source: src/RTLabs/syntax.ma @ 1705

Last change on this file since 1705 was 1705, checked in by campbell, 9 years ago

Checkpoint RTLabs labelling soundness work.

File size: 3.3 KB
RevLine 
[639]1include "basics/logic.ma".
2
[747]3include "common/AST.ma".
[720]4include "common/CostLabel.ma".
[702]5include "common/FrontEndOps.ma".
6include "common/Registers.ma".
[639]7
[702]8include "ASM/Vector.ma".
9include "common/Graphs.ma".
[639]10
11inductive statement : Type[0] ≝
12| St_skip : label → statement
13| St_cost : costlabel → label → statement
[1056]14| St_const : register → constant → label → statement
[1626]15| St_op1 : ∀t,t'. unary_operation t' t → register → register → label → statement (* destination source *)
[1116]16| St_op2 : binary_operation → register → register → register → label → statement (* destination source1 source2 *)
[887]17| St_load : memory_chunk → register → register → label → statement
18| St_store : memory_chunk → register → register → label → statement
[816]19| St_call_id : ident → list register → option register → label → statement
20| St_call_ptr : register → list register → option register → label → statement
[1680]21(* We're not using these just now, and they'd make the Traces.ma proofs more difficult.
[816]22| St_tailcall_id : ident → list register → statement
23| St_tailcall_ptr : register → list register → statement
[1680]24*)
[888]25| St_cond : register → label → label → statement
[750]26| St_jumptable : register → list label → statement
[765]27| St_return : statement
[639]28.
29
[1626]30definition env_has : list (register × typ) → register → typ → Prop ≝
31λl,r,t. Exists ? (λx. 〈r,t〉 = x) l.
32
33definition statement_typed : list (register × typ) → statement → Prop ≝
34λe,s. match s with
35[ St_op1 t t' _ r r' _ ⇒ env_has e r t ∧ env_has e r' t'
36| _ ⇒ True
37].
38
[1316]39definition labels_P : (label → Prop) → statement → Prop ≝
40λP,s. match s with
41[ St_skip l ⇒ P l
42| St_cost _ l ⇒ P l
43| St_const _ _ l ⇒ P l
[1369]44| St_op1 _ _ _ _ _ l ⇒ P l
[1316]45| St_op2 _ _ _ _ l ⇒ P l
46| St_load _ _ _ l ⇒ P l
47| St_store _ _ _ l ⇒ P l
48| St_call_id _ _ _ l ⇒ P l
49| St_call_ptr _ _ _ l ⇒ P l
[1680]50(*
[1316]51| St_tailcall_id _ _ ⇒ True
52| St_tailcall_ptr _ _ ⇒ True
[1680]53*)
[1316]54| St_cond _ l1 l2 ⇒ P l1 ∧ P l2
55| St_jumptable _ ls ⇒ All ? P ls
56| St_return ⇒ True
57].
58
59lemma labels_P_mp : ∀P,Q. (∀l. P l → Q l) → ∀s.labels_P P s → labels_P Q s.
60#P #Q #H * /3/
61#r #l #l' * /3/
62qed.
63
64definition labels_present : graph statement → statement → Prop ≝
65λg,s. labels_P (present ?? g) s.
66
[1626]67definition forall_nodes : ∀A.∀P:A → Prop. graph A → Prop ≝
68λA,P,g. ∀l,n. lookup ?? g l = Some ? n → P n.
69
[1316]70definition graph_closed : graph statement → Prop ≝
[1626]71  λg. forall_nodes ? (labels_present g) g.
72definition graph_typed : list (register × typ) → graph statement → Prop ≝
73  λe. forall_nodes ? (statement_typed e).
[1316]74
[639]75record internal_function : Type[0] ≝
[738]76{ f_labgen    : universe LabelTag
77; f_reggen    : universe RegisterTag
[887]78; f_result    : option (register × typ)
79; f_params    : list (register × typ)
80; f_locals    : list (register × typ)
[639]81; f_stacksize : nat
82; f_graph     : graph statement
[1316]83; f_closed    : graph_closed f_graph
[1626]84; f_typed     : graph_typed (f_locals @ f_params) f_graph
[1316]85; f_entry     : Σl:label. present ?? f_graph l
86; f_exit      : Σl:label. present ?? f_graph l
[639]87}.
88
[764]89(* Note that the global variables will be initialised by the code in main
[1139]90   by this stage, so the only initialisation data is the amount of space to
91   allocate. *)
[639]92
[1675]93definition RTLabs_program ≝ program (λ_.fundef internal_function) nat.
94
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97
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