Simplee.Goa 1.0.5

simplee |> goa

Project which implements lambda calculus parser, and interpreter.

goa |> AST

Contains the definitions of the lambda calculus grammar. Here is an example of the lambda terms:

type GIdentifier = string

type GExpression =
   | GVar      of GIdentifier
   | GApp      of GExpression * GExpression
   | GLambda   of GIdentifier * GExpression

goa |> ofstr

Parses strings and converts them to lambda expressions. The implementation is using the FParse library. Here are several examples of valid strings which are parsed into lambda expressions. In the following example, we get a lambda expression from a given string.

"""\x -> (x y)""" |> gexpr
"""\a b -> b""" |> gexpr

The results of parsing these strings are equivalent to the following lambda expressions built using the provided infix operators:

"x" .>> ("x" .<<. "y")
"a" .>> ("b" .>> ("b" |> gvar))

goa |> combinators

The library provides the standard lambda combinators: S, K, I, M, KI, C, B, Th, B1, V

goa |> eval

The library implements normalization function for lambda expression using beta reduction. There are several convenience variations for such evaluation function where you can pass a logging function, the depth of the evaluation, and a lookup function to replace variables.

// Function with complete list of arguments: logger, depth, lookup
GAnd << GTrue << GTrue |> evalLR logr 100 (fun _ -> None)

// Slim function where the logger is skipped and the depth is set by default to 1000.
// In this example the lookup will replace the 'myID' variable with the ID combinator.
GAnd << GTrue << GTrue |> evald0 (fun s -> if s = "myID" then I |> Some else None)

goa |> bool

The library defines Boolean algebra (GTrue, GFalse, GNot, GOr, GAnd, GBeq)

GNot << GTrue
|> eval (fun _ -> None)
|> g2str
|> function
    | s when s = "λa b.b" -> Ok ()
    | s -> s |> sprintf "The not True is not GFalse [%s]" |> Error

GAnd << GTrue << GFalse
|> eval (fun _ -> None)
|> g2str
|> function
    | s when s = "λb x.x" -> Ok ()
    | s -> s |> sprintf "The AND True False is not GFalse [%s]" |> Error

goa |> numerals

The library defines NUmerals algebra (G0, G1, ..., GSucc, GMul, GPow, GIs0)

let g3 = GAdd << G1 << G2 |> evald0
let g8 = GPow << G2 << G3 |> evald0