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Binary type with addition and multiplication for interaction nets, https://inet.run/playground/
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| // Example usage: | |
| // let bsix = b0(b1(b1(bend()))) | |
| // let nseven = add1(add1(add1(add1(add1(add1(add1(zero()))))))) | |
| // let bseven = ntob(nseven) | |
| // eval @inspect(bmul(bsix, bseven)) // -> takes 75 steps; doing the same with Nat mul takes 123 steps | |
| // Type defitinion | |
| type Bin | |
| // bin-end | |
| node bend( | |
| ------------ | |
| value!: Bin | |
| ) | |
| node b0( | |
| higherbits: Bin | |
| ------------ | |
| value!: Bin | |
| ) | |
| node b1( | |
| higherbits: Bin | |
| ------------ | |
| value!: Bin | |
| ) | |
| // Utilities | |
| node binDup( | |
| target!: Bin | |
| ------------ | |
| result1: Bin, | |
| result2: Bin | |
| ) | |
| rule binDup(target!, result1, result2) b1(higherbits, value!) { | |
| let b, d = binDup(higherbits) | |
| @connect(b1(b), result1) | |
| @connect(b1(d), result2) | |
| } | |
| rule binDup(target!, result1, result2) b0(higherbits, value!) { | |
| let b, d = binDup(higherbits) | |
| @connect(b0(b), result1) | |
| @connect(b0(d), result2) | |
| } | |
| rule binDup(target!, result1, result2) bend(value!) { | |
| @connect(bend(), result1) | |
| @connect(bend(), result2) | |
| } | |
| node binErase( | |
| target!: Bin | |
| ------------ | |
| ) | |
| rule binErase(target!) b1(higherbits, value!) { | |
| binErase(higherbits) | |
| } | |
| rule binErase(target!) b0(higherbits, value!) { | |
| binErase(higherbits) | |
| } | |
| rule binErase(target!) bend(value!) {} | |
| node binDouble( | |
| target!: Bin | |
| ------------ | |
| result: Bin | |
| ) | |
| rule binDouble(target!, result) b0(higherbits, value!) { | |
| @connect(b0(b0(higherbits)), result) | |
| } | |
| rule binDouble(target!, result) b1(higherbits, value!) { | |
| @connect(b0(b1(higherbits)), result) | |
| } | |
| rule binDouble(target!, result) bend(value!) { | |
| @connect(bend(), result) | |
| } | |
| // Basic arithmetic - increment | |
| node badd1( | |
| target!: Bin | |
| ------------ | |
| result: Bin | |
| ) | |
| rule badd1(target!, result) b1(higherbits, value!) { | |
| @connect(b0(badd1(higherbits)), result) | |
| } | |
| rule badd1(target!, result) b0(higherbits, value!) { | |
| @connect(b1(higherbits), result) | |
| } | |
| rule badd1(target!, result) bend(value!) { | |
| @connect(b1(bend()), result) | |
| } | |
| // Basic arithmetic - addition built on top of increment | |
| node badd( | |
| left: Bin, | |
| right!: Bin | |
| ------------ | |
| result: Bin | |
| ) | |
| node baddAdvance( | |
| left!: Bin, | |
| right: Bin | |
| ------------ | |
| result: Bin | |
| ) | |
| rule badd(left, right!, result) b0(higherbits, value!) { | |
| @connect(baddAdvance(left, higherbits), result) | |
| } | |
| rule badd(left, right!, result) b1(higherbits, value!) { | |
| @connect(badd1(baddAdvance(left, higherbits)), result) | |
| } | |
| rule badd(left, right!, result) bend(value!) { | |
| @connect(baddAdvance(left, bend()), result) | |
| } | |
| rule baddAdvance(left!, right, result) b0(higherbits, value!) { | |
| @connect(b0(badd(higherbits, right)), result) | |
| } | |
| rule baddAdvance(left!, right, result) b1(higherbits, value!) { | |
| @connect(b1(badd(higherbits, right)), result) | |
| } | |
| rule baddAdvance(left!, right, result) bend(value!) { | |
| @connect(binDouble(right), result) | |
| } | |
| // Basic arithmetic - multiplication built on top of addition | |
| node bmul( | |
| left: Bin, | |
| right!: Bin | |
| ------------ | |
| result: Bin | |
| ) | |
| rule bmul(left, right!, result) b0(higherbits, value!) { | |
| @connect(b0(bmul(left, higherbits)), result) | |
| } | |
| rule bmul(left, right!, result) b1(higherbits, value!) { | |
| let b, d = binDup(left) | |
| @connect(badd(d, binDouble(bmul(b, higherbits))), result) | |
| } | |
| rule bmul(left, right!, result) bend(value!) { | |
| @connect(bend(), result) | |
| binErase(left) | |
| } | |
| // Conversion to and from Nat | |
| import { | |
| Nat, zero, add1, | |
| natErase, natDup | |
| } from "https://code-of-inet-js.fidb.app/std/datatype/Nat.i" | |
| node natDouble( | |
| target!: Nat | |
| ------------ | |
| result: Nat | |
| ) | |
| rule natDouble(target!, result) zero(value!) { | |
| @connect(zero(), result) | |
| } | |
| rule natDouble(target!, result) add1(prev, value!) { | |
| @connect(add1(add1(natDouble(prev))), result) | |
| } | |
| node ntob( | |
| target!: Nat | |
| ------------ | |
| result: Bin | |
| ) | |
| rule ntob(target!, result) add1(prev, value!) { | |
| @connect(badd1(ntob(prev)), result) | |
| } | |
| rule ntob(target!, result) zero(value!) { | |
| @connect(bend(), result) | |
| } | |
| node bton( | |
| target!: Bin | |
| ------------ | |
| result: Nat | |
| ) | |
| rule bton(target!, result) b0(higherbits, value!) { | |
| @connect(natDouble(bton(higherbits)), result) | |
| } | |
| rule bton(target!, result) b1(higherbits, value!) { | |
| @connect(add1(natDouble(bton(higherbits))), result) | |
| } | |
| rule bton(target!, result) bend(value!) { | |
| @connect(zero(), result) | |
| } | |
| // Ideas for future development: | |
| // - Change bend to bend0/bpos and bend1/bneg to support two's complement signed integers | |
| // - Add subtraction | |
| // - Add division and modulo (could be same node doing both?) |
Ooh... that looks fancy! Updated! ✨
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@bojidar-bg
I re-implemented the language to use JavaScript-like syntax: https://github.com/cicada-lang/inet.js