Formality-Core/python/FormalityCore.py at master · Soonad/Formality-Core · GitHub

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# Term

# ====

def Var(indx):

return {"ctor": "Var", "indx": indx}

def Ref(name):

return {"ctor": "Ref", "name": name}

def Typ():

return {"ctor": "Typ"}

def All(name, bind, body, eras):

return {"ctor": "All", "name": name, "bind": bind, "body": body, "eras": eras}

def Lam(name, body, eras):

return {"ctor": "Lam", "name": name, "body": body, "eras": eras}

def App(func, argm, eras):

return {"ctor": "App", "func": func, "argm": argm, "eras": eras}

def Slf(name, type):

return {"ctor": "Slf", "name": name, "type": type}

def Ins(type, term):

return {"ctor": "Slf", "type": type, "expr": expr}

def Eli(expr):

return {"ctor": "Eli", "expr": expr}

def Ann(expr, type, done):

return {"ctor": "Typ", "expr": expr, "type": type, "done": done}

# List

# ====

def Ext(head, tail):

return {"ctor": "Ext", "head": head, "tail": tail}

def Nil():

return {"ctor": "Nil"}

# Module

# ======

def Def(name, type, term):

return {"ctor": "Def", "name": name, "type": type, "term": term}

# Parsing

# =======

# Finds a value in a list

def find(list, cond, indx = 0):

ctor = list["ctor"]

if ctor == "Ext":

if cond(list["head"], indx):

return {"value": list["head"], "index": indx}

else:

return find(list["tail"], cond, indx + 1)

elif ctor == "Nil":

return None

# Is this a space character?

def is_space(val):

return val == " " or val == "\t" or val == "\n"

# Is this a name-valid character?

def is_name(val):

val = ord(val)

return ((val >= 48 and val < 58) # 0-9

or (val >= 65 and val < 91) # A-Z

or (val >= 95 and val < 96) # _

or (val >= 97 and val < 123)) # a-z

# Returns the first function that doesn't raise, or None

def first_valid(fns):

for [fn, args] in fns:

try:

return fn(*args)

except:

continue

return None

# Drop characters while a condition is met.

def drop_while(cond, code, indx):

while indx < len(code) and cond(code[indx]):

indx += 1

return indx

# Drop spaces

def space(code, indx):

return drop_while(is_space, code, indx)

# Drops spaces and parses an exact string

def parse_str(str, code, indx):

if len(str) == 0:

return [indx, str]

elif indx < len(code) and code[indx] == str[0]:

return parse_str(str[1:], code, indx+1)

else:

raise RuntimeError()

# Parses an optional character

def parse_opt(val, code, indx):

if code[indx] == val:

return [indx + 1, True]

else:

return [indx, False]

# Parses a valid name, non-empty

def parse_nam(code, indx, size = 0):

if indx < len(code) and is_name(code[indx]):

head = code[indx]

[indx, tail] = parse_nam(code, indx + 1, size + 1)

return [indx, head + tail]

elif size > 0:

return [indx, ""]

else:

raise

# Parses a parenthesis, `(<term>)`

def parse_par(code, indx, vars):

[indx, skip] = parse_str("(", code, space(code, indx))

[indx, term] = parse_trm(code, indx, vars)

[indx, skip] = parse_str(")", code, space(code, indx))

return [indx, term]

# Parses a dependent function type, `(<name> : <term>) => <term>`

def parse_all(code, indx, vars):

[indx, skip] = parse_str("(", code, space(code, indx))

[indx, name] = parse_nam(code, space(code, indx))

[indx, skip] = parse_str(":", code, space(code, indx))

[indx, bind] = parse_trm(code, indx, vars)

[indx, eras] = parse_opt(";", code, space(code, indx))

[indx, skip] = parse_str(")", code, space(code, indx))

[indx, skip] = parse_str("->", code, space(code, indx))

[indx, body] = parse_trm(code, indx, Ext(name, vars))

return [indx, All(name, bind, body, eras)];

# Parses a dependent function value, `(<name>) => <term>`

def parse_lam(code, indx, vars):

[indx, skip] = parse_str("(", code, space(code, indx))

[indx, name] = parse_nam(code, space(code, indx))

[indx, eras] = parse_opt(";", code, space(code, indx))

[indx, skip] = parse_str(")", code, space(code, indx))

[indx, skip] = parse_str("=>", code, space(code, indx))

[indx, body] = parse_trm(code, indx, Ext(name, vars))

return [indx, Lam(name, body, eras)]

# Parses the type of types, `Type`

def parse_typ(code, indx, vars):

[indx, skip] = parse_str("Type", code, space(code, indx))

return [indx, Typ()]

# Parses variables, `<name>`

def parse_var(code, indx, vars):

[indx, name] = parse_nam(code, space(code, indx))

got = find(vars, lambda x, i: x == name)

if got:

return [indx, Var(got["index"])]

else:

return [indx, Ref(name)]

# Parses a self type, `#{<name>} <term>`

def parse_slf(code, indx, vars):

[indx, skip] = parse_str("#{", code, space(code, indx))

[indx, name] = parse_nam(code, space(code, indx))

[indx, skip] = parse_str("}", code, space(code, indx))

[indx, type] = parse_trm(code, indx, Ext(name, vars))

return [indx, Slf(name, type)]

# Parses a self instantiation, `#inst{<term>}`

def parse_ins(code, indx, vars):

[indx, skip] = parse_str("#inst{", code, space(code, indx))

[indx, type] = parse_trm(code, indx, vars)

[indx, skip] = parse_str("}", code, space(code, indx))

[indx, expr] = parse_trm(code, indx, vars)

return [indx, Ins(type, expr)]

# Parses a self elimination, `#elim{<term>}`

def parse_eli(code, indx, vars):

[indx, skip] = parse_str("#elim{", code, space(code, indx))

[indx, expr] = parse_trm(code, indx, vars)

[indx, skip] = parse_str("}", code, space(code, indx))

return [indx, Eli(expr)]

# Parses an application, `<term>(<term>)`

def parse_app(code, indx, func, vars):

[indx, skip] = parse_str("(", code, indx)

[indx, argm] = parse_trm(code, indx, vars)

[indx, eras] = parse_opt(";", code, space(code, indx))

[indx, skip] = parse_str(")", code, space(code, indx))

return [indx, App(func, argm, eras)]

# Parses an annotation, `<term> :: <term>`

def parse_ann(code, indx, expr, vars):

[indx, skip] = parse_str("::", code, space(code, indx))

[indx, type] = parse_trm(code, indx, vars)

return [indx, Ann(expr, type, False)]

# Parses a term

def parse_trm(code, indx = 0, vars = Nil()):

# Parses the base term, trying each variant once

base_parse = first_valid([

[parse_all, [code, indx, vars]],

[parse_lam, [code, indx, vars]],

[parse_par, [code, indx, vars]],

[parse_typ, [code, indx, vars]],

[parse_slf, [code, indx, vars]],

[parse_ins, [code, indx, vars]],

[parse_eli, [code, indx, vars]],

[parse_var, [code, indx, vars]],

])

# Parses postfix extensions, trying each variant repeatedly

post_parse = base_parse

while True:

[indx, term] = post_parse

post_parse = first_valid([

[parse_app, [code, indx, term, vars]],

[parse_ann, [code, indx, term, vars]],

])

if not post_parse:

return base_parse

else:

base_parse = post_parse

return None

# Parses a module

def parse_mod(code, indx):

try:

[indx, name] = parse_nam(code, space(code, indx))

[indx, skip] = parse_str(":", code, space(code, indx))

[indx, type] = parse_trm(code, space(code, indx), Nil())

[indx, term] = parse_trm(code, space(code, indx), Nil())

return Ext(Def(name, type, term), parse_mod(code, indx))

except:

return Nil()

# Stringification

# ===============

def stringify_trm(term, vars = Nil()):

ctor = term["ctor"]

if ctor == "Var":

got = find(vars, lambda x, i: i == term["indx"])

if got:

return got["value"]

else:

return "#" + term["indx"]

elif ctor == "Ref":

return term["name"];

elif ctor == "Typ":

return "Type";

elif ctor == "All":

name = term["name"]

bind = stringify_trm(term["bind"], vars)

body = stringify_trm(term["body"], Ext(name, vars))

eras = ";" if term["eras"] else ""

return "("+name+" : "+bind+eras+") -> "+body

elif ctor == "Lam":

name = term["name"]

body = stringify_trm(term["body"], Ext(name, vars))

eras = ";" if term["eras"] else ""

return "("+name+eras+") => "+body

elif ctor == "App":

func = stringify_trm(term["func"], vars)

argm = stringify_trm(term["argm"], vars)

eras = ";" if term["eras"] else ""

return "("+func+")("+argm+eras+")"

elif ctor == "Slf":

name = term["name"]

type = stringify_trm(term["type"], Ext(name, vars))

return "#{"+name+"} "+type

elif ctor == "Ins":

type = stringify_trm(term["type"], vars)

expr = stringify_trm(term["expr"], vars)

return "#inst{"+type+"} "+expr

elif ctor == "Eli":

expr = stringify_trm(term["expr"], vars)

return "#elim{"+expr+"}"

elif ctor == "Ann":

expr = stringify_trm(term["expr"], vars)

type = stringify_trm(term["type"], vars)

return expr+" :: "+type

def stringify_mod(mod):

ctor = mod["ctor"]

if ctor == "Ext":

name = mod["head"]["name"]

type = stringify_trm(mod["head"]["type"], Nil())

term = stringify_trm(mod["head"]["term"], Nil())

defs = stringify_mod(mod["tail"])

return name + " : " + type + "\n " + term + "\n\n" + defs

elif ctor == "Nil":

return ""

Formality-Core/python/FormalityCore.py at master · Soonad/Formality-Core · GitHub

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