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Last change
on this file since 2183 was
1882,
checked in by tranquil, 9 years ago
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big update, alas incomplete:
joint changed a bit, and all BE languages need to be updated
started development of blocks to aid preservation results, but still incomplete
if it breaks too many things, feel free to roll back
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File size:
1.6 KB
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| 1 | include "basics/types.ma". |
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| 2 | |
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| 3 | include "ASM/BitVectorTrie.ma". |
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| 4 | include "common/Identifiers.ma". |
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| 5 | include "common/AST.ma". |
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| 6 | |
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| 7 | axiom LabelTag : String. |
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| 8 | |
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| 9 | definition label ≝ identifier LabelTag. |
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| 10 | |
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| 11 | (* o'caml compiler doesn't make distinction between idents and labels *) |
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| 12 | definition label_to_ident: label → ident ≝ |
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| 13 | λl. |
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| 14 | match l with |
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| 15 | [ an_identifier l ⇒ an_identifier SymbolTag l |
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| 16 | ]. |
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| 17 | |
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| 18 | definition label_eq : ∀x,y:label. (x=y) + (x≠y) ≝ identifier_eq ?. |
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| 19 | |
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| 20 | definition graph : Type[0] → Type[0] ≝ identifier_map LabelTag. |
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| 21 | |
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| 22 | definition graph_fold ≝ |
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| 23 | λA, B: Type[0]. |
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| 24 | λf. |
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| 25 | λgraph: graph A. |
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| 26 | λseed: B. |
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| 27 | match graph with |
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| 28 | [ an_id_map map ⇒ fold A B f map seed |
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| 29 | ]. |
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| 30 | |
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| 31 | axiom graph_add: |
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| 32 | ∀A: Type[0]. |
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| 33 | ∀g: graph A. |
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| 34 | ∀l: label. |
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| 35 | ∀s: A. |
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| 36 | lookup ? ? (add ? ? g l s) l ≠ None ?. |
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| 37 | |
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| 38 | axiom graph_add_eq: |
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| 39 | ∀A: Type[0]. |
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| 40 | ∀g: graph A. |
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| 41 | ∀l: label. |
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| 42 | ∀s: A. |
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| 43 | lookup ? ? (add ? ? g l s) l = Some ? s. |
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| 44 | |
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| 45 | axiom graph_add_lookup: |
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| 46 | ∀A: Type[0]. |
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| 47 | ∀g: graph A. |
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| 48 | ∀l: label. |
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| 49 | ∀s: A. |
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| 50 | ∀to_insert: label. |
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| 51 | lookup ? ? g l ≠ None ? → lookup ? ? (add ? ? g to_insert s) l ≠ None ?. |
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| 52 | |
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| 53 | axiom graph_add_preserve : |
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| 54 | ∀A: Type[0]. |
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| 55 | ∀g: graph A. |
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| 56 | ∀l: label. |
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| 57 | ∀s: A. |
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| 58 | ∀to_insert: label. |
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| 59 | l ≠ to_insert → lookup ? ? g l = lookup ? ? (add ? ? g to_insert s) l. |
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| 60 | |
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| 61 | definition graph_num_nodes: |
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| 62 | ∀A: Type[0].graph A → ℕ ≝ λA,g.|g|. |
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| 63 | |
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| 64 | lemma graph_num_ind : ∀A : Type[0].∀P : graph A → Prop. |
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| 65 | (∀g.(∀g'.|g'|<|g| → P g') → P g) → ∀g.P g. |
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| 66 | #A#P#H#g |
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| 67 | lapply (refl ? (|g|)) |
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| 68 | generalize in ⊢(???%→?); |
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| 69 | #n lapply g -g |
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| 70 | @(nat_elim1 … n) |
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| 71 | #m #G #g #EQs @H >EQs #g' #DEQ @(G ? DEQ g' (refl …)) |
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| 72 | qed. |
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