Last change
on this file since 2942 was
2942,
checked in by sacerdot, 7 years ago

Many changes:
 Coloured graphs are now specified in terms of livebefore
 Type of livebefore changed so that it is now a valuation transformer
 Several axioms can now be inhabited in ERTLptrToLTLProof
Problems:
ERTLtoERTLptrOK is broken beyond my understanding. This pass should have
been unaffected by the changes, but it is not so. Why?

File size:
932 bytes

Line  

1  include "ERTLptr/liveness.ma". 

2  

3  inductive decision: Type[0] ≝ 

4   decision_spill: nat → decision 

5   decision_colour: Register → decision. 

6  

7  (* prop_colouring is the non interferece 

8  prop_colouring 2 and 3 together say that spilled_no is the number of spilled 

9  registers *) 

10  record coloured_graph (before: valuation register_lattice): Type[1] ≝ 

11  { colouring: vertex → decision 

12  ; spilled_no: nat 

13  ; prop_colouring: ∀l. ∀v1, v2: vertex.v1 ≠v2 → 

14  lives v1 (before l) → lives v2 (before l) → colouring v1 ≠ colouring v2 

15  ; prop_spilled_no: (*CSC: the existguarded premise is just to make the proof more general *) 

16  ∀v1:vertex. (∃l. bool_to_Prop (lives v1 (before l))) → ∀i. colouring v1 = decision_spill i → i < spilled_no 

17  }. 

18  

19  definition coloured_graph_computer ≝ 

20  ∀globals. 

21  ∀fn:joint_internal_function ERTLptr globals. 

22  ∀liveafter. 

23  coloured_graph (livebefore globals fn liveafter). 

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