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 199/55 11871/1088 1599875/55
22210i 494/68 2539/254 58602/68
3222i 1206/50 8638/819 804529/50
1022i 4317/69 33369/3139 N/A
4222i 262425/72 2097926/196692 N/A
222210i 1311135/139 8652059/852063 N/A
2222101 2621862/327818 N/A N/A
facty6nt 1112/210 80562/2436 2790150/210
facty9i 1629/287 3746232/130949 N/A
33-fact4 3770/704 16114/912 80706/704
fibo16nt 24931/3042 134135/5673 5462373/3042
fact100i 28502/3752 121854/10565 N/A
35-fact5 72944/13480 805218/16206 4702709/13480
fibo20i 93534/6863 536843/24626 1961507/6863
fact1knt 6215039/1353692 N/A 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]
--exec, -e Process m4(1) macros [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:
# Common combinators
I = x: x;
K = x, y: x;
S = x, y, z: x z (y z);
Y = (a: a a) (a, f: f (a a f));
# Booleans
T = K;
F = K I;
Not = p, a, b: p b a;
And = p, q: p q F;
Or = p, q: p T q;
Xor = p, q: p Not I q;
# Pairs/lists
[] = K T;
[]? = l: l (h, t: F);
Cons = h, t, x: x h t;
Head = l: l T;
Tail = l: l F;
# Church arithmetic
+1 = n, f, x: f (n f x);
+ = m, n, f, x: m f (n f x);
* = m, n, f: m (n f);
^ = m, n: n m;
-1 = n, f, x: n (g, h: h (g f)) (K x) I;
- = m, n: n -1 m;
0? = n: n (K F) T;
# Church numerals
0 = f, x: x;
1 = f, x: f x;
2 = +1 1;
3 = +1 2;
4 = ^ 2 2;
5 = + 2 3;
6 = * 2 3;
7 = +1 6;
8 = ^ 2 3;
9 = ^ 3 2;
10 = * 2 5;
16 = ^ 2 4;
20 = * 2 10;
30 = * 3 10;
32 = ^ 2 5;
64 = ^ 2 6;
100 = ^ 10 2;
128 = ^ 2 7;
256 = ^ 2 8;
512 = ^ 2 9;
1k = ^ 10 3;
1ki = ^ 2 10;
1m = ^ 10 6;
1mi = ^ 2 20;
1g = ^ 10 9;
1gi = ^ 2 30;
# Recursive functions
FactY = Y (f, n: (0? n) 1 (* (f (-1 n)) n));
Fact = n: n (f, i: * (f (+1 i)) i) (K 1) 1;
Fibo = n: n (f, a, b: f (+ a b) a) F 1 0;
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.
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