Simplee.Goa 1.0.15

Install-Package Simplee.Goa -Version 1.0.15
dotnet add package Simplee.Goa --version 1.0.15
<PackageReference Include="Simplee.Goa" Version="1.0.15" />
For projects that support PackageReference, copy this XML node into the project file to reference the package.
paket add Simplee.Goa --version 1.0.15
The NuGet Team does not provide support for this client. Please contact its maintainers for support.
#r "nuget: Simplee.Goa, 1.0.15"
#r directive can be used in F# Interactive, C# scripting and .NET Interactive. Copy this into the interactive tool or source code of the script to reference the package.
// Install Simplee.Goa as a Cake Addin
#addin nuget:?package=Simplee.Goa&version=1.0.15

// Install Simplee.Goa as a Cake Tool
#tool nuget:?package=Simplee.Goa&version=1.0.15
The NuGet Team does not provide support for this client. Please contact its maintainers for support.


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, Y

let sum = "f" .>> ("n" .>> (GIs0 <<. "n" << G0 << ("n" .<< GSucc << ("f" .<< (GPred <<. "n")))))
let g6 = Y << sum << G3

goa |> eval

The library implements evalalization 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)

let gfalse = GNot << GTrue |> evald0
let gfalse1 = GAnd << GTrue << GFalse |> evald0

goa |> numerals

The library defines Numerals algebra:

G0, G1, G2, ... - Church numerals

GSucc, GPred - successor and presecessor

GAdd, GSub, GMul, GPow - add, sub, multiplication, power

GIs0, GEq, GLEq, GGr - is zero, equal, less or equal, and greater

let g3 = GAdd << G1 << G2 |> evald0
let g8 = GPow << G2 << G3 |> evald0
let g7 = GPred << g8
leg gfalse = GIs0 << G1 |> evald0
let gtrue = GLEq << G1 << G3 |> evald0
let gfalse = GGr << G1 << G2 |> evald0

goa |> pairs

The library defines Pairs algebra (GPair, GFst, GSnd, GPhi). The phi combinator takes a pair (_, Gn) and returns (Gn, Gn+1).

let pair = GPair << G1 << G2
let g1 = GFst << pair
let g2 = GSnd << pair
let g2a = GFst << GPhi << pair
let g3 = GSnd << GPhi << pair

NuGet packages

This package is not used by any NuGet packages.

GitHub repositories

This package is not used by any popular GitHub repositories.

Version Downloads Last updated
1.0.15 688 2/6/2018
1.0.11 632 2/4/2018
1.0.10 628 2/4/2018
1.0.5 626 2/4/2018
1.0.4 699 2/1/2018
1.0.1 658 1/31/2018
1.0.0 722 1/30/2018

Fixed several bugs in the evaluation logic. Added quote and bracket abstraction mechanism.