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cur

A language with static dependent-types and dynamic types, type annotations and parentheses, theorem proving and meta-programming.

Noun
cur (plural curs)

1. (archaic) A mongrel.
2. (archaic) A detestable person.

Disclaimer

Cur is currently under active hackery and is not fit for use for any particular purpose. It is fraught with unreadable code, errors, performance bugs, and hacks that should never have been written by a reasonable human being. These may or may not be fixed shortly.

Versioning

Cur is in alpha. Version numbers are 0.N, where N increases when an API changes, or a sub-package depends on a new feature (e.g. if cur-test depends on a feature that did not exist in a previous version).

Getting started

Easy mode:

Install cur via raco pkg install cur. See the docs: raco docs cur. Come ask questions in IRC, #cur on Freenode.

Advanced mode:

Cur is actually distributed as several packages. cur-lib provides the implementation and all standard libraries. cur-doc provides the documentation. cur-test provides a test suite and examples.

You can install the individual packages from the Racket package server, or from local copies of the files:

> pushd cur-lib; raco pkg install; popd
...
> pushd cur-doc; raco pkg install; popd
...
> raco test cur-test
...
... tests passed
> raco test cur-test/cur/tests/stdlib/nat.rkt

Example code

Try it out: open up DrRacket and put the following in the definition area:

#lang cur
(require
 cur/stdlib/bool
 cur/stdlib/nat
 cur/stdlib/sugar)

;; Write dependently-typed code
(if true
    false
    true)

(: + (-> Nat Nat Nat))
(define + plus)
(+ z (s z))

;; Write some macros and Racket meta-programs over dependently-typed code
(begin-for-syntax
  (define (nat->unary n)
    (if (zero? n)
        #`z
        #`(s #,(nat->unary (sub1 n))))))

(define-syntax (define-numbers syn)
  (syntax-case syn ()
    [(_)
     #`(begin
         #,@(for/list ([i (in-range 10)])
              #`(define #,(format-id syn "Nat-~a" i) #,(nat->unary i))))]))

(define-numbers)
;; (define-numbers) generates the following definitions at macro-expansion time:
#|
 |  (define Nat-0 z)
 |  (define Nat-1 (s z))
 |  (define Nat-2 (s (s z)))
 |  (define Nat-3 (s (s (s z))))
 |  (define Nat-4 (s (s (s (s z)))))
 |  (define Nat-5 (s (s (s (s (s z))))))
 |  (define Nat-6 (s (s (s (s (s (s z)))))))
 |  (define Nat-7 (s (s (s (s (s (s (s z))))))))
 |  (define Nat-8 (s (s (s (s (s (s (s (s z)))))))))
 |  (define Nat-9 (s (s (s (s (s (s (s (s (s z))))))))))
 |  (define Nat-10 (s (s (s (s (s (s (s (s (s (s z)))))))))))
 |#

Nat-0
Nat-5

;; Of course, you could just define #%datum to do the right thing:
(require (only-in cur [#%datum old-datum]))
(define-syntax (#%datum syn)
  (syntax-parse syn
    [(_ . x:nat)
     (nat->unary (syntax->datum #'x))]
    [(_ . e)
     #`(old-datum e)]))

0
5

Try entering the following in the interaction area:

(sub1 (s (s z)))

Don't like parenthesis? Use Cur with sweet-expressions:

#lang sweet-exp cur
require
 cur/stdlib/sugar
 cur/stdlib/bool
 cur/stdlib/nat

if true
   false
   true

define + plus

{z + s(z)}

Going further

See https://williamjbowman.com/papers#cur for a draft of a paper on Cur.

Open up cur-tests/cur/tests/stlc.rkt to see an example of the simply-typed lambda-calculus modeled in Cur, with a parser and syntax extension to enable deeply embedding.

Open up examples/proofs-for-free.rkt to see an implementation of the translation defined in Proofs for Free as a meta-program.

Open up cur-lib/cur/ntac to see one way to implement tactics in Cur.

Open up anything in cur-lib/cur/stdlib/ to see some standard dependent-type formalisms.

Open up cur-model/cur/curnel/model/core.rkt to see a model of the core language, <600 lines of code. You can run some Cur code using this model, but the cur-lib/cur/curnel/racket-impl/core.rkt (the default Curnel) is much faster and supports more features.