#The Ivo Programming Language

Ivo (IPA: /aɪvoʊ/) is a programming language based on the Hindley-Milner type system plus undelimited control (call/cc).

#Using the Ivo interpreter

You may run the Ivo interpreter using cabal run [-- args...] or by installing it to your path with cabal install. For information about ivo's command line arguments, please refer to ivo --help (or stack run -- --help).

Type in your command, definition, or expression at the prompt: >> . Expressions will be typechecked, evaluated using call-by-value, and then printed.

Exit the prompt with Ctrl-d (or equivalent).

#Interpreter commands

These commands are available:

• :clear: Clear all of your variable definitions.

• :load <filename>:

  Execute a file containing Ivo definitions and expressions in the interpreter. Variables already defined in the interpreter will be defined in the file; variables defined by the file will be defined in the interpreter.

  The filename may contain spaces, but trailing whitespace will be trimmed.

• :printTypes <both/decls/exprs/off>:

  Print to STDERR the inferred types of top-level declarations, of expressions entered into the interpreters, of both, or of neither.

  This setting defaults to off.

• :trace <off/local/global>:

  • If the argument is local, intermediate expressions will be printed as they are evaluated;

  • If the argument is global, the entire expression will be printed with each evaluation step.

  • The default value is off.

#The Ivo language

#Syntax

The parser's error messages currently are virtually useless, so be very careful with your syntax.

• Variable names: any sequence of letters.
• Function application: f x y
• Lambda abstraction: \x y z. E or λx y z. E
• Let expressions: let x = E; y = F in G
  • The definitions of let expessions may be recursive: let undefined = undefined in undefined.
• Parenthetical expressions: (E)
• Constructors: (), (x, y) (or (,) x y), Left x, Right y, Z, S, [], (x :: xs) (or (:) x xs), Char n.
  • The parentheses around the cons constructor are not optional.
  • Char takes a natural number and turns it into a character.
• Pattern matchers: { Left a -> e ; Right y -> f }
  • Pattern matchers can be applied like functions, e.g. { Z -> x, S -> y } 10 reduces to y.
  • Patterns must use the regular form of the constructor, e.g. (x :: xs) and not ((::) x xs).
  • There are no nested patterns or default patterns.
  • Incomplete pattern matches will crash the interpreter.
• Literals: 1234, [e, f, g, h], 'a, "abc"
  • Strings are represented as lists of characters.
• Type annotations: there are no type annotations; types are inferred only.
• Comments: // line comment, /* block comment */

Top-level contexts (e.g. the REPL or a source code file) allow declarations (let x = E without multiple definitions in ...), which make your definitions available for the rest of the program's execution. You must separate your declarations and expressions with ;.

#Types

Types are checked/inferred using the Hindley-Milner type inference algorithm.

• Functions: a -> b (constructed by \x. e)
• Products: a * b (constructed by (x, y))
• Unit: ★ (constructed by ())
• Sums: a + b (constructed by Left x or Right y)
• Bottom: ⊥ (currently useless because incomplete patterns are allowed)
• The natural numbers: Nat (constructed by Z and S)
• Lists: List a (constructed by [] and (x :: xs))
• Characters: Char (constructed by Char, which takes a Nat)
• Universal quantification (forall): ∀a b. t

#Builtins

Builtins are variables that correspond with a built-in language feature that cannot be replicated by user-written code. They still are just variables though; they do not receive special syntactic treatment.

• callcc : ∀a b. (((a -> b) -> a) -> a): the call-with-current-continuation control flow operator.

Continuations are printed as λ!. ... ! ..., like a lambda abstraction with an argument named ! which is used exactly once; however, continuations are not the same as lambda abstractions because they perform the side effect of modifying the current continuation, and this is not valid syntax you can enter into the REPL.

#Example code

You can see some example code in examples/examples.ivo.