An implementation of "A Categorical Programming Language"
February 8, 2026 · View on GitHub
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: Homebrew (macOS/Linux) 🍺
Install CPL using Homebrew:
$ brew install msakai/tap/cpl
Alternatively, you can tap the repository first:
$ brew tap msakai/tap
$ brew install cpl
Option 3: 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.
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
-
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
-
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.