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b/.doctrees/environment.pickle new file mode 100644 index 0000000..c5734cd Binary files /dev/null and b/.doctrees/environment.pickle differ diff --git a/.doctrees/index.doctree b/.doctrees/index.doctree new file mode 100644 index 0000000..a25a95f Binary files /dev/null and b/.doctrees/index.doctree differ diff --git a/.nojekyll b/.nojekyll new file mode 100644 index 0000000..e69de29 diff --git a/_autosummary/knuckledragger.html b/_autosummary/knuckledragger.html new file mode 100644 index 0000000..1c9bb70 --- /dev/null +++ b/_autosummary/knuckledragger.html @@ -0,0 +1,133 @@ + + + + + + + knuckledragger — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger

+

Modules

+ + + + + + + + + + + + + + + +

kernel

notation

Importing this module will add some syntactic sugar to Z3.

theories

utils

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.kernel.axiom.html b/_autosummary/knuckledragger.kernel.axiom.html new file mode 100644 index 0000000..42c0e65 --- /dev/null +++ b/_autosummary/knuckledragger.kernel.axiom.html @@ -0,0 +1,142 @@ + + + + + + + knuckledragger.kernel.axiom — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.kernel.axiom

+
+
+knuckledragger.kernel.axiom(thm: BoolRef, by=[]) → None
+

Assert an axiom.

+

Axioms are necessary and useful. But you must use great care.

+
+
Parameters:
+
    +

  • thm – The axiom to assert.

    • +

  • by – A python object explaining why the axiom should exist. Often a string explaining the axiom.

    • +
+
+
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.kernel.define.html b/_autosummary/knuckledragger.kernel.define.html new file mode 100644 index 0000000..f6b563f --- /dev/null +++ b/_autosummary/knuckledragger.kernel.define.html @@ -0,0 +1,148 @@ + + + + + + + knuckledragger.kernel.define — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.kernel.define

+
+
+knuckledragger.kernel.define(name: str, args: list[ExprRef], body: ExprRef) → FuncDeclRef
+

Define a non recursive definition. Useful for shorthand and abstraction.

+
+
Parameters:
+
    +

  • name – The name of the term to define.

    • +

  • args – The arguments of the term.

    • +

  • defn – The definition of the term.

    • +
+
+
Returns:
+

A tuple of the defined term and the proof of the definition.

+
+
Return type:
+

tuple[z3.FuncDeclRef, __Proof]

+
+
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.kernel.html b/_autosummary/knuckledragger.kernel.html new file mode 100644 index 0000000..ace50a7 --- /dev/null +++ b/_autosummary/knuckledragger.kernel.html @@ -0,0 +1,301 @@ + + + + + + + knuckledragger.kernel — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.kernel

+

Module Attributes

+ + + + + + +

defns

defn holds definitional axioms for function symbols.

+

Functions

+ + + + + + + + + + + + + + + +

axiom(thm[, by])

Assert an axiom.

define(name, args, body)

Define a non recursive definition.

is_proof(p)

lemma(thm[, by, admit, timeout, dump])

Prove a theorem using a list of previously proved lemmas.

+

Classes

+ + + + + + +

Defn(name, args, body, ax)

+

Exceptions

+ + + + + + +

LemmaError

+
import z3
+from dataclasses import dataclass
+from typing import Any
+import logging
+
+logger = logging.getLogger("knuckeldragger")
+
+
+@dataclass(frozen=True)
+class Proof(z3.Z3PPObject):
+    thm: z3.BoolRef
+    reason: list[Any]
+    admit: bool
+
+    def _repr_html_(self):
+        return "⊦" + repr(self.thm)
+
+    def __repr__(self):
+        return "|- " + repr(self.thm)
+
+
+# It is unlikely that users should be accessing the `Proof` constructor directly.
+# This is not ironclad. If you really want the Proof constructor, I can't stop you.
+__Proof = Proof
+Proof = None
+
+
+def is_proof(p):
+    return isinstance(p, __Proof)
+
+
+class LemmaError(Exception):
+    pass
+
+
+def lemma(
+    thm: z3.BoolRef, by: list[Proof] = [], admit=False, timeout=1000, dump=False
+) -> Proof:
+    """Prove a theorem using a list of previously proved lemmas.
+
+    In essence `prove(Implies(by, thm))`.
+
+    :param thm: The theorem to prove.
+    Args:
+        thm (z3.BoolRef): The theorem to prove.
+        by (list[Proof]): A list of previously proved lemmas.
+        admit     (bool): If True, admit the theorem without proof.
+
+    Returns:
+        Proof: A proof object of thm
+
+    >>> lemma(BoolVal(True))
+
+    >>> lemma(RealVal(1) >= RealVal(0))
+
+    """
+    if admit:
+        logger.warn("Admitting lemma {}".format(thm))
+        return __Proof(thm, by, True)
+    else:
+        s = z3.Solver()
+        s.set("timeout", timeout)
+        for n, p in enumerate(by):
+            if not isinstance(p, __Proof):
+                raise LemmaError("In by reasons:", p, "is not a Proof object")
+            s.assert_and_track(p.thm, "by_{}".format(n))
+        s.assert_and_track(z3.Not(thm), "knuckledragger_goal")
+        if dump:
+            print(s.sexpr())
+        res = s.check()
+        if res != z3.unsat:
+            if res == z3.sat:
+                raise LemmaError(thm, "Countermodel", s.model())
+            raise LemmaError("lemma", thm, res)
+        else:
+            core = s.unsat_core()
+            assert z3.Bool("knuckledragger_goal") in core
+            if len(core) < len(by) + 1:
+                print("WARNING: Unneeded assumptions. Used", core)
+            return __Proof(thm, by, False)
+
+
+def axiom(thm: z3.BoolRef, by=[]) -> Proof:
+    """Assert an axiom.
+
+    Axioms are necessary and useful. But you must use great care.
+
+    Args:
+        thm: The axiom to assert.
+        by: A python object explaining why the axiom should exist. Often a string explaining the axiom.
+    """
+    return __Proof(thm, by, admit=True)
+
+
+@dataclass(frozen=True)
+class Defn:
+    name: str
+    args: list[z3.ExprRef]
+    body: z3.ExprRef
+    ax: Proof
+
+
+defns: dict[z3.FuncDecl, Defn] = {}
+"""
+defn holds definitional axioms for function symbols.
+"""
+z3.FuncDeclRef.defn = property(lambda self: defns[self].ax)
+
+
+def define(name: str, args: list[z3.ExprRef], body: z3.ExprRef) -> z3.FuncDeclRef:
+    """Define a non recursive definition. Useful for shorthand and abstraction.
+
+    Args:
+        name: The name of the term to define.
+        args: The arguments of the term.
+        defn: The definition of the term.
+
+    Returns:
+        tuple[z3.FuncDeclRef, __Proof]: A tuple of the defined term and the proof of the definition.
+    """
+    sorts = [arg.sort() for arg in args] + [body.sort()]
+    f = z3.Function(name, *sorts)
+    if len(args) > 0:
+        def_ax = axiom(z3.ForAll(args, f(*args) == body), by="definition")
+    else:
+        def_ax = axiom(f(*args) == body, by="definition")
+    # assert f not in __sig or __sig[f].eq(   def_ax.thm)  # Check for redefinitions. This is kind of painful. Hmm.
+    # Soft warning is more pleasant.
+    defn = Defn(name, args, body, def_ax)
+    if f not in defns or defns[f].ax.thm.eq(def_ax.thm):
+        defns[f] = defn
+    else:
+        print("WARNING: Redefining function", f, "from", defns[f].ax, "to", def_ax.thm)
+        defns[f] = defn
+    return f
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.kernel.is_proof.html b/_autosummary/knuckledragger.kernel.is_proof.html new file mode 100644 index 0000000..a68f12a --- /dev/null +++ b/_autosummary/knuckledragger.kernel.is_proof.html @@ -0,0 +1,132 @@ + + + + + + + knuckledragger.kernel.is_proof — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.kernel.is_proof

+
+
+knuckledragger.kernel.is_proof(p)
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.kernel.lemma.html b/_autosummary/knuckledragger.kernel.lemma.html new file mode 100644 index 0000000..43edbc3 --- /dev/null +++ b/_autosummary/knuckledragger.kernel.lemma.html @@ -0,0 +1,156 @@ + + + + + + + knuckledragger.kernel.lemma — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.kernel.lemma

+
+
+knuckledragger.kernel.lemma(thm: BoolRef, by: list[None] = [], admit=False, timeout=1000, dump=False) → None
+

Prove a theorem using a list of previously proved lemmas.

+

In essence prove(Implies(by, thm)).

+
+
Parameters:
+
    +

  • thm (z3.BoolRef) – The theorem to prove.

    • +

  • thm – The theorem to prove.

    • +

  • by (list[Proof]) – A list of previously proved lemmas.

    • +

  • admit (bool) – If True, admit the theorem without proof.

    • +
+
+
Returns:
+

A proof object of thm

+
+
Return type:
+

Proof

+
+
+
>>> lemma(BoolVal(True))
+
+
+
>>> lemma(RealVal(1) >= RealVal(0))
+
+
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.notation.QExists.html b/_autosummary/knuckledragger.notation.QExists.html new file mode 100644 index 0000000..b09770d --- /dev/null +++ b/_autosummary/knuckledragger.notation.QExists.html @@ -0,0 +1,133 @@ + + + + + + + knuckledragger.notation.QExists — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.notation.QExists

+
+
+knuckledragger.notation.QExists(vars, hyp, conc)
+

Quantified Exists

+

Shorthand for Exists(vars, And(hyp, conc))

+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.notation.QForAll.html b/_autosummary/knuckledragger.notation.QForAll.html new file mode 100644 index 0000000..99ed73d --- /dev/null +++ b/_autosummary/knuckledragger.notation.QForAll.html @@ -0,0 +1,133 @@ + + + + + + + knuckledragger.notation.QForAll — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.notation.QForAll

+
+
+knuckledragger.notation.QForAll(vars, hyp, conc)
+

Quantified ForAll

+

Shorthand for ForAll(vars, Implies(hyp, conc))

+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.notation.html b/_autosummary/knuckledragger.notation.html new file mode 100644 index 0000000..8ec58c9 --- /dev/null +++ b/_autosummary/knuckledragger.notation.html @@ -0,0 +1,267 @@ + + + + + + + knuckledragger.notation — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.notation

+

Importing this module will add some syntactic sugar to Z3.

+
    +

  • Expr overload by single dispatch

    • +

  • Bool supports &, |, ~

    • +

  • Sorts supports >> for ArraySort

    • +

  • Datatypes support accessor notation

    • +
+

Functions

+ + + + + + + + + + + + +

QExists(vars, hyp, conc)

Quantified Exists

QForAll(vars, hyp, conc)

Quantified ForAll

lookup_cons_recog(self, k)

Enable "dot" syntax for fields of z3 datatypes

+

Classes

+ + + + + + +

SortDispatch([default])

Sort dispatch is modelled after functools.singledispatch It allows for dispatching on the sort of the first argument

+
"""Importing this module will add some syntactic sugar to Z3.
+
+- Expr overload by single dispatch
+- Bool supports `&`, `|`, `~`
+- Sorts supports `>>` for ArraySort
+- Datatypes support accessor notation
+"""
+
+import z3
+
+
+z3.BoolRef.__and__ = lambda self, other: z3.And(self, other)
+z3.BoolRef.__or__ = lambda self, other: z3.Or(self, other)
+z3.BoolRef.__invert__ = lambda self: z3.Not(self)
+
+
+def QForAll(vars, hyp, conc):
+    """Quantified ForAll
+
+    Shorthand for `ForAll(vars, Implies(hyp, conc))`
+
+    """
+    return z3.ForAll(vars, z3.Implies(hyp, conc))
+
+
+def QExists(vars, hyp, conc):
+    """Quantified Exists
+
+    Shorthand for `Exists(vars, And(hyp, conc))`
+
+    """
+    return z3.Exists(vars, z3.And(hyp, conc))
+
+
+z3.SortRef.__rshift__ = lambda self, other: z3.ArraySort(self, other)
+
+
+class SortDispatch:
+    """
+    Sort dispatch is modelled after functools.singledispatch
+    It allows for dispatching on the sort of the first argument
+    """
+
+    def __init__(self, default=None):
+        self.methods = {}
+        self.default = default
+
+    def register(self, sort, func):
+        self.methods[sort] = func
+
+    def __call__(self, *args, **kwargs):
+        return self.methods.get(args[0].sort(), self.default)(*args, **kwargs)
+
+
+add = SortDispatch(z3.ArithRef.__add__)
+z3.ExprRef.__add__ = lambda x, y: add(x, y)
+
+sub = SortDispatch(z3.ArithRef.__sub__)
+z3.ExprRef.__sub__ = lambda x, y: sub(x, y)
+
+mul = SortDispatch(z3.ArithRef.__mul__)
+z3.ExprRef.__mul__ = lambda x, y: mul(x, y)
+
+div = SortDispatch(z3.ArithRef.__div__)
+z3.ExprRef.__truediv__ = lambda x, y: div(x, y)
+
+and_ = SortDispatch()
+z3.ExprRef.__and__ = lambda x, y: and_(x, y)
+
+or_ = SortDispatch()
+z3.ExprRef.__or__ = lambda x, y: or_(x, y)
+
+lt = SortDispatch(z3.ArithRef.__lt__)
+z3.ExprRef.__lt__ = lambda x, y: lt(x, y)
+
+le = SortDispatch(z3.ArithRef.__le__)
+z3.ExprRef.__le__ = lambda x, y: le(x, y)
+
+
+"""
+mul = SortDispatch(z3.ArithRef.__mul__)
+z3.ExprRef.__mul__ = mul
+
+sub = SortDispatch(z3.ArithRef.__sub__)
+z3.ExprRef.__sub__ = sub
+
+matmul = SortDispatch()
+z3.ExprRef.__matmul__ = matmul
+
+le = SortDispatch()
+z3.ExprRef.__le__ = le
+"""
+
+
+def lookup_cons_recog(self, k):
+    """
+    Enable "dot" syntax for fields of z3 datatypes
+    """
+    sort = self.sort()
+    recog = "is_" == k[:3] if len(k) > 3 else False
+    for i in range(sort.num_constructors()):
+        cons = sort.constructor(i)
+        if recog:
+            if cons.name() == k[3:]:
+                recog = sort.recognizer(i)
+                return recog(self)
+        else:
+            for j in range(cons.arity()):
+                acc = sort.accessor(i, j)
+                if acc.name() == k:
+                    return acc(self)
+
+
+z3.DatatypeRef.__getattr__ = lookup_cons_recog
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.notation.lookup_cons_recog.html b/_autosummary/knuckledragger.notation.lookup_cons_recog.html new file mode 100644 index 0000000..8ea11c5 --- /dev/null +++ b/_autosummary/knuckledragger.notation.lookup_cons_recog.html @@ -0,0 +1,132 @@ + + + + + + + knuckledragger.notation.lookup_cons_recog — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.notation.lookup_cons_recog

+
+
+knuckledragger.notation.lookup_cons_recog(self, k)
+

Enable “dot” syntax for fields of z3 datatypes

+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.theories.Int.html b/_autosummary/knuckledragger.theories.Int.html new file mode 100644 index 0000000..0154731 --- /dev/null +++ b/_autosummary/knuckledragger.theories.Int.html @@ -0,0 +1,131 @@ + + + + + + + knuckledragger.theories.Int — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.theories.Int

+
from z3 import IntSort
+from knuckledragger import lemma, axiom
+
+Z = IntSort()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.theories.List.html b/_autosummary/knuckledragger.theories.List.html new file mode 100644 index 0000000..926ce0d --- /dev/null +++ b/_autosummary/knuckledragger.theories.List.html @@ -0,0 +1,128 @@ + + + + + + + knuckledragger.theories.List — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.theories.List

+

+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.theories.Nat.html b/_autosummary/knuckledragger.theories.Nat.html new file mode 100644 index 0000000..775bb22 --- /dev/null +++ b/_autosummary/knuckledragger.theories.Nat.html @@ -0,0 +1,220 @@ + + + + + + + knuckledragger.theories.Nat — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.theories.Nat

+

Defines an algebraic datatype for the Peano natural numbers and useful functions and properties.

+

Module Attributes

+ + + + + + +

Nat

Nat = succ(pred Nat) | zero)

+

Functions

+ + + + + + +

induct(P)

An induction axiom schema for natural numbers.

+
"""
+Defines an algebraic datatype for the Peano natural numbers and useful functions and properties.
+"""
+
+from z3 import Datatype, ForAll, And, Implies, Consts, If, Function, IntSort, Ints
+from knuckledragger import axiom, lemma, define
+import knuckledragger.notation as notation
+
+Z = IntSort()
+x, y = Ints("x y")
+
+
+Nat = Datatype("Nat")
+"""Nat = succ(pred Nat) | zero)"""
+Nat.declare("zero")
+Nat.declare("succ", ("pred", Nat))
+Nat = Nat.create()
+
+
+n, m, k = Consts("n m k", Nat)
+
+
+def induct(P):
+    """An induction axiom schema for natural numbers."""
+    return axiom(
+        Implies(
+            And(P(Nat.zero), ForAll([n], Implies(P(n), P(Nat.succ(n))))),
+            # -----------------------------------------------------------
+            ForAll([n], P(n)),
+        ),
+        ("nat_induction", P),
+    )
+
+
+reify = Function("reify", Nat, Z)
+# """reify  Nat  Z maps a natural number to the built in Z3 integers"""
+reify_def = axiom(
+    ForAll([n], reify(n) == If(Nat.is_zero(n), 0, reify(Nat.pred(n)) + 1))
+)
+
+
+reflect = Function("reflect", Z, Nat)
+# """reflect  Z  Nat maps an integer to a natural number"""
+# reflect_def = axiom(
+#    ForAll([x], reflect(x) == If(x <= 0, Nat.zero, Nat.succ(reflect(x - 1))))
+# )
+reflect = define("reflect", [x], If(x <= 0, Nat.zero, Nat.succ(reflect(x - 1))))
+
+reflect_reify = lemma(
+    ForAll([n], reflect(reify(n)) == n),
+    by=[reflect.defn, reify_def, induct(lambda n: reflect(reify(n)) == n)],
+)
+
+reify_ge_0 = lemma(
+    ForAll([n], reify(n) >= 0), by=[reify_def, induct(lambda n: reify(n) >= 0)]
+)
+
+zero_homo = lemma(reify(Nat.zero) == 0, by=[reify_def])
+
+succ_homo = lemma(
+    ForAll([n], reify(Nat.succ(n)) == 1 + reify(n)),
+    by=[reify_def, induct(lambda n: reify(Nat.succ(n)) == 1 + reify(n))],
+)
+
+
+add = Function("add", Nat, Nat, Nat)
+add_def = axiom(
+    ForAll([n, m], add(n, m) == If(Nat.is_zero(n), m, Nat.succ(add(Nat.pred(n), m))))
+)
+notation.add.register(Nat, add)
+
+
+add_0_n = lemma(ForAll([n], Nat.zero + n == n), by=[add_def])
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.theories.Nat.induct.html b/_autosummary/knuckledragger.theories.Nat.induct.html new file mode 100644 index 0000000..e39fd4a --- /dev/null +++ b/_autosummary/knuckledragger.theories.Nat.induct.html @@ -0,0 +1,135 @@ + + + + + + + knuckledragger.theories.Nat.induct — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.theories.Nat.induct

+
+
+knuckledragger.theories.Nat.induct(P)
+

An induction axiom schema for natural numbers.

+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.theories.Real.html b/_autosummary/knuckledragger.theories.Real.html new file mode 100644 index 0000000..a44fb2f --- /dev/null +++ b/_autosummary/knuckledragger.theories.Real.html @@ -0,0 +1,179 @@ + + + + + + + knuckledragger.theories.Real — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.theories.Real

+
import z3
+from z3 import ForAll, Function
+from knuckledragger import lemma, axiom
+import knuckledragger as kd
+
+R = z3.RealSort()
+RFun = z3.ArraySort(R, R)
+RSeq = z3.ArraySort(z3.IntSort(), R)
+
+x, y, z = z3.Reals("x y z")
+
+plus = Function("plus", R, R, R)
+plus_def = axiom(ForAll([x, y], plus(x, y) == x + y), "definition")
+
+plus_0 = lemma(ForAll([x], plus(x, 0) == x), by=[plus_def])
+plus_comm = lemma(ForAll([x, y], plus(x, y) == plus(y, x)), by=[plus_def])
+plus_assoc = lemma(
+    z3.ForAll([x, y, z], plus(x, plus(y, z)) == plus(plus(x, y), z)), by=[plus_def]
+)
+
+mul = Function("mul", R, R, R)
+mul_def = axiom(ForAll([x, y], mul(x, y) == x * y), "definition")
+
+mul_zero = lemma(ForAll([x], mul(x, 0) == 0), by=[mul_def])
+mul_1 = lemma(ForAll([x], mul(x, 1) == x), by=[mul_def])
+mul_comm = lemma(ForAll([x, y], mul(x, y) == mul(y, x)), by=[mul_def])
+mul_assoc = lemma(
+    ForAll([x, y, z], mul(x, mul(y, z)) == mul(mul(x, y), z)), by=[mul_def]
+)
+mul_distrib = lemma(
+    ForAll([x, y, z], mul(x, plus(y, z)) == plus(mul(x, y), mul(x, z))),
+    by=[mul_def, plus_def],
+)
+
+
+abs = kd.define("abs", [x], z3.If(x >= 0, x, -x))
+
+abs_idem = kd.lemma(ForAll([x], abs(abs(x)) == abs(x)), by=[abs.defn])
+abd_neg = kd.lemma(ForAll([x], abs(-x) == abs(x)), by=[abs.defn])
+abs_ge_0 = kd.lemma(ForAll([x], abs(x) >= 0), by=[abs.defn])
+
+nonneg = kd.define("nonneg", [x], abs(x) == x)
+nonneg_ge_0 = kd.lemma(ForAll([x], nonneg(x) == (x >= 0)), by=[nonneg.defn, abs.defn])
+
+max = kd.define("max", [x, y], z3.If(x >= y, x, y))
+max_comm = kd.lemma(ForAll([x, y], max(x, y) == max(y, x)), by=[max.defn])
+max_assoc = kd.lemma(
+    ForAll([x, y, z], max(x, max(y, z)) == max(max(x, y), z)), by=[max.defn]
+)
+max_idem = kd.lemma(ForAll([x], max(x, x) == x), by=[max.defn])
+max_ge = kd.lemma(ForAll([x, y], max(x, y) >= x), by=[max.defn])
+max_ge_2 = kd.lemma(ForAll([x, y], max(x, y) >= y), by=[max.defn])
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.theories.Seq.html b/_autosummary/knuckledragger.theories.Seq.html new file mode 100644 index 0000000..e8c79c9 --- /dev/null +++ b/_autosummary/knuckledragger.theories.Seq.html @@ -0,0 +1,133 @@ + + + + + + + knuckledragger.theories.Seq — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.theories.Seq

+
from knuckledragger.theories.Nat import Nat
+from knuckledragger.theories.Real import R
+from z3 import ArraySort
+
+"""A Sequence type of Nat -> R"""
+Seq = ArraySort(Nat, R)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.theories.html b/_autosummary/knuckledragger.theories.html new file mode 100644 index 0000000..acbae8c --- /dev/null +++ b/_autosummary/knuckledragger.theories.html @@ -0,0 +1,144 @@ + + + + + + + knuckledragger.theories — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.theories

+

Modules

+ + + + + + + + + + + + + + + + + + +

Int

List

Nat

Defines an algebraic datatype for the Peano natural numbers and useful functions and properties.

Real

Seq

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.utils.expr_to_tptp.html b/_autosummary/knuckledragger.utils.expr_to_tptp.html new file mode 100644 index 0000000..9796efb --- /dev/null +++ b/_autosummary/knuckledragger.utils.expr_to_tptp.html @@ -0,0 +1,134 @@ + + + + + + + knuckledragger.utils.expr_to_tptp — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.utils.expr_to_tptp

+
+
+knuckledragger.utils.expr_to_tptp(expr: ExprRef)
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.utils.html b/_autosummary/knuckledragger.utils.html new file mode 100644 index 0000000..4989a6f --- /dev/null +++ b/_autosummary/knuckledragger.utils.html @@ -0,0 +1,341 @@ + + + + + + + knuckledragger.utils — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.utils

+

Functions

+ + + + + + + + + + + + + + + + + + + + + +

expr_to_tptp(expr)

lemma_db()

Scan all modules for Proof objects and return a dictionary of them.

lemma_smt(thm[, by, sig])

Replacement for lemma that returns smtlib string for experimentation with other solvers

lemma_tptp(thm[, by, sig, timeout, command])

Returns tptp strings

open_binder(l)

z3_sort_tptp(sort)

+

Classes

+ + + + + + +

Calc(vars, lhs)

calc is for equational reasoning.

+
from knuckledragger.kernel import lemma, is_proof
+import z3
+import subprocess
+import sys
+
+
+class Calc:
+    """
+    calc is for equational reasoning.
+    One can write a sequence of formulas interspersed with useful lemmas.
+    """
+
+    def __init__(self, vars, lhs):
+        # TODO: hyps=None for conditional rewriting. assumpt, assume=[]
+        self.vars = vars
+        self.terms = [lhs]
+        self.lemmas = []
+
+    def ForAll(self, body):
+        if len(self.vars) == 0:
+            return body
+        else:
+            return z3.ForAll(self.vars, body)
+
+    def eq(self, rhs, by=[]):
+        self.lemmas.append(lemma(self.ForAll(self.terms[-1] == rhs), by=by))
+        self.terms.append(rhs)
+        return self
+
+    # TODO: lt, le, gt, ge chaining. Or custom op.
+
+    def __repr__(self):
+        return "... = " + repr(self.terms[-1])
+
+    def qed(self):
+        return lemma(self.ForAll(self.terms[0] == self.terms[-1]), by=self.lemmas)
+
+
+def lemma_smt(thm: z3.BoolRef, by=[], sig=[]) -> list[str]:
+    """
+    Replacement for lemma that returns smtlib string for experimentation with other solvers
+    """
+    output = []
+    output.append(";;declarations")
+    for f in sig:
+        if isinstance(f, z3.FuncDeclRef):
+            output.append(f.sexpr())
+        elif isinstance(f, z3.SortRef):
+            output.append("(declare-sort " + f.sexpr() + " 0)")
+        elif isinstance(f, z3.ExprRef):
+            output.append(f.decl().sexpr())
+    output.append(";;axioms")
+    for e in by:
+        if is_proof(e):
+            output.append("(assert " + e.thm.sexpr() + ")")
+    output.append(";;goal")
+    output.append("(assert " + z3.Not(thm).sexpr() + ")")
+    output.append("(check-sat)")
+    return output
+
+
+def open_binder(l: z3.QuantifierRef):
+    vars = [
+        z3.Const(l.var_name(i).upper(), l.var_sort(i))
+        for i in reversed(range(l.num_vars()))
+    ]
+    return vars, z3.substitute_vars(l.body(), *vars)
+
+
+def expr_to_tptp(expr: z3.ExprRef):
+    if isinstance(expr, z3.IntNumRef):
+        return str(expr.as_string())
+    elif isinstance(expr, z3.QuantifierRef):
+        vars, body = open_binder(expr)
+        body = expr_to_tptp(body)
+        vs = ", ".join([v.sexpr() + ":" + z3_sort_tptp(v.sort()) for v in vars])
+        if expr.is_forall():
+            return f"(![{vs}] : {body})"
+        elif expr.is_exists():
+            return f"(?[{vs}] : {body})"
+        elif expr.is_lambda():
+            return f"(^[{vs}] : {body})"
+    children = list(map(expr_to_tptp, expr.children()))
+    head = expr.decl().name()
+    if head == "true":
+        return "$true"
+    elif head == "false":
+        return "$false"
+    elif head == "and":
+        return "({})".format(" & ".join(children))
+    elif head == "or":
+        return "({})".format(" | ".join(children))
+    elif head == "=":
+        return "({} = {})".format(children[0], children[1])
+    elif head == "=>":
+        return "({} => {})".format(children[0], children[1])
+    elif head == "not":
+        return "~({})".format(children[0])
+    elif head == "ite":
+        return "$ite({}, {}, {})".format(*children)
+    elif head == "<":
+        return "$less({},{})".format(*children)
+    elif head == "<=":
+        return "$lesseq({},{})".format(*children)
+    elif head == ">":
+        return "$greater({},{})".format(*children)
+    elif head == ">=":
+        return "$greatereq({},{})".format(*children)
+    elif head == "+":
+        return "$sum({},{})".format(*children)
+    elif head == "-":
+        return "$difference({},{})".format(*children)
+    elif head == "*":
+        return "$product({},{})".format(*children)
+    elif head == "/":
+        return "$quotient({},{})".format(*children)
+    else:
+        if len(children) == 0:
+            return head
+        return f"{head}({', '.join(children)})"
+
+
+z3.ExprRef.tptp = expr_to_tptp
+
+
+def z3_sort_tptp(sort: z3.SortRef):
+    match sort.name():
+        case "Int":
+            return "$int"
+        case "Bool":
+            return "$o"
+        case "Real":
+            return "$real"
+        case "Array":
+            return "({} > {})".format(
+                z3_sort_tptp(sort.domain()), z3_sort_tptp(sort.range())
+            )
+        case x:
+            return x.lower()
+
+
+z3.SortRef.tptp = z3_sort_tptp
+
+
+def lemma_tptp(thm: z3.BoolRef, by=[], sig=[], timeout=None, command=None):
+    """
+    Returns tptp strings
+    """
+    output = []
+    for f in sig:
+        if isinstance(f, z3.FuncDeclRef):
+            dom = " * ".join([f.domain(i).tptp() for i in range(f.arity())])
+            output.append(f"tff(sig, type, {f.name()} : ({dom}) > {f.range().tptp()}).")
+        elif isinstance(f, z3.SortRef):
+            output.append(f"tff(sig, type, {f.tptp()} : $tType).")
+        elif isinstance(f, z3.ExprRef):
+            output.append(f"tff(sig, type, {f.sexpr()} : {f.sort().tptp()}).")
+    for e in by:
+        if is_proof(e):
+            output.append(f"tff(hyp, axiom, {e.thm.tptp()} ).")
+    output.append(f"tff(goal,conjecture,{thm.tptp()} ).")
+    if command == None:
+        return output
+    else:
+        with open("/tmp/temp.p", "w") as f:
+            f.writelines(output)
+        command.append("/tmp/temp.p")
+        res = subprocess.run(
+            command,
+            timeout=timeout,
+            capture_output=True,
+        )
+        return res
+
+
+def lemma_db():
+    """Scan all modules for Proof objects and return a dictionary of them."""
+    db = {}
+    for modname, mod in sys.modules.items():
+        thms = {name: thm for name, thm in mod.__dict__.items() if is_proof(thm)}
+        if len(thms) > 0:
+            db[modname] = thms
+    return db
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.utils.lemma_db.html b/_autosummary/knuckledragger.utils.lemma_db.html new file mode 100644 index 0000000..50e5154 --- /dev/null +++ b/_autosummary/knuckledragger.utils.lemma_db.html @@ -0,0 +1,135 @@ + + + + + + + knuckledragger.utils.lemma_db — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.utils.lemma_db

+
+
+knuckledragger.utils.lemma_db()
+

Scan all modules for Proof objects and return a dictionary of them.

+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.utils.lemma_smt.html b/_autosummary/knuckledragger.utils.lemma_smt.html new file mode 100644 index 0000000..f70a8fe --- /dev/null +++ b/_autosummary/knuckledragger.utils.lemma_smt.html @@ -0,0 +1,135 @@ + + + + + + + knuckledragger.utils.lemma_smt — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

knuckledragger.utils.lemma_smt

+
+
+knuckledragger.utils.lemma_smt(thm: BoolRef, by=[], sig=[]) → list[str]
+

Replacement for lemma that returns smtlib string for experimentation with other solvers

+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.utils.lemma_tptp.html b/_autosummary/knuckledragger.utils.lemma_tptp.html new file mode 100644 index 0000000..3108722 --- /dev/null +++ b/_autosummary/knuckledragger.utils.lemma_tptp.html @@ -0,0 +1,135 @@ + + + + + + + knuckledragger.utils.lemma_tptp — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
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knuckledragger.utils.lemma_tptp

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+knuckledragger.utils.lemma_tptp(thm: BoolRef, by=[], sig=[], timeout=None, command=None)
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Returns tptp strings

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+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.utils.open_binder.html b/_autosummary/knuckledragger.utils.open_binder.html new file mode 100644 index 0000000..a592add --- /dev/null +++ b/_autosummary/knuckledragger.utils.open_binder.html @@ -0,0 +1,134 @@ + + + + + + + knuckledragger.utils.open_binder — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + +
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knuckledragger.utils.open_binder

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+knuckledragger.utils.open_binder(l: QuantifierRef)
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+ + + + \ No newline at end of file diff --git a/_autosummary/knuckledragger.utils.z3_sort_tptp.html b/_autosummary/knuckledragger.utils.z3_sort_tptp.html new file mode 100644 index 0000000..ce13a7d --- /dev/null +++ b/_autosummary/knuckledragger.utils.z3_sort_tptp.html @@ -0,0 +1,132 @@ + + + + + + + knuckledragger.utils.z3_sort_tptp — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + +
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+

knuckledragger.utils.z3_sort_tptp

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+knuckledragger.utils.z3_sort_tptp(sort: SortRef)
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+ + + + \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.kernel.axiom.rst.txt b/_sources/_autosummary/knuckledragger.kernel.axiom.rst.txt new file mode 100644 index 0000000..2901db9 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.kernel.axiom.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.kernel.axiom +=========================== + +.. currentmodule:: knuckledragger.kernel + +.. autofunction:: axiom \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.kernel.define.rst.txt b/_sources/_autosummary/knuckledragger.kernel.define.rst.txt new file mode 100644 index 0000000..8d410ae --- /dev/null +++ b/_sources/_autosummary/knuckledragger.kernel.define.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.kernel.define +============================ + +.. currentmodule:: knuckledragger.kernel + +.. autofunction:: define \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.kernel.is_proof.rst.txt b/_sources/_autosummary/knuckledragger.kernel.is_proof.rst.txt new file mode 100644 index 0000000..d00b5b2 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.kernel.is_proof.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.kernel.is\_proof +=============================== + +.. currentmodule:: knuckledragger.kernel + +.. autofunction:: is_proof \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.kernel.lemma.rst.txt b/_sources/_autosummary/knuckledragger.kernel.lemma.rst.txt new file mode 100644 index 0000000..5f51bc2 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.kernel.lemma.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.kernel.lemma +=========================== + +.. currentmodule:: knuckledragger.kernel + +.. autofunction:: lemma \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.kernel.rst.txt b/_sources/_autosummary/knuckledragger.kernel.rst.txt new file mode 100644 index 0000000..43fde69 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.kernel.rst.txt @@ -0,0 +1,55 @@ +knuckledragger.kernel +===================== + +.. automodule:: knuckledragger.kernel + + + + .. rubric:: Module Attributes + + .. autosummary:: + + defns + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + axiom + define + is_proof + lemma + + + + + + .. rubric:: Classes + + .. autosummary:: + + Defn + + + + + + .. rubric:: Exceptions + + .. autosummary:: + + LemmaError + + + + + + + +.. literalinclude:: ../../knuckledragger/kernel.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.notation.QExists.rst.txt b/_sources/_autosummary/knuckledragger.notation.QExists.rst.txt new file mode 100644 index 0000000..991e8a0 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.notation.QExists.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.notation.QExists +=============================== + +.. currentmodule:: knuckledragger.notation + +.. autofunction:: QExists \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.notation.QForAll.rst.txt b/_sources/_autosummary/knuckledragger.notation.QForAll.rst.txt new file mode 100644 index 0000000..c777e7e --- /dev/null +++ b/_sources/_autosummary/knuckledragger.notation.QForAll.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.notation.QForAll +=============================== + +.. currentmodule:: knuckledragger.notation + +.. autofunction:: QForAll \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.notation.lookup_cons_recog.rst.txt b/_sources/_autosummary/knuckledragger.notation.lookup_cons_recog.rst.txt new file mode 100644 index 0000000..88de256 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.notation.lookup_cons_recog.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.notation.lookup\_cons\_recog +=========================================== + +.. currentmodule:: knuckledragger.notation + +.. autofunction:: lookup_cons_recog \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.notation.rst.txt b/_sources/_autosummary/knuckledragger.notation.rst.txt new file mode 100644 index 0000000..2508fa0 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.notation.rst.txt @@ -0,0 +1,42 @@ +knuckledragger.notation +======================= + +.. automodule:: knuckledragger.notation + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + QExists + QForAll + lookup_cons_recog + + + + + + .. rubric:: Classes + + .. autosummary:: + + SortDispatch + + + + + + + + + + + +.. literalinclude:: ../../knuckledragger/notation.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.rst.txt b/_sources/_autosummary/knuckledragger.rst.txt new file mode 100644 index 0000000..02609e5 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.rst.txt @@ -0,0 +1,38 @@ +knuckledragger +============== + +.. automodule:: knuckledragger + + + + + + + + + + + + + + + + + + + +.. rubric:: Modules + +.. autosummary:: + :toctree: + :recursive: + + kernel + notation + theories + utils + + + +.. literalinclude:: ../../knuckledragger.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.theories.Int.rst.txt b/_sources/_autosummary/knuckledragger.theories.Int.rst.txt new file mode 100644 index 0000000..4f61736 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.theories.Int.rst.txt @@ -0,0 +1,27 @@ +knuckledragger.theories.Int +=========================== + +.. automodule:: knuckledragger.theories.Int + + + + + + + + + + + + + + + + + + + + + +.. literalinclude:: ../../knuckledragger/theories/Int.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.theories.List.rst.txt b/_sources/_autosummary/knuckledragger.theories.List.rst.txt new file mode 100644 index 0000000..56a8070 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.theories.List.rst.txt @@ -0,0 +1,27 @@ +knuckledragger.theories.List +============================ + +.. automodule:: knuckledragger.theories.List + + + + + + + + + + + + + + + + + + + + + +.. literalinclude:: ../../knuckledragger/theories/List.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.theories.Nat.induct.rst.txt b/_sources/_autosummary/knuckledragger.theories.Nat.induct.rst.txt new file mode 100644 index 0000000..f64e75f --- /dev/null +++ b/_sources/_autosummary/knuckledragger.theories.Nat.induct.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.theories.Nat.induct +================================== + +.. currentmodule:: knuckledragger.theories.Nat + +.. autofunction:: induct \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.theories.Nat.rst.txt b/_sources/_autosummary/knuckledragger.theories.Nat.rst.txt new file mode 100644 index 0000000..7fd336c --- /dev/null +++ b/_sources/_autosummary/knuckledragger.theories.Nat.rst.txt @@ -0,0 +1,40 @@ +knuckledragger.theories.Nat +=========================== + +.. automodule:: knuckledragger.theories.Nat + + + + .. rubric:: Module Attributes + + .. autosummary:: + + Nat + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + induct + + + + + + + + + + + + + + + +.. literalinclude:: ../../knuckledragger/theories/Nat.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.theories.Real.rst.txt b/_sources/_autosummary/knuckledragger.theories.Real.rst.txt new file mode 100644 index 0000000..e7ffff5 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.theories.Real.rst.txt @@ -0,0 +1,27 @@ +knuckledragger.theories.Real +============================ + +.. automodule:: knuckledragger.theories.Real + + + + + + + + + + + + + + + + + + + + + +.. literalinclude:: ../../knuckledragger/theories/Real.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.theories.Seq.rst.txt b/_sources/_autosummary/knuckledragger.theories.Seq.rst.txt new file mode 100644 index 0000000..43d5edb --- /dev/null +++ b/_sources/_autosummary/knuckledragger.theories.Seq.rst.txt @@ -0,0 +1,27 @@ +knuckledragger.theories.Seq +=========================== + +.. automodule:: knuckledragger.theories.Seq + + + + + + + + + + + + + + + + + + + + + +.. literalinclude:: ../../knuckledragger/theories/Seq.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.theories.rst.txt b/_sources/_autosummary/knuckledragger.theories.rst.txt new file mode 100644 index 0000000..3e7f228 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.theories.rst.txt @@ -0,0 +1,39 @@ +knuckledragger.theories +======================= + +.. automodule:: knuckledragger.theories + + + + + + + + + + + + + + + + + + + +.. rubric:: Modules + +.. autosummary:: + :toctree: + :recursive: + + Int + List + Nat + Real + Seq + + + +.. literalinclude:: ../../knuckledragger/theories.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.utils.expr_to_tptp.rst.txt b/_sources/_autosummary/knuckledragger.utils.expr_to_tptp.rst.txt new file mode 100644 index 0000000..6426b8a --- /dev/null +++ b/_sources/_autosummary/knuckledragger.utils.expr_to_tptp.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.utils.expr\_to\_tptp +=================================== + +.. currentmodule:: knuckledragger.utils + +.. autofunction:: expr_to_tptp \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.utils.lemma_db.rst.txt b/_sources/_autosummary/knuckledragger.utils.lemma_db.rst.txt new file mode 100644 index 0000000..9a1cd10 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.utils.lemma_db.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.utils.lemma\_db +============================== + +.. currentmodule:: knuckledragger.utils + +.. autofunction:: lemma_db \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.utils.lemma_smt.rst.txt b/_sources/_autosummary/knuckledragger.utils.lemma_smt.rst.txt new file mode 100644 index 0000000..39f4d0c --- /dev/null +++ b/_sources/_autosummary/knuckledragger.utils.lemma_smt.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.utils.lemma\_smt +=============================== + +.. currentmodule:: knuckledragger.utils + +.. autofunction:: lemma_smt \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.utils.lemma_tptp.rst.txt b/_sources/_autosummary/knuckledragger.utils.lemma_tptp.rst.txt new file mode 100644 index 0000000..d5fff8b --- /dev/null +++ b/_sources/_autosummary/knuckledragger.utils.lemma_tptp.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.utils.lemma\_tptp +================================ + +.. currentmodule:: knuckledragger.utils + +.. autofunction:: lemma_tptp \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.utils.open_binder.rst.txt b/_sources/_autosummary/knuckledragger.utils.open_binder.rst.txt new file mode 100644 index 0000000..6dee6a4 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.utils.open_binder.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.utils.open\_binder +================================= + +.. currentmodule:: knuckledragger.utils + +.. autofunction:: open_binder \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.utils.rst.txt b/_sources/_autosummary/knuckledragger.utils.rst.txt new file mode 100644 index 0000000..44be779 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.utils.rst.txt @@ -0,0 +1,45 @@ +knuckledragger.utils +==================== + +.. automodule:: knuckledragger.utils + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + expr_to_tptp + lemma_db + lemma_smt + lemma_tptp + open_binder + z3_sort_tptp + + + + + + .. rubric:: Classes + + .. autosummary:: + + Calc + + + + + + + + + + + +.. literalinclude:: ../../knuckledragger/utils.py + :language: python \ No newline at end of file diff --git a/_sources/_autosummary/knuckledragger.utils.z3_sort_tptp.rst.txt b/_sources/_autosummary/knuckledragger.utils.z3_sort_tptp.rst.txt new file mode 100644 index 0000000..e78fd51 --- /dev/null +++ b/_sources/_autosummary/knuckledragger.utils.z3_sort_tptp.rst.txt @@ -0,0 +1,6 @@ +knuckledragger.utils.z3\_sort\_tptp +=================================== + +.. currentmodule:: knuckledragger.utils + +.. autofunction:: z3_sort_tptp \ No newline at end of file diff --git a/_sources/index.rst.txt b/_sources/index.rst.txt new file mode 100644 index 0000000..ed8bac1 --- /dev/null +++ b/_sources/index.rst.txt @@ -0,0 +1,22 @@ +Welcome to knuckledragger's documentation! +========================================== + +.. include:: ../README.md + :parser: myst_parser.sphinx_ + +.. toctree:: + :maxdepth: 2 + :caption: Contents: + +.. autosummary:: + :toctree: _autosummary + :recursive: + + knuckledragger + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` +* :ref:`search` diff --git a/_static/_sphinx_javascript_frameworks_compat.js b/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. 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+ if (re2.test(w)) + w = w + "e"; + else if (re3.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + else if (re4.test(w)) + w = w + "e"; + } + } + + // Step 1c + re = /^(.+?)y$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(s_v); + if (re.test(stem)) + w = stem + "i"; + } + + // Step 2 + re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step2list[suffix]; + } + + // Step 3 + re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step3list[suffix]; + } + + // Step 4 + re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/; + re2 = /^(.+?)(s|t)(ion)$/; + if (re.test(w)) { + var fp = re.exec(w); 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+ +/** + * Simple result scoring code. + */ +if (typeof Scorer === "undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms, highlightTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + const contentRoot = document.documentElement.dataset.content_root; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = contentRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = contentRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) { + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + // highlight search terms in the description + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + } + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms, anchor) + ); + // highlight search terms in the summary + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + "Search finished, found ${resultCount} page(s) matching the search query." + ).replace('${resultCount}', resultCount); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms, + highlightTerms, +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms, highlightTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms, highlightTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; +// Helper function used by query() to order search results. +// Each input is an array of [docname, title, anchor, descr, score, filename]. +// Order the results by score (in opposite order of appearance, since the +// `_displayNextItem` function uses pop() to retrieve items) and then alphabetically. +const _orderResultsByScoreThenName = (a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString, anchor) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + for (const removalQuery of [".headerlink", "script", "style"]) { + htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() }); + } + if (anchor) { + const anchorContent = htmlElement.querySelector(`[role="main"] ${anchor}`); + if (anchorContent) return anchorContent.textContent; + + console.warn( + `Anchored content block not found. Sphinx search tries to obtain it via DOM query '[role=main] ${anchor}'. Check your theme or template.` + ); + } + + // if anchor not specified or not found, fall back to main content + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent) return docContent.textContent; + + console.warn( + "Content block not found. Sphinx search tries to obtain it via DOM query '[role=main]'. Check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + _parseQuery: (query) => { + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + return [query, searchTerms, excludedTerms, highlightTerms, objectTerms]; + }, + + /** + * execute search (requires search index to be loaded) + */ + _performSearch: (query, searchTerms, excludedTerms, highlightTerms, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // Collect multiple result groups to be sorted separately and then ordered. + // Each is an array of [docname, title, anchor, descr, score, filename]. + const normalResults = []; + const nonMainIndexResults = []; + + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase().trim(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + const score = Math.round(Scorer.title * queryLower.length / title.length); + const boost = titles[file] === title ? 1 : 0; // add a boost for document titles + normalResults.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score + boost, + filenames[file], + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id, isMain] of foundEntries) { + const score = Math.round(100 * queryLower.length / entry.length); + const result = [ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]; + if (isMain) { + normalResults.push(result); + } else { + nonMainIndexResults.push(result); + } + } + } + } + + // lookup as object + objectTerms.forEach((term) => + normalResults.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + normalResults.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) { + normalResults.forEach((item) => (item[4] = Scorer.score(item))); + nonMainIndexResults.forEach((item) => (item[4] = Scorer.score(item))); + } + + // Sort each group of results by score and then alphabetically by name. + normalResults.sort(_orderResultsByScoreThenName); + nonMainIndexResults.sort(_orderResultsByScoreThenName); + + // Combine the result groups in (reverse) order. + // Non-main index entries are typically arbitrary cross-references, + // so display them after other results. + let results = [...nonMainIndexResults, ...normalResults]; + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + return results.reverse(); + }, + + query: (query) => { + const [searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms] = Search._parseQuery(query); + const results = Search._performSearch(searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms, highlightTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + if (!terms.hasOwnProperty(word)) { + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + } + if (!titleTerms.hasOwnProperty(word)) { + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: titleTerms[term], score: Scorer.partialTitle }); + }); + } + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (!fileMap.has(file)) fileMap.set(file, [word]); + else if (fileMap.get(file).indexOf(word) === -1) fileMap.get(file).push(word); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords, anchor) => { + const text = Search.htmlToText(htmlText, anchor); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/_static/sphinx_highlight.js b/_static/sphinx_highlight.js new file mode 100644 index 0000000..8a96c69 --- /dev/null +++ b/_static/sphinx_highlight.js @@ -0,0 +1,154 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + const rest = document.createTextNode(val.substr(pos + text.length)); + parent.insertBefore( + span, + parent.insertBefore( + rest, + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + /* There may be more occurrences of search term in this node. So call this + * function recursively on the remaining fragment. + */ + _highlight(rest, addItems, text, className); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

' + + '' + + _("Hide Search Matches") + + "

" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(() => { + /* Do not call highlightSearchWords() when we are on the search page. + * It will highlight words from the *previous* search query. + */ + if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords(); + SphinxHighlight.initEscapeListener(); +}); diff --git a/genindex.html b/genindex.html new file mode 100644 index 0000000..b272aac --- /dev/null +++ b/genindex.html @@ -0,0 +1,307 @@ + + + + + + Index — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Index
    • +
  • +
    • +
+
+
+
+
+ + +

Index

+ +
+ A + | D + | E + | I + | K + | L + | M + | O + | Q + | Z + +
+

A

+ + +
+ +

D

+ + +
+ +

E

+ + +
+ +

I

+ + + +
+ +

K

+ + + +
    +
  • + knuckledragger + +
    • +
  • + knuckledragger.kernel + +
    • +
  • + knuckledragger.notation + +
    • +
  • + knuckledragger.theories + +
    • +
  • + knuckledragger.theories.Int + +
    • +
    +
  • + knuckledragger.theories.List + +
    • +
  • + knuckledragger.theories.Nat + +
    • +
  • + knuckledragger.theories.Real + +
    • +
  • + knuckledragger.theories.Seq + +
    • +
  • + knuckledragger.utils + +
    • +
+ +

L

+ + + +
+ +

M

+ + +
+ +

O

+ + +
+ +

Q

+ + + +
+ +

Z

+ + +
+ + + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 0000000..06a10fc --- /dev/null +++ b/index.html @@ -0,0 +1,166 @@ + + + + + + + Welcome to knuckledragger’s documentation! — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Welcome to knuckledragger’s documentation!

+
+

Knuckledragger

+

Open In Colab

+drawing +

Knuckledragger is an attempt at creating a down to earth, highly automated interactive proof assistant in python. It is not attempting to be the most interesting, expressive, or flexible logic in the world. The goal is to support applications like software verification, calculus, equational reasoning, and numerical bounds. A no-install colab tutorial is available here

+
+
+

Installation

+
python3 -m pip install git+https://github.com/philzook58/knuckledragger.git
+
+
+

Or to install locally

+
git clone https://github.com/philzook58/knuckledragger.git
+cd knuckledragger
+python3 -m pip install -e .
+
+
+
+
+

Blog Posts

+ +
+
+

Design

+

It is not desirable or within my capabilities to build a giant universe in which to live. The goal is to take a subtle blade and bolt together things that already exist.

+

Using widespread and commonly supported languages gives a huge leg up in terms of tooling and audience. Python is the modern lingua franca of computing. It has a first class interactive experience and extensive bindings to projects in other languages.

+

Core functionality comes from Z3. The Z3 python api is a de facto standard. The term and formula data structures of knuckledragger are literally Z3 python terms and formula. To some degree, knuckledragger is a metalayer to guide Z3 through proofs it could perhaps do on its own, but it would get lost.

+

A hope is to be able to use easy access to Jupyter, copilot, ML ecosystems, sympy, cvxpy, numpy, scipy, Julia, Prolog, Maude, calcium, flint, Mathematica, and sage will make metaprogramming in this system very powerful. I maintain the option to just trust these results but hopefully they can be translated into arguments the kernel can understand.

+

The core logic is more or less multi-sorted first order logic aka SMT-LIB2.

+

Big features that ATPs do not often support are induction, definitions, and other axiom schema. Knuckledragger supports these.

+

Other theorem provers of interest: cvc5, Vampire, eprover, Twee, egglog, nanoCoP.

+

The de Bruijn criterion is going to be bent or broken in certain senses. Attention is paid to what is kernel and what is not. Proof objects are basically trees recording chains of lemmas discharged by Automated Theorem Prover (ATP) calls. Soundness will be attempted, accidental misuse will be made difficult but not impossible.

+

Isabelle and ACL2 are the strongest influences. If you want dependent type theory, you are at a level of investment and sophistication that is behooves you to be in another system. Should there be a strong automated DTT solver someday, I will reconsider.

+

I maintain the right to change my mind about anything.

+
+
+
+
+ + + + + + +

knuckledragger

+
+
+

Indices and tables

+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/objects.inv b/objects.inv new file mode 100644 index 0000000..aa4d90d Binary files /dev/null and b/objects.inv differ diff --git a/py-modindex.html b/py-modindex.html new file mode 100644 index 0000000..ad70f98 --- /dev/null +++ b/py-modindex.html @@ -0,0 +1,166 @@ + + + + + + Python Module Index — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Python Module Index
    • +
  • +
    • +
+
+
+
+
+ + +

Python Module Index

+ +
+ k +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
 
+ k
+ knuckledragger +
    + knuckledragger.kernel +
    + knuckledragger.notation +
    + knuckledragger.theories +
    + knuckledragger.theories.Int +
    + knuckledragger.theories.List +
    + knuckledragger.theories.Nat +
    + knuckledragger.theories.Real +
    + knuckledragger.theories.Seq +
    + knuckledragger.utils +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/search.html b/search.html new file mode 100644 index 0000000..e4f0cd2 --- /dev/null +++ b/search.html @@ -0,0 +1,121 @@ + + + + + + Search — knuckledragger 0.1 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Search
    • +
  • +
    • +
+
+
+
+
+ + + + +
+ +
+ +
+
+ +
+
+
+
+ + + + + + + + + \ No newline at end of file diff --git a/searchindex.js b/searchindex.js new file mode 100644 index 0000000..259b495 --- /dev/null +++ b/searchindex.js @@ -0,0 +1 @@ +Search.setIndex({"alltitles": {"Blog Posts": [[24, "blog-posts"]], "Design": [[24, "design"]], "Indices and tables": [[24, "indices-and-tables"]], "Installation": [[24, "installation"]], "Knuckledragger": [[24, "knuckledragger"]], "Welcome to knuckledragger\u2019s documentation!": [[24, null]], "knuckledragger": [[0, null]], "knuckledragger.kernel": [[1, null]], "knuckledragger.kernel.axiom": [[2, null]], "knuckledragger.kernel.define": [[3, null]], "knuckledragger.kernel.is_proof": [[4, null]], "knuckledragger.kernel.lemma": [[5, null]], "knuckledragger.notation": [[6, null]], "knuckledragger.notation.QExists": [[7, null]], "knuckledragger.notation.QForAll": [[8, null]], "knuckledragger.notation.lookup_cons_recog": [[9, null]], "knuckledragger.theories": [[10, null]], "knuckledragger.theories.Int": 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