This package implements the pure untyped lambda calculus using interaction nets, providing both CLI and API.

Its browserified version is available as an online demo:

https://codedot.github.io/lambda/

The following encodings of the lambda calculus are included:

• normal, a domino-effect-based version of Token-Passing Nets: Call-by-Need for Free (François-Régis Sinot), described in arXiv:1304.2290v8 (this is the default algorithm);

• closed, a version of normal based on An Interaction Net Implementation of Closed Reduction (Ian Mackie);

• optimal, the approach of 10.4204/EPTCS.225.7 applied to Lambdascope (Vincent van Oostrom et al);

• abstract, an experimental version of Lamping's abstract algorithm, described in arXiv:1701.04691v2;

• turning, an undocumented non-optimal experimental algorithm.

All versions include the embedded read-back mechanism described in Section 7 of 10.4204/EPTCS.225.7.

This package provides the lambda command with the following interface:

Usage: lambda [options] (<file> | -e <expr>)

Options:
  --algo, -a     Select algorithm                             [string]
  --debug, -d    Enable step-by-step evaluation              [boolean]
  --expr, -e     Process argument as expression              [boolean]
  --inet, -i     Show interaction net                        [boolean]
  --perf, -p     Print benchmarks                            [boolean]
  --stats, -s    Write statistics to file                     [string]
  --term, -t     Output expanded term                        [boolean]
  --help, -h     Show help                                   [boolean]
  --version, -v  Show version number                         [boolean]

CLI predefines a number of commonly used combinators:

I = x: x;
K = x, y: x;
S = x, y, z: x z (y z);
T = K;
F = K I;
AND = p, q: p q F;
OR = p, q: p T q;
NOT = p: (a, b: p b a);
C0 = f, x: x;
C1 = f, x: f x;
C2 = f, x: f (f x);
C3 = f, x: f (f (f x));
C4 = f, x: f (f (f (f x)));
C5 = f, x: f (f (f (f (f x))));
C6 = f, x: f (f (f (f (f (f x)))));
C7 = f, x: f (f (f (f (f (f (f x))))));
C8 = f, x: f (f (f (f (f (f (f (f x)))))));
C9 = f, x: f (f (f (f (f (f (f (f (f x))))))));
C10 = f, x: f (f (f (f (f (f (f (f (f (f x)))))))));
SUCC = n: (f, x: f (n f x));
PLUS = m, n: (f, x: m f (n f x));
MULT = m, n: (f: m (n f));
EXP = m, n: n m;
PRED = n: (f, x: n (g, h: h (g f)) (K x) I);
MINUS = m, n: n PRED m;
ZERO = n: n (K F) T;
Y = (a: a a) (self, f: f (self self f));

require("@alexo/lambda") returns a function of a lambda term defined in a variant of the lambda calculus called Macro Lambda Calculus (MLC) that allows macro definitions in order to input complex expressions. The last term in the input is the term whose normal form is to be found.

For developing and testing purposes, the package also exports two additional functions .prepare(term) and .debug(). The .debug() function applies a single reduction step to the interaction net compiled by the previous .prepare() call and returns a human-readable string representation of the current interaction net state.

Input consists of an optional list of macro definitions and a term:

%token NAME /* [A-Za-z][A-Za-z0-9]* */

%%

text : defs term
     ;
defs : /* empty */
     | defs NAME '=' term ';'
     ;
term : appl
     | abst
     ;
abst : NAME ',' abst
     | NAME ':' term
     ;
appl :      atom
     | appl atom
     ;
atom : '(' term ')'
     |     NAME
     ;

Copyright (c) 2017 Anton Salikhmetov

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.