Refactor towards a working QuickJS version (117473e)

Refactor towards a working QuickJS version

dkl9 commited on 2023-196 12:46:40
Showing 10 changed files, with 242 additions and 41 deletions.

Code is now organised in files in a module-ish format, reducing
circular and unclear dependencies. You can run `qjs qjs_rtensor.js`
to get RTensor in the terminal. Things are probably still very buggy.

maths_ast.js 63cf85b..546999d
maths_parser.js 6fb6274..5a05dad
qjs_rtensor.js 0000000..2cae77d
rtensor_common.js 0000000..85b43ea
rtensor_lib.js c24f1dc..39db4ea
types/basic.js 38454e2..3b40ccc
types/bigint.js ecf1943..a85b80d
types/complex.js 4a75ca0..103e49d
types/mathsfunc.js 1d08660..6795914
types/real.js a7cb942..89cf26b

maths_ast.js

View file @ 117473e

@@ -1,16 +1,27 @@
 "use strict";
 
+import {fts, OPS} from "./rtensor_common.js";
+import {} from "./types/bigint.js";
+import {Complex} from "./types/complex.js";
+import {MathsFunc} from "./types/mathsfunc.js";
+import {} from "./types/real.js";
+
 const isArray = x => (typeof x == "object" && x.constructor == Array);
 const NUMERIC_TYPES = {
     integer: BigInt,
     complex: Complex,
     real: Number,
 };
-const nti = (new URLSearchParams(window.location.search)).get("nt") || "a";
-const NumericType = NUMERIC_TYPES[nti] || Number;
+let nti;
+try {
+    nti = (new URLSearchParams(window.location.search)).get("nt") || "a";
+} catch (_e) {
+    nti = scriptArgs[1] || "a";
+}
+export const NumericType = NUMERIC_TYPES[nti] || Number;
 
 // a: tensor, b: tensor, o: binary function of numbers
-function vecOp(a, b, o) {
+export function vecOp(a, b, o) {
     const tra = tensorRank(a);
     const trb = tensorRank(b);
     if (tra == trb && tra >= 1 && a.length == b.length) {
@@ -25,7 +36,7 @@ function vecOp(a, b, o) {
 }
 
 // true iff any elements of v is null or NaN
-function anyNaN(v) {
+export function anyNaN(v) {
     return v.map ?
         v.map(x => anyNaN(x)).reduce((a, b) => (a || b), false) :
         (v == null || (typeof v == "number" && isNaN(v)) || (v.invalid && v.invalid()));
@@ -38,7 +49,7 @@ function tensorRank(t) {
 }
 
 // node in an abstract syntax tree, as produced by NewParser
-class AST {
+export class AST {
     constructor(ts, l, m, r, len) {
         switch (ts) {
             // identifier: l == Token (tt == 1), m, r == undefined

maths_parser.js

View file @ 117473e

@@ -1,6 +1,9 @@
 "use strict";
 // maths parser, by dkl9, 2021-05 to 2021-07, used as part of rtensor
 
+import {OPS} from "./rtensor_common.js";
+import {AST} from "./maths_ast.js";
+
 // whitespace characters
 const WSPACE = [" ", "\t", "\n"];
 // characters for starting identifiers
@@ -21,13 +24,6 @@ const LCHAR = [];
 for (let c = 0; c <= 9; c++) {
     LCHAR.push(String.fromCodePoint(c + 48));
 }
-// operator text
-const OPS = [
-    "+",  "-",  "*",  "/",
-    "^",  "\\", "==", "-/",
-    ",",  "<",  "=>", "=",
-    "..",
-];
 // precedence of binary operators (greater == lower)
 const PREC = [
     4,  4,  3,  3,
@@ -79,7 +75,7 @@ const normIntLit = s => (s.replace(/^0+/, "") || "0");
 // 8 (right square bracket)
 // value depends on tt: 1 => ident text, 2 => int value, 3 => operator id
 // 4, 5, 6, 7, 8 => undefined
-class Token {
+export class Token {
     constructor(tt, text) {
         this.tt = tt;
         switch (this.tt) {
@@ -111,7 +107,7 @@ class Token {
 }
 
 // source text surrounded by an interface to provide tokens from it on demand
-class TokenStream {
+export class TokenStream {
     constructor(source) {
         this.toks = [];
         this.tind = -1;
@@ -226,7 +222,7 @@ class TokenStream {
 // each function parses a particular structure,
 // returning an AST (with .len, measured in tokens) if successful
 // or null if failed
-class NewParser {
+export class NewParser {
     // statement -> expr[9]
     static statement(stream) {
         let tc = 0;

qjs_rtensor.js

View file @ 117473e

...	...	@@ -0,0 +1,158 @@
	1	+import {fts} from "./rtensor_common.js";
	2	+import {AST} from "./maths_ast.js";
	3	+import {TokenStream, NewParser} from "./maths_parser.js";
	4	+import {BUILTIN_FUNCS} from "./rtensor_lib.js";
	5	+import * as std from "std";
	6	+import * as os from "os";
	7	+
	8	+const calcVars = Object.fromEntries(Object.entries(BUILTIN_FUNCS));
	9	+calcVars["_"] = [];
	10	+const pastInps = [];
	11	+var histPos = 0;
	12	+
	13	+function evalInp(inpText) {
	14	+ let disp;
	15	+ let perr = false;
	16	+ const st = inpText.split(";");
	17	+ for (let i = 0; i < st.length; i++) {
	18	+ const wt = st[i];
	19	+ const lexer = new TokenStream(wt);
	20	+ const ast = NewParser.statement(lexer);
	21	+ if (ast === null) {
	22	+ disp = "syntax error";
	23	+ break;
	24	+ } else {
	25	+ perr = perr \|\| (lexer.tind != lexer.toks.length - 1);
	26	+ try {
	27	+ const res = ast.evaluate(calcVars, false);
	28	+ if (res != null) { calcVars["_"] = res; }
	29	+ const svn = "_ans_" + pastInps.length.toString();
	30	+ calcVars[svn] = res;
	31	+ disp = (res == null) ? "evaluation error" : (svn + " = " + fts(res));
	32	+ } catch (err) {
	33	+ disp = err;
	34	+ }
	35	+ }
	36	+ }
	37	+ return disp + (perr ? "\npossible syntax error" : "");
	38	+}
	39	+
	40	+function getEscSeq(fhs) {
	41	+ let r = "";
	42	+ while (/[A-H]$/.exec(r) == null) {
	43	+ r += String.fromCharCode(fhs.getByte());
	44	+ }
	45	+ return r;
	46	+}
	47	+
	48	+// returns Array [newt, newwi]
	49	+function histFetch(oldt) {
	50	+ const t = pastInps[histPos] \|\| oldt;
	51	+ const wi = t.length;
	52	+ std.out.puts("\r\x1b[" + PRLEN + "C\x1b[K" + t +
	53	+ "\r\x1b[" + (wi + PRLEN) + "C");
	54	+ return [t, wi];
	55	+}
	56	+
	57	+function wf(t) {
	58	+ std.out.puts(t);
	59	+ std.out.flush();
	60	+}
	61	+
	62	+if (os.isatty(std.in)) {
	63	+ os.ttySetRaw(std.in);
	64	+}
	65	+
	66	+const PROMPT = "> ";
	67	+const PRLEN = PROMPT.length;
	68	+
	69	+let t;
	70	+while (true) {
	71	+ if (os.isatty(std.in)) {
	72	+ wf(PROMPT);
	73	+ t = "";
	74	+ let wi = 0;
	75	+ let nmi = true;
	76	+ while (nmi) {
	77	+ const nc = std.in.getByte();
	78	+ switch (nc) {
	79	+ // ^D
	80	+ case 4:
	81	+ t = "quit";
	82	+ nmi = false;
	83	+ break;
	84	+ // escape
	85	+ case 27:
	86	+ const es = getEscSeq(std.in);
	87	+ // up arrow
	88	+ if (es == "[A") {
	89	+ histPos--;
	90	+ const ra = histFetch(t);
	91	+ t = ra[0]; wi = ra[1];
	92	+ wf("\r\x1b[" + PRLEN + "C" + t);
	93	+ // down arrow
	94	+ } else if (es == "[B") {
	95	+ histPos++;
	96	+ const ra = histFetch(t);
	97	+ t = ra[0]; wi = ra[1];
	98	+ // right arrow
	99	+ } else if (es == "[C") {
	100	+ wi = (wi == t.length) ? wi : (wi + 1);
	101	+ wf("\x1b[C");
	102	+ // left arrow
	103	+ } else if (es == "[D") {
	104	+ wi = (wi == 0) ? wi : (wi - 1);
	105	+ wf("\x1b[D");
	106	+ // ctrl-right arrow
	107	+ } else if (es == "[1;5C") {
	108	+ //
	109	+ // ctrl-left arrow
	110	+ } else if (es == "[1;5D") {
	111	+ //
	112	+ // home
	113	+ } else if (es == "[H") {
	114	+ wi = 0;
	115	+ wf("\r\x1b[" + PRLEN + "C");
	116	+ // end
	117	+ } else if (es == "[F") {
	118	+ wi = t.length;
	119	+ wf("\r\x1b[" + (wi + PRLEN) + "C");
	120	+ }
	121	+ break;
	122	+ // backspace
	123	+ case 8:
	124	+ case 127:
	125	+ if (wi > 0) {
	126	+ wi--;
	127	+ t = t.slice(0, wi) + t.slice(wi + 1);
	128	+ wf("\x1b[D\x1b[K" +
	129	+ (t.slice(wi) ? (t.slice(wi) + "\x1b[" + t.slice(wi).length + "D") : ""));
	130	+ } else {
	131	+ wf("\x07");
	132	+ }
	133	+ break;
	134	+ // newline
	135	+ case 13:
	136	+ nmi = false;
	137	+ wf("\n");
	138	+ break;
	139	+ // printable?
	140	+ default:
	141	+ wf(String.fromCharCode(nc));
	142	+ t = t.slice(0, wi) + String.fromCharCode(nc) + t.slice(wi);
	143	+ wi++;
	144	+ }
	145	+ }
	146	+ } else {
	147	+ t = std.in.getline();
	148	+ }
	149	+ pastInps.push(t);
	150	+ histPos = pastInps.length;
	151	+ if (t == "quit" \|\| t == null) {
	152	+ break;
	153	+ }
	154	+ if (t == "") {
	155	+ continue;
	156	+ }
	157	+ console.log(evalInp(t));
	158	+}

rtensor_common.js

View file @ 117473e

...	...	@@ -0,0 +1,29 @@
	1	+"use strict";
	2	+
	3	+// operator text
	4	+export const OPS = [
	5	+ "+", "-", "*", "/",
	6	+ "^", "\\", "==", "-/",
	7	+ ",", "<", "=>", "=",
	8	+ "..",
	9	+];
	10	+
	11	+// stringify a vecalc value for presentation
	12	+export function fts(v) {
	13	+ if (v == null) {
	14	+ return "nonexistent";
	15	+ } else if (v.constructor === Array) {
	16	+ switch (v.length) {
	17	+ case 0:
	18	+ return "[ ]";
	19	+ default:
	20	+ return "[" + v.map(x => fts(x)).join(", ") + "]";
	21	+ }
	22	+ } else if (v.constructor.name === "MathsFunc" \|\| v.constructor === Function) {
	23	+ return "function";
	24	+ } else if (v.constructor === null) {
	25	+ return "null";
	26	+ } else {
	27	+ return v.toString();
	28	+ }
	29	+}

rtensor_lib.js

View file @ 117473e

@@ -1,6 +1,12 @@
 "use strict";
 
-const IDENT_AST = new AST(1, new Token(1, ""));
+import {fts} from "./rtensor_common.js";
+import {Complex} from "./types/complex.js";
+import {MathsFunc} from "./types/mathsfunc.js";
+import {AST, vecOp, NumericType, anyNaN} from "./maths_ast.js";
+import {Token} from "./maths_parser.js";
+
+export const IDENT_AST = new AST(1, new Token(1, ""));
 
 function elemwiseFunc(f) {
     const ref = (args, de) =>
@@ -11,7 +17,7 @@ function elemwiseFunc(f) {
     return new MathsFunc([[[IDENT_AST], ref]], {});
 }
 
-const BUILTIN_FUNCS = {
+export const BUILTIN_FUNCS = {
     // numeric
     "abs": elemwiseFunc(x => x.mag()),
     "floor": elemwiseFunc(x => x.floor()),
@@ -314,24 +320,4 @@ function dl(v) {
     return null;
 }
 
-window.onerror = (m, s, l, c, e) => dl(`${s}:${l}:${c}: ${m}`);
-
-// stringify a vecalc value for presentation
-function fts(v) {
-    if (v == null) {
-        return "nonexistent";
-    } else if (v.constructor === Array) {
-        switch (v.length) {
-            case 0:
-                return "[ ]";
-            default:
-                return "[" + v.map(x => fts(x)).join(", ") + "]";
-        }
-    } else if (v.constructor === MathsFunc || v.constructor === Function) {
-        return "function";
-    } else if (v.constructor === null) {
-        return "null";
-    } else {
-        return v.toString();
-    }
-}
+try { window.onerror = (m, s, l, c, e) => dl(`${s}:${l}:${c}: ${m}`); } catch (_e) {}

types/basic.js

View file @ 117473e

...	...	@@ -1,6 +1,6 @@
1	1	"use strict";
2	2
3		-class BasicNumber {
	3	+export class BasicNumber {
4	4	constructor() {}
5	5
6	6	sub(z) {
...	...	@@ -36,3 +36,5 @@ class BasicNumber {
36	36
37	37	// because the prototype fields are nonenumerable argh
38	38	BasicNumber.keys = ["sub", "div", "pow", "log", "isNeg", "rangeTo", "dir"];
	39	+
	40	+["zero", "one", "add", "neg", "mul", "recip", "exp", "ln", "sqrt", "sin", "cos", "asin", "acos", "atan", "eq", "lt", "mag", "floor"].forEach(o => BasicNumber.prototype[o] = function() { throw `${o} not defined for current number type`; });

types/bigint.js

View file @ 117473e

@@ -1,5 +1,7 @@
 "use strict";
 
+import {BasicNumber} from "./basic.js";
+
 BasicNumber.keys.forEach(k => (BigInt.prototype[k] = BasicNumber.prototype[k]));
 
 BigInt.ify = function(x) {

types/complex.js

View file @ 117473e

@@ -1,6 +1,8 @@
 "use strict";
 
-class Complex extends BasicNumber {
+import {BasicNumber} from "./basic.js";
+
+export class Complex extends BasicNumber {
     constructor(x, y) {
         super();
         this.re = x;
@@ -89,6 +91,16 @@ class Complex extends BasicNumber {
         return this.re == z.re && this.im == z.im;
     }
 
+    lt(z) {
+        if ((((this.re < z.re) && (this.im <= z.im)) || ((this.re <= z.re) && (this.im < z.im))) && (this.mag() < z.mag())) {
+            return true;
+        } else if ((((this.re > z.re) && (this.im >= z.im)) || ((this.re >= z.re) && (this.im > z.im))) && (this.mag() > z.mag())) {
+            return false;
+        } else {
+            throw `cannot unambiguously compare complex values ${this} and ${z}`;
+        }
+    }
+
     sqrt() {
         return this.pow(new Complex(0.5, 0));
     }

types/mathsfunc.js

View file @ 117473e

@@ -1,5 +1,8 @@
 "use strict";
 
+import {fts} from "../rtensor_common.js";
+import {BasicNumber} from "./basic.js";
+
 // check if vectors (Arrays of numbers) a and b are completely equal
 const vecEq = (a, b) => (a?.eq && b?.eq) ?
     (a.eq(b)) :
@@ -11,7 +14,7 @@ const vecEq = (a, b) => (a?.eq && b?.eq) ?
 // each case is a list of zero or more identifiers or constant values
 // (in the form of ASTs)
 // each expr is an expression (wow); more precisely, a function of the variables
-class MathsFunc extends BasicNumber {
+export class MathsFunc extends BasicNumber {
     // cems is an Array of Array-pairs of Array of AST and functions
     // de is an evaluation input in accordance with AST.evaluate
     constructor(cems, de) {

types/real.js

View file @ 117473e

@@ -1,5 +1,7 @@
 "use strict";
 
+import {BasicNumber} from "./basic.js";
+
 BasicNumber.keys.forEach(k => (Number.prototype[k] = BasicNumber.prototype[k]));
 
 Number.ify = function(x) {


...	...	@@ -1,16 +1,27 @@
1	1	"use strict";
2	2
	3	+import {fts, OPS} from "./rtensor_common.js";
	4	+import {} from "./types/bigint.js";
	5	+import {Complex} from "./types/complex.js";
	6	+import {MathsFunc} from "./types/mathsfunc.js";
	7	+import {} from "./types/real.js";
	8	+
3	9	const isArray = x => (typeof x == "object" && x.constructor == Array);
4	10	const NUMERIC_TYPES = {
5	11	integer: BigInt,
6	12	complex: Complex,
7	13	real: Number,
8	14	};
9		-const nti = (new URLSearchParams(window.location.search)).get("nt") \|\| "a";
10		-const NumericType = NUMERIC_TYPES[nti] \|\| Number;
	15	+let nti;
	16	+try {
	17	+ nti = (new URLSearchParams(window.location.search)).get("nt") \|\| "a";
	18	+} catch (_e) {
	19	+ nti = scriptArgs[1] \|\| "a";
	20	+}
	21	+export const NumericType = NUMERIC_TYPES[nti] \|\| Number;
11	22
12	23	// a: tensor, b: tensor, o: binary function of numbers
13		-function vecOp(a, b, o) {
	24	+export function vecOp(a, b, o) {
14	25	const tra = tensorRank(a);
15	26	const trb = tensorRank(b);
16	27	if (tra == trb && tra >= 1 && a.length == b.length) {
...	...	@@ -25,7 +36,7 @@ function vecOp(a, b, o) {
25	36	}
26	37
27	38	// true iff any elements of v is null or NaN
28		-function anyNaN(v) {
	39	+export function anyNaN(v) {
29	40	return v.map ?
30	41	v.map(x => anyNaN(x)).reduce((a, b) => (a \|\| b), false) :
31	42	(v == null \|\| (typeof v == "number" && isNaN(v)) \|\| (v.invalid && v.invalid()));
...	...	@@ -38,7 +49,7 @@ function tensorRank(t) {
38	49	}
39	50
40	51	// node in an abstract syntax tree, as produced by NewParser
41		-class AST {
	52	+export class AST {
42	53	constructor(ts, l, m, r, len) {
43	54	switch (ts) {
44	55	// identifier: l == Token (tt == 1), m, r == undefined

...	...	@@ -1,6 +1,9 @@
1	1	"use strict";
2	2	// maths parser, by dkl9, 2021-05 to 2021-07, used as part of rtensor
3	3
	4	+import {OPS} from "./rtensor_common.js";
	5	+import {AST} from "./maths_ast.js";
	6	+
4	7	// whitespace characters
5	8	const WSPACE = [" ", "\t", "\n"];
6	9	// characters for starting identifiers
...	...	@@ -21,13 +24,6 @@ const LCHAR = [];
21	24	for (let c = 0; c <= 9; c++) {
22	25	LCHAR.push(String.fromCodePoint(c + 48));
23	26	}
24		-// operator text
25		-const OPS = [
26		- "+", "-", "*", "/",
27		- "^", "\\", "==", "-/",
28		- ",", "<", "=>", "=",
29		- "..",
30		-];
31	27	// precedence of binary operators (greater == lower)
32	28	const PREC = [
33	29	4, 4, 3, 3,
...	...	@@ -79,7 +75,7 @@ const normIntLit = s => (s.replace(/^0+/, "") \|\| "0");
79	75	// 8 (right square bracket)
80	76	// value depends on tt: 1 => ident text, 2 => int value, 3 => operator id
81	77	// 4, 5, 6, 7, 8 => undefined
82		-class Token {
	78	+export class Token {
83	79	constructor(tt, text) {
84	80	this.tt = tt;
85	81	switch (this.tt) {
...	...	@@ -111,7 +107,7 @@ class Token {
111	107	}
112	108
113	109	// source text surrounded by an interface to provide tokens from it on demand
114		-class TokenStream {
	110	+export class TokenStream {
115	111	constructor(source) {
116	112	this.toks = [];
117	113	this.tind = -1;
...	...	@@ -226,7 +222,7 @@ class TokenStream {
226	222	// each function parses a particular structure,
227	223	// returning an AST (with .len, measured in tokens) if successful
228	224	// or null if failed
229		-class NewParser {
	225	+export class NewParser {
230	226	// statement -> expr[9]
231	227	static statement(stream) {
232	228	let tc = 0;

...	...	@@ -1,6 +1,12 @@
1	1	"use strict";
2	2
3		-const IDENT_AST = new AST(1, new Token(1, ""));
	3	+import {fts} from "./rtensor_common.js";
	4	+import {Complex} from "./types/complex.js";
	5	+import {MathsFunc} from "./types/mathsfunc.js";
	6	+import {AST, vecOp, NumericType, anyNaN} from "./maths_ast.js";
	7	+import {Token} from "./maths_parser.js";
	8	+
	9	+export const IDENT_AST = new AST(1, new Token(1, ""));
4	10
5	11	function elemwiseFunc(f) {
6	12	const ref = (args, de) =>
...	...	@@ -11,7 +17,7 @@ function elemwiseFunc(f) {
11	17	return new MathsFunc([[[IDENT_AST], ref]], {});
12	18	}
13	19
14		-const BUILTIN_FUNCS = {
	20	+export const BUILTIN_FUNCS = {
15	21	// numeric
16	22	"abs": elemwiseFunc(x => x.mag()),
17	23	"floor": elemwiseFunc(x => x.floor()),
...	...	@@ -314,24 +320,4 @@ function dl(v) {
314	320	return null;
315	321	}
316	322
317		-window.onerror = (m, s, l, c, e) => dl(`${s}:${l}:${c}: ${m}`);
318		-
319		-// stringify a vecalc value for presentation
320		-function fts(v) {
321		- if (v == null) {
322		- return "nonexistent";
323		- } else if (v.constructor === Array) {
324		- switch (v.length) {
325		- case 0:
326		- return "[ ]";
327		- default:
328		- return "[" + v.map(x => fts(x)).join(", ") + "]";
329		- }
330		- } else if (v.constructor === MathsFunc \|\| v.constructor === Function) {
331		- return "function";
332		- } else if (v.constructor === null) {
333		- return "null";
334		- } else {
335		- return v.toString();
336		- }
337		-}
	323	+try { window.onerror = (m, s, l, c, e) => dl(`${s}:${l}:${c}: ${m}`); } catch (_e) {}

...	...	@@ -1,5 +1,7 @@
1	1	"use strict";
2	2
	3	+import {BasicNumber} from "./basic.js";
	4	+
3	5	BasicNumber.keys.forEach(k => (BigInt.prototype[k] = BasicNumber.prototype[k]));
4	6
5	7	BigInt.ify = function(x) {

...	...	@@ -1,6 +1,8 @@
1	1	"use strict";
2	2
3		-class Complex extends BasicNumber {
	3	+import {BasicNumber} from "./basic.js";
	4	+
	5	+export class Complex extends BasicNumber {
4	6	constructor(x, y) {
5	7	super();
6	8	this.re = x;
...	...	@@ -89,6 +91,16 @@ class Complex extends BasicNumber {
89	91	return this.re == z.re && this.im == z.im;
90	92	}
91	93
	94	+ lt(z) {
	95	+ if ((((this.re < z.re) && (this.im <= z.im)) \|\| ((this.re <= z.re) && (this.im < z.im))) && (this.mag() < z.mag())) {
	96	+ return true;
	97	+ } else if ((((this.re > z.re) && (this.im >= z.im)) \|\| ((this.re >= z.re) && (this.im > z.im))) && (this.mag() > z.mag())) {
	98	+ return false;
	99	+ } else {
	100	+ throw `cannot unambiguously compare complex values ${this} and ${z}`;
	101	+ }
	102	+ }
	103	+
92	104	sqrt() {
93	105	return this.pow(new Complex(0.5, 0));
94	106	}

...	...	@@ -1,5 +1,8 @@
1	1	"use strict";
2	2
	3	+import {fts} from "../rtensor_common.js";
	4	+import {BasicNumber} from "./basic.js";
	5	+
3	6	// check if vectors (Arrays of numbers) a and b are completely equal
4	7	const vecEq = (a, b) => (a?.eq && b?.eq) ?
5	8	(a.eq(b)) :
...	...	@@ -11,7 +14,7 @@ const vecEq = (a, b) => (a?.eq && b?.eq) ?
11	14	// each case is a list of zero or more identifiers or constant values
12	15	// (in the form of ASTs)
13	16	// each expr is an expression (wow); more precisely, a function of the variables
14		-class MathsFunc extends BasicNumber {
	17	+export class MathsFunc extends BasicNumber {
15	18	// cems is an Array of Array-pairs of Array of AST and functions
16	19	// de is an evaluation input in accordance with AST.evaluate
17	20	constructor(cems, de) {