-
Notifications
You must be signed in to change notification settings - Fork 25
/
algebra.js
144 lines (134 loc) · 4.53 KB
/
algebra.js
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
// TODO commute literals on the left side of a target operand, when possible
module.exports = solve;
function solve(target, source) {
return solve.semantics.solve(target, source);
}
solve.semantics = {
solve: function (target, source) {
while (true) {
// simplify the target
while (this.simplifiers.hasOwnProperty(target.type)) {
var simplification = this.simplifiers[target.type](target);
if (simplification) {
target = simplification;
} else {
break;
}
}
var canRotateTargetToSource = this.rotateTargetToSource.hasOwnProperty(target.type);
var canRotateSourceToTarget = this.rotateSourceToTarget.hasOwnProperty(source.type);
// solve for bindable target (rotate terms to source)
if (!canRotateTargetToSource && !canRotateSourceToTarget) {
break;
} else if (canRotateTargetToSource) {
source = this.rotateTargetToSource[target.type](target, source);
target = target.args[0];
} else if (canRotateSourceToTarget) {
target = this.rotateSourceToTarget[source.type](target, source);
source = source.args[0];
}
}
return [target, source];
},
simplifiers: {
// !!x -> x
not: function (syntax) {
var left = syntax.args[0];
if (left.type === "not") {
return left.args[0];
}
},
// "" + x -> x.toString()
add: function (syntax) {
var left = syntax.args[0];
if (left.type === "literal" && left.value === "") {
// "" + x
// toString(x)
// because this can be bound bidirectionally with toNumber(y)
return {
type: "toString",
args: [syntax.args[1]]
};
}
},
// DeMorgan's law applied to `some` so we only have to implement
// `every`.
// some{x} -> !every{!x}
someBlock: function (syntax) {
return {type: "not", args: [
{type: "everyBlock", args: [
syntax.args[0],
{type: "not", args: [
syntax.args[1]
]}
]}
]};
}
},
rotateTargetToSource: {
// e.g.,
// !y = x
// y = !x
reflect: function (target, source) {
return {type: target.type, args: [source]};
},
// e.g.,
// y + 1 = x
// y = x - 1
invert: function (target, source, operator) {
return {type: operator, args: [
source,
target.args[1]
]};
},
toNumber: function (target, source) {
return this.reflect(target, source);
},
toString: function (target, source) {
return this.reflect(target, source);
},
not: function (target, source) {
return this.reflect(target, source);
},
neg: function (target, source) {
return this.reflect(target, source);
},
add: function (target, source) {
return this.invert(target, source, 'sub');
},
sub: function (target, source) {
return this.invert(target, source, 'add');
},
mul: function (target, source) {
return this.invert(target, source, 'div');
},
div: function (target, source) {
return this.invert(target, source, 'mul');
},
pow: function (target, source) {
return this.invert(target, source, 'root');
},
root: function (target, source) {
return this.invert(target, source, 'pow');
},
// terms.join(delimiter) <- string
// terms <- string.split(delimiter)
join: function (target, source) {
return this.invert(target, source, 'split');
},
split: function (target, source) {
return this.invert(target, source, 'join');
}
},
rotateSourceToTarget: {
// y = x.rangeContent()
// y.rangeContent() = x
rangeContent: function (target, source) {
if (target.type === "rangeContent") {
return target;
} else {
return {type: source.type, args: [target]};
}
}
}
};