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:
closed
, the approach of arXiv:1304.2290v8 applied to
An Interaction Net Implementation of Closed Reduction
by Ian Mackie, this is the default algorithm;
optimal
, an implementation of
Lambdascope by Vincent van Oostrom et al;
abstract
, an experimental algorithm described in
arXiv:1701.04691v2.
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 CLOSED OPTIMAL ABSTRACT
counter 58/6 143/4 N/A
w2eta 137/16 205/7 37/7
22210ii 1740/182 7886/70 731/70
3222ii 5896/545 164197/43 1182/43
1022ii 23026/2085 2489461/59 4298/59
4222ii 1442259/131124 N/A 262401/64
222210ii 6685119/655415 N/A 2359812/201
cfact4 15506/887 56890/691 3711/691
yfact4 24150/1741 526971/760 4168/760
cfact5 799868/16170 3074471/13462 69147/13462
yfact5 857864/22267 N/A 69780/13550
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]
--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 /* [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.
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