b) with pair is
|   pi1: prod -> a
|   pi2: prod -> b
| end object;
right object prod(+,+) defined
cpl> edit
| right object exp(a,b) with curry is
|   eval: prod(exp,a) -> b
| end object;
right object exp(-,+) defined
cpl> edit
| left object nat with pr is
|   0: 1 -> nat
|   s: nat -> nat
| end object;
left object nat defined
cpl> show pair(pi2,eval)
pair(pi2,eval)
    : prod(exp(*a,*b),*a) -> prod(*a,*b)
cpl> let add=eval.prod(pr(curry(pi2), curry(s.eval)), I)
add : prod(nat,nat) -> nat  defined
cpl> simp add.pair(s.s.0, s.0)
s.s.s.0
    : 1 -> nat
cpl> help
  exit                        exit the interpreter
  quit                        ditto
  bye                         ditto
  edit                        enter editing mode
  simp [full] <exp>           evaluate expression
  show <exp>                  print type of expression
  show function <name>        print information of function
  show object <functor>       print information of functor
  load <filename>             load from file
  set trace [on|off]          enable/disable trace
  reset                       remove all definitions
cpl> exit

For more examples, see the samples/ directory. For step-by-step explanations, see the Tutorial below.

Tutorial

A comprehensive tutorial that covers CPL usage and the category theory concepts behind it. No prior knowledge of category theory is required.

• Tutorial (English)
• チュートリアル (日本語)

Topics covered: terminal objects, products, coproducts, exponential objects, natural numbers, lists, infinite lists, and the duality between left object and right object.

License

This program is licensed under the BSD-style license. (See the file COPYING.)

Copyright (C) 2004-2026 Masahiro Sakai masahiro.sakai@gmail.com

Author

Masahiro Sakai masahiro.sakai@gmail.com

📖 Bibliography

1. Tatsuya Hagino, “A Categorical Programming Language”. Ph.D. Thesis, University of Edinburgh, 1987. available at https://web.sfc.keio.ac.jp/~hagino/index.html.en

2. Tatsuya Hagino, “Categorical Functional Programming Language”. Computer Software, Vol 7, No.1. Advances in Software Science and Technology 4, 1992. ISBN 0-12-037104-9.