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

Its browserified version is available as an online demo.

The following encodings of the lambda calculus are included:

• abstract, an impure solution to the problem of matching fans in Lamping's abstract algorithm, described in arXiv:1710.07516, this is the default algorithm;

• closed, the approach of arXiv:1304.2290v8 applied to An Interaction Net Implementation of Closed Reduction by Ian Mackie;

• optimal, an implementation of Lambdascope by Vincent van Oostrom et al.

The embedded read-back mechanism is described in Section 7 of 10.4204/EPTCS.225.7.

The following is output of the test.sh script provided in the package:

SAMPLE          ABSTRACT         CLOSED        OPTIMAL
counter             27/4           58/6          143/4
w2eta               37/7         137/16          205/7
1021              173/45     11747/1058      717218/45
22210i            728/69       1719/181        7826/69
3222i            1179/42       5635/544      163882/42
1022i            4295/58     21997/2084     2488384/58
4222i          262398/63 1376718/131123            N/A
222210i      2359809/200 6619578/655414            N/A
2222101   4719108/590024            N/A            N/A
cfact4          3715/692      15560/888      56928/692
yfact4          4168/760     24150/1741     526971/760
cfact5       69151/13463   799931/16171  3074509/13463
yfact5       69780/13550   857864/22267            N/A

T/B should be read as total of T interactions, of which B were β-reductions.

This package provides the lambda command with the following interface:

Usage: lambda [options] (<term> | -f <file>)

Options:
  --algo, -a     Select algorithm         [string]
  --debug, -d    Evaluate step by step   [boolean]
  --file, -f     Read term from file     [boolean]
  --inet, -i     Show interaction net    [boolean]
  --limit, -l    Limit interactions       [number]
  --macros, -m   Read macros from file    [string]
  --perf, -p     Print benchmarks        [boolean]
  --stats, -s    Save 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

%%

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.