Use sympy for time variable

stl.py

@@ -1,6 +1,4 @@
 # -*- coding: utf-8 -*-
-# TODO: create lens convenience functions
-#    x.lens().set()
 # TODO: create iso lens between sugar and non-sugar
 # TODO: supress + given a + (-b). i.e. want a - b
 
@@ -10,10 +8,12 @@ from typing import Union
 from enum import Enum
 from sympy import Symbol
 
+from lenses import lens
+
 VarKind = Enum("VarKind", ["x", "u", "w"])
 str_to_varkind = {"x": VarKind.x, "u": VarKind.u, "w": VarKind.w}
-dt = Symbol('dt', positive=True)
-
+dt_sym = Symbol('dt', positive=True)
+t_sym = Symbol('t', positive=True)
 
 class LinEq(namedtuple("LinEquality", ["terms", "op", "const"])):
     def __repr__(self):
@@ -30,7 +30,7 @@ class LinEq(namedtuple("LinEquality", ["terms", "op", "const"])):
 
 class Var(namedtuple("Var", ["kind", "id", "time"])):
     def __repr__(self):
-        time_str = "[t + {}]".format(self.time)
+        time_str = "[{}]".format(self.time)
         return "{k}{i}{t}".format(k=self.kind.name, i=self.id, t=time_str)
 
 
@@ -106,3 +106,23 @@ def walk(stl, bfs=False):
 
 def tree(stl):
     return {x:set(x.children()) for x in walk(stl) if x.children()}
+
+
+def time_lens(phi:"STL") -> lens:
+    return _time_lens(phi).bind(phi)
+
+
+def _time_lens(phi):
+    if isinstance(phi, LinEq):
+        return lens().terms.each_().var.time
+
+    if isinstance(phi, NaryOpSTL):
+        child_lens = [lens()[i].add_lens(_time_lens(c)) for i, c
+                      in enumerate(phi.children())]
+        return lens().args.tuple_(*child_lens).each_()
+    else:
+        return lens().arg.add_lens(_time_lens(phi.arg))
+
+
+def set_time(phi, *, t, dt=0.1):
+    return time_lens(phi).call("evalf", subs={t_sym: t, dt_sym: dt})

stl_parser.py

@@ -116,7 +116,7 @@ class STLVisitor(NodeVisitor):
         (var_kind, iden), time_node = children
 
         time_node = list(flatten(time_node))
-        time = time_node[0] if len(time_node) > 0 else 0
+        time = time_node[0] if len(time_node) > 0 else stl.t_sym
             
         return stl.Var(var_kind, iden, time)
 
@@ -124,13 +124,13 @@ class STLVisitor(NodeVisitor):
         return children[3]* children[5]
 
     def visit_prime(self, *_):
-        return -stl.dt
+        return -stl.dt_sym
 
     def visit_const(self, const, children):
         return float(const.text)
 
     def visit_dt(self, *_):
-        return stl.dt
+        return stl.dt_sym
 
     def visit_term(self, _, children):
         coeffs, var = children