branching and very basic merging of slots

lib/point.js

@@ -1,10 +1,11 @@
 import { Type } from "../primitives/types.js";
 import { typedFnType } from "../structures/types.js"
 import { Double } from "../primitives/types.js";
+import { makeTypeConstructor } from "../type_constructor.js";
 
 // Create nominal types
-export const PointCartesian2D = { symbol: Symbol('PointCartesian2D'), params: [] };
+export const PointCartesian2D = makeTypeConstructor(Symbol('PointCartesian2D'))(0);
-export const PointPolar2D     = { symbol: Symbol('PointPolar2D')    , params: [] };
+export const PointPolar2D     = makeTypeConstructor(Symbol('PointPolar2D'))(0);
 
 export const cart2polar = ({x, y}) => {
   const r = Math.sqrt(x*x + y*y);

lib/point_structural.js

@@ -0,0 +1,140 @@
+import { prettyT, typedFnType } from "../structures/types.js"
+import { Double } from "../primitives/types.js";
+import { makeConstructor, makeConstructorType, makeGetters, makeGettersTypes, structType } from "../structures/struct.js";
+import { constructorProduct } from "../structures/product.js";
+import { makeTypeConstructor } from "../type_constructor.js";
+
+const cartFields = [
+  constructorProduct("x")(Double),
+  constructorProduct("y")(Double),
+];
+
+const polarFields = [
+  constructorProduct("r")(Double),
+  constructorProduct("θ")(Double),
+];
+
+// Nominal types:
+export const NPoint2DCartesian = makeTypeConstructor(Symbol('Point2DCartesian'))(0);
+export const NPoint2DPolar     = makeTypeConstructor(Symbol('Point2DPolar'))(0);
+
+// Structural types:
+export const SPoint2DCartesian = structType(cartFields);  // (Double, (Double, Unit))
+export const SPoint2DPolar     = structType(polarFields); // (Double, (Double, Unit))
+
+export const constructorPoint2DCartesian = makeConstructor(cartFields);
+export const constructorPoint2DPolar     = makeConstructor(polarFields);
+
+export const constructorPoint2DCartesianFnType = makeConstructorType(NPoint2DCartesian)(cartFields);
+export const constructorPoint2DPolarFnType     = makeConstructorType(NPoint2DPolar)(polarFields);
+
+export const [getX, getY] = makeGetters(cartFields);
+export const [getR, getΘ] = makeGetters(polarFields);
+
+export const [getXFnType, getYFnType] = makeGettersTypes(NPoint2DCartesian)(cartFields);
+export const [getRFnType, getΘFnType] = makeGettersTypes(NPoint2DPolar)(polarFields);
+
+export const cart2polar = cart => {
+  const x = getX(cart);
+  const y = getY(cart);
+  const r = Math.sqrt(x*x + y*y);
+  const θ = Math.atan(y/x);
+  return constructorPoint2DPolar(r)(θ);
+};
+
+export const polar2cart = polar => {
+  const r = getR(polar);
+  const θ = getΘ(polar);
+  const x = r * Math.cos(θ);
+  const y = r * Math.sin(θ);
+  return constructorPoint2DCartesian(x)(y);
+};
+
+export const cart2Str = cart => {
+  const x = getX(cart);
+  const y = getY(cart);
+  return {l: `{x: ${x}, y: ${y}}`};
+};
+
+export const polar2Str = polar => {
+  const r = getR(polar);
+  const θ = getΘ(polar);
+  return {l: `{r: ${r}, θ: ${θ}}`};
+};
+
+// export const translate = dx => dy => ({x, y}) => {
+//   return {x: x+dx, y: y+dy};
+// };
+
+// export const rotate = dθ => ({r, θ}) => {
+//   return {r, θ: θ+dθ};
+// };
+
+// export const scale = dr => ({r, θ}) => {
+//   return {r: r+dr, θ};
+// };
+
+// const examplePoint = {x: 1, y: 2};
+
+const examplePointCart = constructorPoint2DCartesian(1)(2);
+const examplePointPolar = constructorPoint2DCartesian(0)(5);
+
+console.log(prettyT(getXFnType));
+
+export const ModulePoint = {l:[
+  // {i: -1                 , t: Double},
+  // {i: 2                  , t: Double},
+  // {i: examplePoint       , t: Point2DCartesian},
+
+  {i: examplePointCart, t: SPoint2DCartesian},
+  {i: examplePointCart, t: NPoint2DCartesian},
+
+  {i: examplePointPolar, t: SPoint2DPolar},
+  {i: examplePointPolar, t: NPoint2DPolar},
+
+  // {i: SPoint2DCartesian   , t: Type},
+  // {i: SPoint2DPolar       , t: Type},
+
+  // {i: NPoint2DCartesian   , t: Type},
+  // {i: NPoint2DPolar       , t: Type},
+
+  {i: getX, t: getXFnType},
+  {i: getY, t: getYFnType},
+  {i: getR, t: getRFnType},
+  {i: getΘ, t: getΘFnType},
+
+  ...typedFnType(cart2polar, fnType => fnType(NPoint2DCartesian)(NPoint2DPolar)),
+  ...typedFnType(polar2cart, fnType => fnType(NPoint2DPolar)(NPoint2DCartesian)),
+
+  // ...typedFnType(polar2cart, fnType => fnType(Point2DPolar)(Point2DCartesian)),
+
+  // // Double -> Double -> PointCartesian2D -> PointCartesian2D
+  // ...typedFnType(translate, fnType =>
+  //   fnType
+  //     (Double)
+  //     (fnType
+  //       (Double)
+  //       (fnType
+  //         (Point2DCartesian)
+  //         (Point2DCartesian)))),
+
+  // ...typedFnType(cart2tuple, fnType => fnType(Point2DCartesian)(prodType(Double)(Double))),
+  
+  // ...typedFnType(polar2tuple, fnType => fnType(Point2DPolar)(prodType(Double)(Double))),
+
+  // // Double -> PointPolar2D -> PointPolar2D
+  // ...typedFnType(rotate, fnType =>
+  //   fnType
+  //     (Double)
+  //     (fnType
+  //       (Point2DPolar)
+  //       (Point2DPolar))),
+
+  // // Double -> PointPolar2D -> PointPolar2D
+  // ...typedFnType(scale, fnType =>
+  //   fnType
+  //     (Double)
+  //     (fnType
+  //       (Point2DPolar)
+  //       (Point2DPolar))),
+]};

lib/symbol.js

@@ -6,6 +6,8 @@ import { typedFnType } from "../structures/types.js";
 // The way instances of SymbolT are currently encoded, their constructor is not a valid DOPE function, because it is impure.
 // The only way to construct symbols is to do it in JS code.
 
+// At some point, we should start encoding SymbolTs as UUIDs rather than JS-Symbols.
+
 export const ModuleSymbol = {l:[
   {i: SymbolT, t: Type},
 

primitives/generic_type.js

@@ -1,6 +1,6 @@
 import { constructorLeft, constructorRight } from "../structures/sum.js";
-import { fnType, setType, sumType, typedFnType } from "../structures/types.js";
+import { setType, sumType, typedFnType } from "../structures/types.js";
-import { GenericType, SymbolT, Type, Unit } from "./types.js";
+import { Any, GenericType, SymbolT, Type, Unit } from "./types.js";
 import { unit } from "./unit.js";
 
 export const getType     = genericType => genericType.type;
@@ -11,11 +11,11 @@ export const toNonGeneric = genericType => (genericType.typeVars.size === 0)
   : constructorLeft(unit);
 
 export const ModuleGenericType = {l:[
-  {i: GenericType, t: Type},
+  {i: GenericType, t: Any},
 
-  ...typedFnType(getType, fnType => fnType(GenericType)(Type)),
+  // ...typedFnType(getType, fnType => fnType(GenericType)(Type)),
 
-  ...typedFnType(getTypeVars, fnType => fnType(GenericType)(setType(SymbolT))),
+  // ...typedFnType(getTypeVars, fnType => fnType(GenericType)(setType(SymbolT))),
 
   ...typedFnType(toNonGeneric, fnType => fnType(GenericType)(sumType(Unit)(Type))),
 ]};

primitives/types.js

@@ -10,6 +10,7 @@ const SymbolChar   = Symbol('Char');
 const SymbolUnit   = Symbol('Unit');
 const SymbolSymbol = Symbol('Symbol');
 const SymbolType   = Symbol('Type');
+const symbolAny = Symbol('Any');
 const SymbolGenericType = Symbol('GenericType');
 
 export const Int     = makeTypeConstructor(SymbolInt)(0);
@@ -23,10 +24,13 @@ export const Unit    = makeTypeConstructor(SymbolUnit)(0);
 
 export const SymbolT = makeTypeConstructor(SymbolSymbol)(0);
 
+// Types are typed by Any
 export const Type    = makeTypeConstructor(SymbolType)(0);
 
 export const GenericType = makeTypeConstructor(SymbolGenericType)(0);
 
+// Everything is typed by Any
+export const Any = makeTypeConstructor(symbolAny)(0);
 
 export const ModuleSymbols = {l:[
   {i: SymbolInt   , t: SymbolT},
@@ -39,3 +43,5 @@ export const ModuleSymbols = {l:[
   {i: SymbolType  , t: SymbolT},
   {i: SymbolGenericType, t: SymbolT},
 ]};
+
+

progress.txt

@@ -1,72 +1,24 @@
-status:
+done:
   - everything is properly typed, up to the meta-circular level
   - primitives
   - structures: list, product, sum
       can compose structures, e.g., create list of list of product of sum of ...
       list type is specialized for ListOfByte to use Uint8Array
-  - generics currently implemented in two ways:
+  - generic types and type inferencing
-      1) similar to "templates" (as in C++):
-         a generic function or type is a function that takes a Type, and produces a specific variant
-      2) experimental implementation of polymorphic types and type inferencing
-         values currently treated as white-box, hardcoded generic types (e.g., list, function) in type inferencing algorithm
-
-wip:
-  - interfaces via typeclasses?
-
-  - revise the way types are encoded
-     we need only one 'type of type' (called 'kind' in Haskell), and we can call it 'Type'.
-     types explicitly contain their underlying types. the type inferencing algorithm needs this information.
-
-      Int
-       { symbol: Int, params: [] }
-
-      [Int]
-       { symbol: List, params: [{ symbol: Int, params: [] }] }
-
-      [[Int]]
-       { symbol: List,
-         params: [{ symbol: List, params: [{symbol: Int, params: []}]}]}
-
-      Int -> Bool
-       { symbol: Function, params: [
-            { symbol: Int, params: [] },
-            { symbol: Bool, params: [] },
-         ]
-       }
-
-      Int | Bool
-       { symbol: Sum, params: [
-            { symbol: Int, params: [] },
-            { symbol: Bool, params: [] },
-         ]
-       }
-
-      (Int, Bool)
-       { symbol: Product, params: [
-            { symbol: Int, params: [] },
-            { symbol: Bool, params: [] },
-         ]
-       }
-
-      Point2D   <-- custom nominal type! maybe it contains two Doubles, but we don't expose this
-       { symbol: Point2D, params: [] }
-
-      Type constructors are just functions that return a 'Type'.
-         For instance:
-         lsType :: Type -> Type
-         fnType :: Type -> Type -> Type
-
-      The sad(?) part about all of this, is that I'm converging with Haskell/Lean.
-
 
 todo:
-  - rename Type to a NominalType?
+  - to support sets of slots, need comparison of slots
-      const nominalType = (name, params) => ({left: name, right: params});
+      => comparison of values
-    type of every nominal type is (String, [Type])
+        => problem: how to compare transformed values? their inputs can come from different types
+
+      (a) tedious: put in every value:
+            - the type
+            - a comparison function for that type
+          then first compare types, if types match, compare values.
+          could generalize this by writing a compare function on 'typed' values.
+
+      (b) dirty: use 'magic' function that compares any JS value
+
+  - typeclass mechanism
 
   - what about type links: they connect anything to its type... what is the type of 'anything'?
-
-  - treat all values as polymorphic? (non-polymorphic values simply have empty set of type variables)
-
-  - type inferencing can be reduced to finding a graph isomorphism?
-

scripts/generics.js

@@ -1,6 +1,6 @@
 import { Bool, Int } from "../primitives/types.js";
 import { fnType, lsType, prettyT } from "../structures/types.js";
-import { assign, makeGeneric, unify } from "./generics.js";
+import { assign, makeGeneric, unify } from "../generics/generics.js";
 
 // a -> Int
 const a_to_Int = makeGeneric(a => fnType(a)(Int));

scripts/main.js

@@ -6,8 +6,8 @@ import { isFunction, prettyT } from '../structures/types.js';
 import { ModuleStd } from '../stdlib.js';
 import { Double, GenericType, Int, SymbolT, Type } from "../primitives/types.js";
 import { eqType } from '../primitives/type.js';
-import { Any } from '../typed.js';
+import { Any } from "../primitives/types.js";
-import { assign, assignFn, makeGeneric, onlyOccurring } from '../generics/generics.js';
+import { assignFn, makeGeneric, onlyOccurring } from '../generics/generics.js';
 
 
 // import {emitKeypressEvents} from 'node:readline';
@@ -48,6 +48,15 @@ class Context {
 
       this.types.getdefault(i, true).add(t);
       this.types.getdefault(i, true).add(Any);
+      if (t.typeVars) {
+        // console.log("generic:", prettyT(t));
+        this.types.getdefault(t, true).add(GenericType);
+      }
+      else {
+        // console.log("non-generic:", prettyT(t));
+        this.types.getdefault(t, true).add(Type);
+      }
+      
       this.instances.getdefault(t, true).add(i);
       this.instances.getdefault(Any, true).add(i);
     }
@@ -318,7 +327,7 @@ async function callFunction(fn, fnT) {
   }
   else {
     inType = fnT.params[0];
-    choices = [...ctx.instances.getdefault(inType)].flatMap(i => toChoices([i, ctx.types.getdefault(i)]));
+    choices = [...ctx.instances.getdefault(inType)].flatMap(i => toChoices([i, [inType]]));
   }
   
   const choice = await select({
@@ -337,7 +346,7 @@ async function callFunction(fn, fnT) {
     i = await createInstance(inType);
     t = inType;
     if (i === undefined) {
-      return;
+      return callFunction(fn, fnT);
     }
   }
   else {
@@ -345,7 +354,8 @@ async function callFunction(fn, fnT) {
     t = choice.t;
   }
   const genT = t.typeVars ? t : makeGeneric(() => t);
-  const assignedFnType = assignFn(fnT, genT);
+  const genFnT = fnT.typeVars ? fnT : makeGeneric(() => fnT);
+  const assignedFnType = assignFn(genFnT, genT);
   await apply(i, fn, assignedFnType);
   return callFunction(fn, fnT);
 }
@@ -417,11 +427,10 @@ async function transform(i, t) {
 
 async function apply(i, fn, fnT) {
   const result = fn(i);
-  // console.log(fn, '(', i, ')', '=', result);
   let resultType;
-  // console.log(fnT);
   if (fnT.typeVars) {
-    resultType = onlyOccurring(fnT.type.params[1], fnT.typeVars);
+    const res = onlyOccurring(fnT.type.params[1], fnT.typeVars);
+    resultType = res.typeVars.size > 0 ? res : res.type;
   }
   else {
     resultType = fnT.params[1];

scripts/num.js

@@ -3,7 +3,7 @@ import { makeGeneric } from "../generics/generics.js";
 import { Double, Int } from "../primitives/types.js";
 import { fnType } from "../structures/types.js";
 import { pretty } from '../util/pretty.js';
-import { getMul, NumInstances } from "./num.js";
+import { getMul, NumInstances } from "../typeclasses/num.js";
 import { numDictType } from "./num_type.js";
 
 const square = numDict => x => getMul(numDict)(x)(x);

scripts/rbtree_bench.js

@@ -54,7 +54,7 @@ function benchmark(N) {
     const endTime = Date.now();
     return endTime - startTime;
   }
-  const durCopying = (N <= 20000) ? copying() : "";
+  const durCopying = (N <= 50000) ? copying() : "";
   console.log("copying:", durCopying, "ms");
 
   // slower than slowest

scripts/versioning.js

@@ -0,0 +1,122 @@
+import { pretty } from "../util/pretty.js";
+import { newLiteral, transform, read, getReadDependencies, verifyValue } from "../versioning/value.js";
+import { merge, merge2, newSlot, overwrite } from "../versioning/slot.js";
+import createRBTree from "functional-red-black-tree";
+import { add, emptySet, RBTreeWrapper } from "../structures/set.js";
+
+const inc = x => x + 1;
+
+
+console.log("##############");
+console.log("## Counting ##");
+console.log("##############");
+
+const counterOneSlot = newSlot(Symbol('counter'))(newLiteral(1));
+const valueOne = read(counterOneSlot);
+console.log(pretty({valueOne}));
+const onePlusOne = transform(valueOne)(newLiteral(inc));
+console.log(pretty({onePlusOne}));
+const onePlusOnePlusOne = transform(onePlusOne)(newLiteral(inc));
+console.log(pretty({onePlusOnePlusOne}));
+
+verifyValue(valueOne);
+verifyValue(onePlusOne);
+verifyValue(onePlusOnePlusOne);
+
+
+
+console.log("#############");
+console.log("## Summing ##");
+console.log("#############");
+
+const priceSlot = newSlot(Symbol('price'))(newLiteral(20.66));
+const taxSlot   = newSlot(Symbol('tax'))(newLiteral(4.34));
+
+const total =
+  transform(read(priceSlot))(
+    transform(read(taxSlot))(
+      newLiteral(tax => price => price + tax)));
+
+console.log(pretty({total}))
+
+const totalPlusOne = transform(total)(newLiteral(inc));
+
+console.log(pretty({totalPlusOne}));
+
+verifyValue(totalPlusOne);
+
+console.log("getReadDependencies(totalPlusOne):", getReadDependencies(totalPlusOne));
+
+
+
+console.log("###############");
+console.log("## Branching ##");
+console.log("###############");
+
+const fiveSlot  = newSlot(Symbol('counter'))(newLiteral(5));
+const sixSlot   = overwrite(fiveSlot)(newLiteral(6));
+const sevenSlot = overwrite(fiveSlot)(newLiteral(7));
+const eightSlot = overwrite(fiveSlot)(newLiteral(8));
+
+const numCompare = x => y => {
+  if (typeof(x) !== 'number' || typeof(y) !== 'number') {
+    throw new Error(`was only meant to compare numbers! got ${x} and ${y}`);
+  }
+  return (x < y) ? -1 : (x > y) ? 1 : 0;
+};
+const intMerge = merge(numCompare);
+const intMerge2 = merge2(numCompare);
+
+const sixSevenSlot = intMerge(sixSlot)(sevenSlot);
+const sevenEightSlot = intMerge(sevenSlot)(eightSlot);
+
+// console.log(compareSlots(intCompare)(fiveSlot)(fiveSlot));
+// console.log(compareSlots(intCompare)(sixSlot)(sixSlot));
+// console.log(compareSlots(intCompare)(fiveSlot)(sixSlot));
+// console.log(compareSlots(intCompare)(sixSlot)(fiveSlot));
+
+const sixSevenEightSlot = intMerge2(sixSevenSlot)(sevenEightSlot);
+
+console.log(pretty({sixSevenEightSlot}));
+
+// console.log("########################");
+// console.log("## Heterogeneous data ##");
+// console.log("########################");
+
+// const strCompare = x => y => {
+//   if (typeof(x) !== 'string' || typeof(y) !== 'string') {
+//     throw new Error(`was only meant to compare strings! got ${x} and ${y}`);
+//   }
+//   return (x < y) ? -1 : (x > y) ? 1 : 0;
+// };
+
+// // Slot<Int>
+// const numberOfSheepSlot  = newSlot(Symbol('numberOfSheep'))(newLiteral(5));
+// const alternativeNumberOfSheepSlot = newSlot(Symbol('alternativeNumberOfSheep'))(newLiteral(6));
+// // Slot<String>
+// const labelSlot  = newSlot(Symbol('label'))(newLiteral("number of sheep"));
+
+// const combineFn = newLiteral(label => numberOfSheep => `${label}: ${numberOfSheep}`)
+
+// // Slot<String>
+// const labelAndValueSlotA = overwrite(labelSlot)(
+//   transform(read(numberOfSheepSlot))(
+//     transform(read(labelSlot))(combineFn)));
+
+// const labelAndValueSlotB = overwrite(labelSlot)(
+//   transform(read(alternativeNumberOfSheepSlot))(
+//     transform(read(labelSlot))(combineFn)));
+      
+// console.log(
+//   add(add(emptySet(compareSlots(strCompare)))(labelAndValueSlotA))(labelAndValueSlotB)
+// );
+
+// merge()(labelSlot)(labelAndValueSlot)
+
+
+console.log("#############")
+console.log("## RB Tree ##")
+console.log("#############")
+
+// just a small experiment
+console.log(new RBTreeWrapper(createRBTree().insert(1).insert(1).insert(2)));

scripts/versioning2.js

@@ -1,130 +0,0 @@
-import { pretty } from "../util/pretty.js";
-import { deepEqual } from "../util/util.js";
-
-// UUID -> Computation<a> -> Slot<a>
-const newSlot = uuid => computation => ({
-  overwrites: uuid,
-  computation,
-  // depth: 1,
-});
-
-// a -> Computation<a>
-const newValue = val => ({
-  kind: "value",
-  out: val,
-});
-
-// Slot<a> -> Computation<a>
-const read = slot => ({
-  kind: "read",
-  slot,
-  out: slot.computation.out,
-});
-
-// Computation<a> -> Computation<a -> b> -> Computation<b>
-const transform = input => fn => {
-  const output = fn.out(input.out);
-  if (input.kind === "value") {
-    // optimization: sandwich everything together
-    return {
-      kind: "value",
-      out: output,
-    };
-  }
-  else {
-    return {
-      kind: "transformation",
-      in: input,
-      fn,
-      out: output,
-    };
-  }
-};
-
-const verifyComputation = (computation, indent=0) => {
-  const printIndent = (...args) => {
-    console.log(" ".repeat(indent*2), ...args);
-  }
-  const compare = (a,b, kind) => {
-    if (typeof a === 'function' && typeof b === 'function') {
-      printIndent("cannot compare functions", `(${kind})`);
-    }
-    else if (deepEqual(a, b)) {
-      printIndent(`ok (${kind})`);
-    }
-    else {
-      printIndent(`bad (${kind})`);
-    }
-  }
-  if (computation.kind === "value") {
-    compare(1, 1, "value");
-  }
-  else if (computation.kind === "read") {
-    compare(computation.out, computation.slot.computation.out, "read");
-  }
-  else if (computation.kind === "transformation") {
-    compare(computation.fn.out(computation.in.out),
-      computation.out, "transformation");
-    
-    verifyComputation(computation.in, indent+1);
-    verifyComputation(computation.fn, indent+1);
-  }
-}
-
-const getReadDependencies = computation => {
-  if (computation.kind === "value") {
-    return new Set();
-  }
-  else if (computation.kind === "read") {
-    return new Set([computation.slot]);
-  }
-  else if (computation.kind === "transformation") {
-    return new Set([
-      ...getReadDependencies(computation.in),
-      ...getReadDependencies(computation.fn),
-    ]);
-  }
-}
-
-
-const inc = x => x + 1;
-
-// const counterOne = newSlot(Symbol('counter'))(newValue(1));
-// const valueOne = read(counterOne);
-// console.log(pretty({valueOne}));
-// const onePlusOne = transform(valueOne)(newValue(inc));
-// console.log(pretty({onePlusOne}));
-// const onePlusOnePlusOne = transform(onePlusOne)(newValue(inc));
-// console.log(pretty({onePlusOnePlusOne}));
-
-// verifyComputation(valueOne);
-// verifyComputation(onePlusOne);
-// verifyComputation(onePlusOnePlusOne);
-
-
-const priceSlot = newSlot(Symbol('price'))(newValue(20.66));
-const taxSlot   = newSlot(Symbol('tax'))(newValue(4.34));
-
-console.log(pretty({price: priceSlot}));
-
-const computeTotal = tax => {
-  const addTax = price => price + tax;
-  return addTax;
-};
-
-const total =
-  transform(read(priceSlot))(
-    transform(read(taxSlot))(
-      newValue(computeTotal)));
-
-console.log(pretty({total}))
-
-const totalPlusOne = transform(total)(newValue(inc));
-
-console.log(pretty({totalPlusOne}));
-
-verifyComputation(totalPlusOne);
-
-
-
-console.log("getReadDependencies(totalPlusOne):", getReadDependencies(totalPlusOne));

structures/list.js

@@ -1,4 +1,4 @@
-import { typedFnType } from "./types.js";
+import { fnType, typedFnType } from "./types.js";
 import { Char, GenericType, Type } from "../primitives/types.js";
 import { Int } from "../primitives/types.js";
 import { makeGeneric } from "../generics/generics.js";
@@ -11,6 +11,7 @@ const emptyListType = makeGeneric(a => lsType(a));
 const get = ls => i => ls.l[i];
 const put = ls => i => elem => ({l: ls.l.with(Number(i), elem)});
 const push = ls => elem => ({l:ls.l.concat([elem])});
+const map = ls => fn => ({ l: ls.l.map(elem => fn(elem)) });
 
 export const String = lsType(Char); // alias
 export const Module = lsType(Typed);
@@ -60,4 +61,14 @@ export const ModuleList = {l:[
           (lsType(a))
         )
     ), GenericType),
+
+  // [a] -> (a -> b) -> [b]
+  ...typedFnType(map, fnType =>
+    makeGeneric((a, b) =>
+      fnType
+        (lsType(a))
+        (fnType
+          (fnType(a)(b))
+          (lsType(b))
+        )), GenericType),
 ]};

structures/nominal.js

@@ -1,76 +0,0 @@
-import { SymbolT, Type } from "../primitives/types.js";
-import { makeTypeConstructor } from "../type_constructor.js";
-import { Module, String } from "./list.js";
-import { prodType, fnType, lsType } from "./types.js";
-
-function capitalizeFirstLetter(val) {
-  return String(val).charAt(0).toUpperCase() + String(val).slice(1);
-}
-
-export const createStruct = (typeVars, symbol, fields) => {
-  const makeConstructor = (remainingFields, obj={}) => {
-    if (remainingFields.length===0) {
-      return obj;
-    }
-    const {left: fieldName} = remainingFields[remainingFields.length-1];
-    return v => makeConstructor(
-        remainingFields.slice(0,-1),
-        Object.assign({[fieldName]: v}, obj));
-  };
-  const constructor = makeConstructor(fields);
-
-  const type = makeTypeConstructor(symbol)(typeVars.size);
-  const types = [ type ];
-  const recordFnType = inType => outType => {
-    const fnT = fnType(inType)(outType);
-    types.push(fnT);
-    return fnT;
-  }
-
-  const makeConstructorType = (remainingFields, type) => {
-    if (remainingFields.length===0) {
-      return type;
-    }
-    const {right: fieldType} = remainingFields[remainingFields.length-1];
-    return recordFnType(makeConstructorType(remainingFields.slice(0,-1)))(fieldType);
-  };
-  const constructorType = makeConstructorType(fields);
-
-  const functions = [
-    ["constructor", constructor, constructorType],
-    ...fields.map(({left: fieldName, right: fieldType}) => {
-      const getterName = 'get'+capitalizeFirstLetter(fieldName);
-      const getter = {
-        // stupid trick to give the JS-function a computed name.
-        // only important for debugging, so it says [Function: getAge] instead of [Function (anonymous)]:
-        [getterName]: obj => obj[fieldName],
-      }[getterName];
-      if (typeVars.has(fieldType)) {
-        // getterFnType = recordFnType(type)(fieldType)
-      }
-      const getterFnType = recordFnType(type)(fieldType);
-      return [fieldName, getter, getterFnType];
-    }),
-  ];
-
-  const module = {l:[
-    {i: type, t: Type},
-
-    ...functions.flatMap(([_, getter, getterFnType]) => [
-      {i: getter      , t: getterFnType},
-    ]),
-
-    ...types.map(type => ({i: type, t: Type})),
-  ]};
-
-  return {
-    module,
-    constructor,
-    functions: Object.fromEntries(functions),
-  };
-};
-
-export const createNominalADTModuleFnType =
-  fnType(SymbolT)
-        (fnType(lsType(prodType(String)(Type)))
-               (Module));

structures/product.js

@@ -4,9 +4,9 @@ import { typedFnType } from "./types.js";
 import { prodType } from "./types.js";
 
 // In JS, all products are encoded in the same way:
-const constructor = left => right => ({left, right});
+export const constructorProduct = l => r => ({l, r});
-const getLeft     = product => product.left;
+export const getLeft     = product => product.l;
-const getRight    = product => product.right;
+export const getRight    = product => product.r;
 
 export const ModuleProduct = {l: [
   // binary type constructor
@@ -21,7 +21,7 @@ export const ModuleProduct = {l: [
   ),
 
   // a -> b -> (a, b)
-  ...typedFnType(constructor, fnType =>
+  ...typedFnType(constructorProduct, fnType =>
     makeGeneric((a, b) =>
       fnType
         (a)

structures/set.js

@@ -1,39 +1,60 @@
-import { setType, typedFnType } from "./types.js";
+import { fnType, setType } from "./types.js";
-import { Bool, GenericType, Type } from "../primitives/types.js";
+import { Int } from "../primitives/types.js";
 import { makeGeneric } from "../generics/generics.js";
 
-// 'normal' implementation
+import createRBTree from "functional-red-black-tree";
-const emptySet = new Set();
+import { inspect } from "node:util";
-const emptySetType = makeGeneric(a => setType(a));
+
-const has = set => elem => set.has(elem);
+export class RBTreeWrapper {
-const add = set => elem => new Set([...set, elem]);
+  constructor(tree) {
+    this.tree = tree;
+  }
+  [inspect.custom](depth, options, inspect) {
+    const entries = [];
+    this.tree.forEach((key,val) => {entries.push(`${inspect(key)} => ${inspect(val)}`);});
+    return `RBTree(${this.tree.length}) {${entries.join(', ')}}`;
+  }
+}
+
+// (a -> a -> Int) -> Set(a)
+export const emptySet = compareFn => new RBTreeWrapper(createRBTree((x, y) => compareFn(x)(y)));
+
+// const emptySetType = makeGeneric(a => fnType(fnType(a)(fnType(a)(Int)))(setType(a)));
+
+export const has = set => key => set.tree.get(key) === true;
+export const add = set => key => set.tree.get(key) === true ? set : new RBTreeWrapper(set.tree.insert(key, true));
+export const remove = set => key => new RBTreeWrapper(set.tree.remove(key));
+
+export const forEach = set => fn => {
+  set.tree.forEach(key => { fn(key); });
+};
 
 export const ModuleSet = {l:[
-  // Type -> Type
+  // // Type -> Type
-  ...typedFnType(setType, fnType =>
+  // ...typedFnType(setType, fnType =>
-    fnType
+  //   fnType
-      /* in  */ (Type)
+  //     /* in  */ (Type)
-      /* out */ (Type)
+  //     /* out */ (Type)
-  ),
+  // ),
 
-  {i: emptySet    , t: emptySetType},
+  // {i: emptySet    , t: emptySetType},
-  {i: emptySetType, t: GenericType },
+  // {i: emptySetType, t: GenericType },
 
-  ...typedFnType(has, fnType =>
+  // ...typedFnType(has, fnType =>
-    makeGeneric(a =>
+  //   makeGeneric(a =>
-      fnType
+  //     fnType
-        /* in  */ (setType(a))
+  //       /* in  */ (setType(a))
-        /* out */ (fnType
+  //       /* out */ (fnType
-          /* in  */ (a)
+  //         /* in  */ (a)
-          /* out */ (Bool)
+  //         /* out */ (Bool)
-        )), GenericType),
+  //       )), GenericType),
 
-  ...typedFnType(add, fnType =>
+  // ...typedFnType(add, fnType =>
-    makeGeneric(a =>
+  //   makeGeneric(a =>
-      fnType
+  //     fnType
-        /* in  */ (setType(a))
+  //       /* in  */ (setType(a))
-        /* out */ (fnType
+  //       /* out */ (fnType
-          /* in  */ (a)
+  //         /* in  */ (a)
-          /* out */ (setType(a))
+  //         /* out */ (setType(a))
-        )), GenericType),
+  //       )), GenericType),
 ]};

structures/struct.js

@@ -0,0 +1,65 @@
+import { Unit } from "../primitives/types.js";
+import { unit } from "../primitives/unit.js";
+import { constructorProduct, getLeft, getRight } from "./product.js";
+import { fnType, prodType } from "./types.js";
+
+function capitalizeFirstLetter(val) {
+  return String(val).charAt(0).toUpperCase() + String(val).slice(1);
+}
+
+// [{l: "x", r: Double}, {l: "y", r: Double}] => (Double × (Double × Unit))
+export const structType = fields => {
+  if (fields.length === 0) {
+    return Unit;
+  }
+  const [field, ...rest] = fields;
+  const fieldType = getRight(field);
+  return prodType(fieldType)(structType(rest));
+};
+
+export const makeConstructor = fields => {
+  const internal = (nParams, ret) => {
+    if (nParams === 0) {
+      const result = ret(unit);
+      return result;
+    }
+    return nextParam => {
+      const wrappedName = 'wrapped_' + ret.name;
+      const newRet = {
+        [wrappedName]: inner => constructorProduct(nextParam)(ret(inner)),
+      }[wrappedName];
+      return internal(nParams-1, newRet);
+    }
+  };
+  const id = x => x;
+  return internal(fields.length, id);
+};
+
+export const makeConstructorType = type => fields => {
+  if (fields.length === 0) {
+    return type;
+  }
+  const [field, ...rest] = fields;
+  const fieldType = getRight(field);
+  return fnType(fieldType)(makeConstructorType(rest));
+};
+
+export const makeGetters = fields => {
+  if (fields.length === 0) {
+    return [];
+  }
+  const [field, ...rest] = fields;
+  const fieldName = getLeft(field);
+  const getterName = `get${capitalizeFirstLetter(fieldName)}`;
+  return [
+    { [getterName]: obj => getLeft(obj) }[getterName],
+    ...makeGetters(rest).map(getter => ({[getter.name]: obj => getter(getRight(obj))}[getter.name])),
+  ];
+};
+
+export const makeGettersTypes = type => fields => {
+  return fields.map(field => {
+    const fieldType = getRight(field);
+    return fnType(type)(fieldType);
+  });
+};

structures/types.js

@@ -69,13 +69,13 @@ export function prettyT(type) {
     }
   }
   if (type.symbol === symbolFunction) {
-    return `${prettyT(type.params[0])} -> ${prettyT(type.params[1])}`;
+    return `(${prettyT(type.params[0])} -> ${prettyT(type.params[1])})`;
   }
   if (type.symbol === symbolList) {
     return `[${prettyT(type.params[0])}]`;
   }
   if (type.symbol === symbolProduct) {
-    return `(${prettyT(type.params[0])}, ${prettyT(type.params[1])})`;
+    return `(${prettyT(type.params[0])} × ${prettyT(type.params[1])})`;
   }
   if (type.symbol === symbolSum) {
     return `(${prettyT(type.params[0])} | ${prettyT(type.params[1])})`;

structures/versioned.js

@@ -1,68 +0,0 @@
-import { makeGeneric } from "../generics/generics.js";
-import { Bool } from "../primitives/types.js";
-import { makeTypeConstructor } from "../type_constructor.js";
-import { getEq } from "../typeclasses/eq.js";
-import { eqDictType } from "../typeclasses/eq_type.js";
-import { fnType, setType } from "./types.js";
-
-const symbolVersioned = Symbol("Versioned");
-export const versionedType = makeTypeConstructor(symbolVersioned)(1);
-
-
-export const constructor = parents => alternatives  => {
-  return { parents, alternatives };
-}
-
-const constructorType = makeGeneric(a =>
-  fnType
-    (setType(versionedType(a)))
-    (fnType
-      (setType(a))
-      (versionedType(a))
-    )
-);
-
-const initial = x => ({ parents: new Set(), alternatives: new Set(x) });
-
-const initialFnType = makeGeneric(a => fnType(a)(versionedType(a)));
-
-const eq = eqDict => vA => vB => {
-  return getEq(eqDict)(vA.value,vB.value) // compare values
-      && (vA.parents.symmetricDifference(vB.parents).size === 0); // compare parents
-}
-
-// EqDict a -> Versioned a -> Versioned a -> Bool
-const eqVersioned = makeGeneric(a =>
-  fnType
-    (eqDictType(a))
-    (fnType
-      (versionedType(a))
-      (fnType
-        (versionedType(a))
-        (Bool)
-      )
-    )
-);
-
-// EqDict a -> Versioned a -> Versioned a -> Versioned a -> Versioned a
-export const mergeThreeWay = eqDict => vLCA => vA => vB => {
-  if (eq(eqDict)(vLCA)(vA)) {
-    return vB; // vB successor of vA
-  }
-  if (eq(eqDict)(vLCA)(vB)) {
-    return vA; // vA successor of vB
-  }
-  return mergeConcurrent(vLCA)(vA)(vB);
-};
-
-export const mergePrimitives = vA => vB => vA.union(vB);
-
-// Versioned a -> Versioned a -> Versioned a
-export const mergePrimitivesType = makeGeneric(a => 
-  fnType
-    (versionedType(a))
-    (fnType
-      (versionedType(a))
-      (versionedType(a))
-    )
-);

type_constructor.js

@@ -24,7 +24,10 @@ const makeTypeConstructorInternal = (symbol, n_ary, params = []) => {
   }
   else {
     const m = new DefaultMap(typeParam => makeTypeConstructorInternal(symbol, n_ary - 1, params.concat([typeParam])));
-    return typeParam => m.getdefault(typeParam, true);
+    const fnName = 'make'+symbol.description+'Type';
+    return {
+      [fnName]: typeParam => m.getdefault(typeParam, true),
+    }[fnName];
   }
 };
 

typeclasses/eq.js

@@ -3,7 +3,7 @@ import { GenericType, SymbolT, Type, Unit } from "../primitives/types";
 import { typedFnType } from "../structures/types";
 import { Bool, Byte, Char, Double, Int } from "../primitives/types";
 import { deepEqual } from "../util/util";
-import { eqDictType } from "./eq_type";
+import { eqDictType } from "./eq_dict";
 
 export const getEq = numDict => numDict.eq;
 

typeclasses/eq_dict.js

@@ -0,0 +1,4 @@
+import { makeTypeConstructor } from "../type_constructor.js";
+
+const eqDictSymbol = Symbol('EqDict');
+export const eqDictType = makeTypeConstructor(eqDictSymbol)(1);

typeclasses/eq_type.js

@@ -1,8 +0,0 @@
-import { DefaultMap } from "../util/defaultmap.js";
-
-const eqDictSymbol = Symbol('EqDict');
-const eqDictTypeRegistry = new DefaultMap(a => ({
-  symbol: eqDictSymbol,
-  params: [a],
-}));
-export const eqDictType = a => eqDictTypeRegistry.getdefault(a, true);

typeclasses/num_dict.js

@@ -0,0 +1,4 @@
+import { makeTypeConstructor } from "../type_constructor.js";
+
+const numDictSymbol = Symbol("NumDict");
+export const numDictType = makeTypeConstructor(numDictSymbol)(1);

typeclasses/num_type.js

@@ -1,8 +0,0 @@
-import { DefaultMap } from "../util/defaultmap.js";
-
-const numDictSymbol = Symbol("NumDict");
-const numDictTypeRegistry = new DefaultMap(a => ({
-  symbol: numDictSymbol,
-  params: [a],
-}));
-export const numDictType = a => numDictTypeRegistry.getdefault(a, true);

typeclasses/show.js

@@ -0,0 +1,9 @@
+import { cart2Str, NPoint2DCartesian, NPoint2DPolar, polar2Str } from "../lib/point.js";
+import { Type } from "../primitives/types.js";
+import { prettyT } from "../structures/types.js";
+
+export const ShowInstances = new Map([
+  [Type             , {show: prettyT}],
+  [NPoint2DCartesian, {show: cart2Str}],
+  [NPoint2DPolar    , {show: polar2Str}],
+]);

typeclasses/show_dict.js

@@ -0,0 +1,5 @@
+import { makeTypeConstructor } from "../type_constructor.js";
+
+const showDictSymbol = Symbol('ShowDict');
+export const showDictType = makeTypeConstructor(showDictSymbol)(1);
+

typed.js

@@ -1,11 +1,7 @@
 import { typedFnType } from "./structures/types.js";
-import { Type } from "./primitives/types.js";
+import { Any, Type } from "./primitives/types.js";
 import { makeTypeConstructor } from "./type_constructor.js";
 
-// Everything is (implicitly) typed by the Any type.
-const symbolAny = Symbol('Any');
-export const Any = makeTypeConstructor(symbolAny)(0);
-
 // A type-link, connecting a value to its Type.
 const symbolTyped = Symbol('Typed');
 export const Typed = makeTypeConstructor(symbolTyped)(0);

util/pretty.js

@@ -1,6 +1,5 @@
 import { inspect } from 'node:util';
 
-
 export function pretty(obj) {
-  return inspect(obj, { colors: true, depth: null });
+  return inspect(obj, { colors: true, depth: null, breakLength: 120 });
 }

util/util.js

@@ -12,6 +12,20 @@ export function deepEqual(a, b) {
     }
     return true;
   }
+  if (a instanceof Set) {
+    if (!(b instanceof Set)) {
+      return false;
+    }
+    if (a.size !== b.size) {
+      return false;
+    }
+    for (const entry of a) {
+      if (!b.has(entry)) {
+        return false;
+      }
+    }
+    return true;
+  }
   const keysA = Object.keys(a);
   const keysB = Object.keys(b);
   if (keysA.length !== keysB.length) return false;

versioning/slot.js

@@ -0,0 +1,96 @@
+import { add, emptySet, forEach } from "../structures/set.js";
+import { deepEqual } from "../util/util.js";
+import {inspect} from "node:util";
+
+// UUID -> Value<a> -> Slot<a>
+export const newSlot = uuid => value => ({
+  overwrites: uuid,
+  value,
+  depth: 1,
+  [inspect.custom]: (depth, options, inspect) => `newSlot(${inspect(uuid)}, ${inspect(value)})`,
+});
+
+export const compareSlots = compareElems => slotA => slotB => {
+  if (slotA.depth < slotB.depth) {
+    return -1;
+  }
+  if (slotB.depth < slotA.depth) {
+    return 1;
+  }
+  return compareValues(compareElems)(slotA.value)(slotB.value);
+};
+
+export const compareValues = compareElems => valA => valB => {
+  if (valA.kind < valB.kind) {
+    return -1;
+  }
+  if (valB.kind < valA.kind) {
+    return 1;
+  }
+  if (valA.kind === "literal") {
+    return compareElems(valA.out)(valB.out);
+  }
+  if (valA.kind === "read") {
+    return compareSlots(compareElems)(valA.slot)(valB.slot);
+  }
+  if (valA.kind === "transformation") {
+    const cmpIn = compareValues(compareElems)(valA.in)(valB.in);
+    if (cmpIn !== 0) {
+      return cmpIn;
+    }
+    return compareValues(compareElems)(valA.fn)(valB.fn);
+  }
+};
+
+
+// Slot<a> -> Value<a> -> Slot<a>
+export const overwrite = slot => value => ({
+  overwrites: slot,
+  value,
+  depth: slot.depth + 1,
+  // [inspect.custom]: (depth, options, inspect) => `overwrite(${inspect(slot)}, ${inspect(value)})`,
+});
+
+const findLCA = slotA => slotB => {
+  if (deepEqual(slotA, slotB)) {
+    return slotA;
+  }
+  if (slotA.depth > slotB.depth) {
+    return findLCA(slotA.overwrites)(slotB)
+  }
+  else {
+    return findLCA(slotB.overwrites)(slotA)
+  }
+};
+
+// Slot<a> -> Slot<a> -> MergeResult<a>
+export const merge = compareElems => slotA => slotB => {
+  const lca = findLCA(slotA)(slotB);
+  if (lca === undefined) {
+    throw new Error("Could not find LCA");
+  }
+  if (deepEqual(lca, slotA)) {
+    return add(emptySet(compareSlots(compareElems)))(slotB);
+    // return new Set([slotB]); // B is successor of A -> fast-forward
+  }
+  if (deepEqual(lca, slotB)) {
+    return add(emptySet(compareSlots(compareElems)))(slotA);
+    // return new Set([slotA]); // A is successor of B -> fast-forward
+  }
+  return add(add(emptySet(compareSlots(compareElems)))(slotA))(slotB);
+  // return new Set([slotA, slotB]);
+};
+
+// MergeResult<a> -> MergeResult<a> -> MergeResult<a>
+export const merge2 = compareElems => mA => mB => {
+  let result = emptySet(compareSlots(compareElems));
+  forEach(mA)(slotOfA => {
+    forEach(mB)(slotOfB => {
+      const merged = merge(compareElems)(slotOfA)(slotOfB);
+      forEach(merged)(merged => {
+        result = add(result)(merged);
+      });
+    });
+  });
+  return result;
+};

versioning/value.js

@@ -0,0 +1,95 @@
+import { deepEqual } from "../util/util.js";
+import {inspect} from "node:util";
+
+// A Value is either:
+//   - a literal, without any dependencies.
+//   - read from a slot. the Value then has a read-dependency on that slot.
+//   - a transformation of another Value, by a function. the function is also a Value.
+
+// a -> Value<a>
+export const newLiteral = val => ({
+  kind: "literal",
+  out: val,
+  [inspect.custom]: (depth, options, inspect) => `newLiteral(${inspect(val)})`,
+});
+
+// Slot<a> -> Value<a>
+export const read = slot => ({
+  kind: "read",
+  slot,
+  out: slot.value.out,
+  [inspect.custom]: (depth, options, inspect) => `read(${inspect(slot)})`,
+});
+
+// Value<a> -> Value<a -> b> -> Value<b>
+export const transform = input => fn => {
+  const output = fn.out(input.out);
+  const _inspect = (depth, options, inspect) => `transform(${inspect(input)}, ${inspect(fn)})`;
+  if (input.kind === "literal") {
+    // optimization: sandwich everything together
+    return {
+      kind: "literal",
+      out: output,
+      // [inspect.custom]: _inspect,
+    };
+  }
+  else {
+    return {
+      kind: "transformation",
+      in: input,
+      fn,
+      out: output,
+      // [inspect.custom]: _inspect,
+    };
+  }
+};
+
+// Value<a> -> Set<Slot<Any>>
+export const getReadDependencies = value => {
+  if (value.kind === "literal") {
+    return new Set();
+  }
+  else if (value.kind === "read") {
+    return new Set([value.slot]);
+  }
+  else if (value.kind === "transformation") {
+    return new Set([
+      ...getReadDependencies(value.in),
+      ...getReadDependencies(value.fn),
+    ]);
+  }
+};
+
+// for debugging
+export const verifyValue = (value, indent = 0) => {
+  let success = true;
+  const printIndent = (...args) => {
+    console.log(" ".repeat(indent * 2), ...args);
+  };
+  const compare = (a, b, kind) => {
+    if (typeof a === 'function' && typeof b === 'function') {
+      printIndent("note: cannot compare functions", `(${kind})`);
+    }
+    else if (deepEqual(a, b)) {
+      printIndent(`ok (${kind})`);
+    }
+    else {
+      printIndent(`bad (${kind})`);
+      success = false;
+    }
+  };
+  if (value.kind === "literal") {
+    compare(1, 1, "literal");
+  }
+  else if (value.kind === "read") {
+    compare(value.out, value.slot.value.out, "read");
+  }
+  else if (value.kind === "transformation") {
+    compare(value.fn.out(value.in.out),
+      value.out, "transformation");
+
+    success &= verifyValue(value.in, indent + 1);
+    success &= verifyValue(value.fn, indent + 1);
+  }
+  return success;
+};