Nona : Lazy Programming Language with Dependent Types

Experimental Nano with dependent types
Latest version: Nona-0.8.6

   __________________________
  / ___  / ___  / ___  / _  |
 / /  / / /__/ / /  / / __  |
/_/  /_/______/_/  /_/_/ |__|     by Comcx

NOTE! Codes in /src are out-of-date
EXE file which is fresh can be used directly

Getting Started!

Nona only support Windows 64bits and Linux 64bits platform right now.

Jump to the directory where Nona-x.x.exe lies,  
(cond 
    (use-windows 
      (input command: '.\Nona-0.8.6.exe' or just double click the EXE file))
    (use-linux
      (input command: '.\Nona-0.8.6-linux')))

Incomplete Intro

• Expression :=

  Format	Explanation
  Variable	Single variable
  (Fun params)	Lambda application
  (: Expr type)	Type signature
  (= (bindings) Expr)	Bindings
  (=o (pattern) Expr)	Recursive bindings
  (=: (bindings) Expr)	Inductive families
  (if Expr Expr Expr)	Conditional
  (\ (params) Expr)	Lambda abstraction
  (-> (: a t) b)	Dependent function space

  
  

• Declaration :=

  • (= pattern Expression)
  • (=o pattern Expression)
  • (=: var Type)
  • (: Expr Type)
  
  

• Preluded terms:

  Terms	Explanation
  (0 1 2 ..)	with type Int
  (+ - * /)	for Integers
  "_"	with type String
  (true false)	with type Bool
  (Int Bool String Symbol IO)	which is Set
  (, fst snd)	for tuples !note moved to lib right now!!
  :: () list	for lists
  print	to print
  ...

• REPL use

  • Global environment:
    You can:
    type in (= <pattern> <expression>) to add definition to global environment;
    type in (=o <pattern> <expression>) to add recursive definition to global environment;
    type in (=: <variable> <type>) to construct new types to global environment.

  • Commands:
    version to show current version
    (quit) to quit repl
    (help) to ask for help
    (type <expr>) to show type info
    (na <file>) to load defs
    (no <file>) to load *.no files
    ...

Features

• Lexical scope mangement
• Purely functional
• Inductive family
• Dependent type system
• Type inference with unification
• Church numeral can be built(refer to lib/Prelude.na)
• First class record and typeclass
• String == (List Symbol)
  ...

Examples

(Module Test ( -- The test file


-- Ploymorphism & Dependent types
(= (: id (-> (: a Set) a a)) (\ (a x) x))
(= (: .  (-> (: a Set) (: b Set) (: c Set) (-> b c) (-> a b) (-> a c))) 
    (\ (a b c f g x) (f (g x))))
(= (: weird (-> (: x Int) (if (== x 0) Int Bool) String))
    (\ (x a) "OK"))


-- Boolean functions
(= (not b)   (if b false true))
(= (and (: a Bool) (: b Bool)) (if a b false))
(= (or  a b) (if a true b))
(= (xor a b) (if (and (or a b) (not (and a b))) true false))


-- Inductive dependent sum pair
(=: Sum (-> (: A Set) (: B (-> A Set)) Set))
(=: ,   (-> (: A Set) (: B (-> A Set)) (: a A) (: b (B a)) (Sum A B)))

-- Recursion
(=o ((: fact (-> Int Int)) n)
  (if (== n 0) 1 (* n (fact (- n 1)))))

(: foldl-Int (-> (: b Set) (-> b Int b) b (List Int) b))
(=o (foldl-Int b h x xs)
    (if (== (head Int xs) 0) x
      (foldl-Int b h (h x (head Int xs)) (tail Int xs))))

(: circle (-> (: a Set) a Int (List a)))
(=o (circle a x n)
  (if (== n 0) (() a) (:: a x (circle a x (- n 1)))))

(=o ((: ^ (-> Int Int Int)) x n)
  (if (== n 0) 1 (* x (^ x (- n 1)))))


))--------- end of Test ---------((

Drawbacks

• Not support weak normal head form(WNHF), not completely lazy...
• Lack support of pattern matching for dependent types
• ...