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| """Utilities for string manipulation in the DSL."""
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| MAP_SYMBOL = {
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| 'T': 'perp',
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| 'P': 'para',
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| 'D': 'cong',
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| 'S': 'simtri',
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| 'I': 'circle',
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| 'M': 'midp',
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| 'O': 'cyclic',
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| 'C': 'coll',
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| '^': 'eqangle',
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| '/': 'eqratio',
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| '%': 'eqratio',
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| '=': 'contri',
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| 'X': 'collx',
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| 'A': 'acompute',
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| 'R': 'rcompute',
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| 'Q': 'fixc',
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| 'E': 'fixl',
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| 'V': 'fixb',
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| 'H': 'fixt',
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| 'Z': 'fixp',
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| 'Y': 'ind',
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| }
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| def map_symbol(c: str) -> str:
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| return MAP_SYMBOL[c]
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| def map_symbol_inv(c: str) -> str:
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| return {v: k for k, v in MAP_SYMBOL.items()}[c]
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| def _gcd(x: int, y: int) -> int:
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| while y:
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| x, y = y, x % y
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| return x
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| def simplify(n: int, d: int) -> tuple[int, int]:
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| g = _gcd(n, d)
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| return (n // g, d // g)
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| def pretty2r(a: str, b: str, c: str, d: str) -> str:
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| if b in (c, d):
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| a, b = b, a
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|
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| if a == d:
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| c, d = d, c
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| return f'{a} {b} {c} {d}'
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| def pretty2a(a: str, b: str, c: str, d: str) -> str:
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| if b in (c, d):
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| a, b = b, a
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|
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| if a == d:
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| c, d = d, c
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| return f'{a} {b} {c} {d}'
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|
|
| def pretty_angle(a: str, b: str, c: str, d: str) -> str:
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| if b in (c, d):
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| a, b = b, a
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| if a == d:
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| c, d = d, c
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|
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| if a == c:
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| return f'\u2220{b}{a}{d}'
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| return f'\u2220({a}{b}-{c}{d})'
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|
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|
|
| def pretty_nl(name: str, args: list[str]) -> str:
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| """Natural lang formatting a predicate."""
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| if name == 'aconst':
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| a, b, c, d, y = args
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| return f'{pretty_angle(a, b, c, d)} = {y}'
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| if name == 'rconst':
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| a, b, c, d, y = args
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| return f'{a}{b}:{c}{d} = {y}'
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| if name == 'acompute':
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| a, b, c, d = args
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| return f'{pretty_angle(a, b, c, d)}'
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| if name in ['coll', 'C']:
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| return '' + ','.join(args) + ' are collinear'
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| if name == 'collx':
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| return '' + ','.join(list(set(args))) + ' are collinear'
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| if name in ['cyclic', 'O']:
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| return '' + ','.join(args) + ' are concyclic'
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| if name in ['midp', 'midpoint', 'M']:
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| x, a, b = args
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| return f'{x} is midpoint of {a}{b}'
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| if name in ['eqangle', 'eqangle6', '^']:
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| a, b, c, d, e, f, g, h = args
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| return f'{pretty_angle(a, b, c, d)} = {pretty_angle(e, f, g, h)}'
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| if name in ['eqratio', 'eqratio6', '/']:
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| return '{}{}:{}{} = {}{}:{}{}'.format(*args)
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| if name == 'eqratio3':
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| a, b, c, d, o, o = args
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| return f'S {o} {a} {b} {o} {c} {d}'
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| if name in ['cong', 'D']:
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| a, b, c, d = args
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| return f'{a}{b} = {c}{d}'
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| if name in ['perp', 'T']:
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| if len(args) == 2:
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| ab, cd = args
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| return f'{ab} \u27c2 {cd}'
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| a, b, c, d = args
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| return f'{a}{b} \u27c2 {c}{d}'
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| if name in ['para', 'P']:
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| if len(args) == 2:
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| ab, cd = args
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| return f'{ab} \u2225 {cd}'
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| a, b, c, d = args
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| return f'{a}{b} \u2225 {c}{d}'
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| if name in ['simtri2', 'simtri', 'simtri*']:
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| a, b, c, x, y, z = args
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| return f'\u0394{a}{b}{c} is similar to \u0394{x}{y}{z}'
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| if name in ['contri2', 'contri', 'contri*']:
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| a, b, c, x, y, z = args
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| return f'\u0394{a}{b}{c} is congruent to \u0394{x}{y}{z}'
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| if name in ['circle', 'I']:
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| o, a, b, c = args
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| return f'{o} is the circumcenter of \\Delta {a}{b}{c}'
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| if name == 'foot':
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| a, b, c, d = args
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| return f'{a} is the foot of {b} on {c}{d}'
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|
|
|
|
| def pretty(txt: str) -> str:
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| """Pretty formating a predicate string."""
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| if isinstance(txt, str):
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| txt = txt.split(' ')
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| name, *args = txt
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| if name == 'ind':
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| return 'Y ' + ' '.join(args)
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| if name in ['fixc', 'fixl', 'fixb', 'fixt', 'fixp']:
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| return map_symbol_inv(name) + ' ' + ' '.join(args)
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| if name == 'acompute':
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| a, b, c, d = args
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| return 'A ' + ' '.join(args)
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| if name == 'rcompute':
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| a, b, c, d = args
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| return 'R ' + ' '.join(args)
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| if name == 'aconst':
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| a, b, c, d, y = args
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| return f'^ {pretty2a(a, b, c, d)} {y}'
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| if name == 'rconst':
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| a, b, c, d, y = args
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| return f'/ {pretty2r(a, b, c, d)} {y}'
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| if name == 'coll':
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| return 'C ' + ' '.join(args)
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| if name == 'collx':
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| return 'X ' + ' '.join(args)
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| if name == 'cyclic':
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| return 'O ' + ' '.join(args)
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| if name in ['midp', 'midpoint']:
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| x, a, b = args
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| return f'M {x} {a} {b}'
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| if name == 'eqangle':
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| a, b, c, d, e, f, g, h = args
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| return f'^ {pretty2a(a, b, c, d)} {pretty2a(e, f, g, h)}'
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| if name == 'eqratio':
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| a, b, c, d, e, f, g, h = args
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| return f'/ {pretty2r(a, b, c, d)} {pretty2r(e, f, g, h)}'
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| if name == 'eqratio3':
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| a, b, c, d, o, o = args
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| return f'S {o} {a} {b} {o} {c} {d}'
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| if name == 'cong':
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| a, b, c, d = args
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| return f'D {a} {b} {c} {d}'
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| if name == 'perp':
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| if len(args) == 2:
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| ab, cd = args
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| return f'T {ab} {cd}'
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| a, b, c, d = args
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| return f'T {a} {b} {c} {d}'
|
| if name == 'para':
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| if len(args) == 2:
|
| ab, cd = args
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| return f'P {ab} {cd}'
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| a, b, c, d = args
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| return f'P {a} {b} {c} {d}'
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| if name in ['simtri2', 'simtri', 'simtri*']:
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| a, b, c, x, y, z = args
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| return f'S {a} {b} {c} {x} {y} {z}'
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| if name in ['contri2', 'contri', 'contri*']:
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| a, b, c, x, y, z = args
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| return f'= {a} {b} {c} {x} {y} {z}'
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| if name == 'circle':
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| o, a, b, c = args
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| return f'I {o} {a} {b} {c}'
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| if name == 'foot':
|
| a, b, c, d = args
|
| return f'F {a} {b} {c} {d}'
|
| return ' '.join(txt)
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|
|
