author | blanchet |
Thu, 28 Aug 2014 00:40:38 +0200 | |
changeset 58061 | 3d060f43accb |
parent 57230 | src/HOL/Tools/SMT2/z3_new_replay_util.ML@ec5ff6bb2a92 |
child 58776 | 95e58e04e534 |
permissions | -rw-r--r-- |
58061 | 1 |
(* Title: HOL/Tools/SMT/z3_replay_util.ML |
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Author: Sascha Boehme, TU Muenchen |
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Helper functions required for Z3 proof replay. |
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*) |
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signature Z3_REPLAY_UTIL = |
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sig |
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(*theorem nets*) |
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val thm_net_of: ('a -> thm) -> 'a list -> 'a Net.net |
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val net_instances: (int * thm) Net.net -> cterm -> (int * thm) list |
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(*proof combinators*) |
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val under_assumption: (thm -> thm) -> cterm -> thm |
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val discharge: thm -> thm -> thm |
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(*a faster COMP*) |
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type compose_data |
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val precompose: (cterm -> cterm list) -> thm -> compose_data |
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val precompose2: (cterm -> cterm * cterm) -> thm -> compose_data |
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val compose: compose_data -> thm -> thm |
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(*simpset*) |
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val add_simproc: Simplifier.simproc -> Context.generic -> Context.generic |
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val make_simpset: Proof.context -> thm list -> simpset |
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end; |
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structure Z3_Replay_Util: Z3_REPLAY_UTIL = |
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struct |
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|
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(* theorem nets *) |
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fun thm_net_of f xthms = |
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let fun insert xthm = Net.insert_term (K false) (Thm.prop_of (f xthm), xthm) |
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in fold insert xthms Net.empty end |
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fun maybe_instantiate ct thm = |
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try Thm.first_order_match (Thm.cprop_of thm, ct) |
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|> Option.map (fn inst => Thm.instantiate inst thm) |
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|
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local |
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fun instances_from_net match f net ct = |
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let |
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val lookup = if match then Net.match_term else Net.unify_term |
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val xthms = lookup net (Thm.term_of ct) |
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fun select ct = map_filter (f (maybe_instantiate ct)) xthms |
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fun select' ct = |
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let val thm = Thm.trivial ct |
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in map_filter (f (try (fn rule => rule COMP thm))) xthms end |
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in (case select ct of [] => select' ct | xthms' => xthms') end |
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in |
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fun net_instances net = |
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instances_from_net false (fn f => fn (i, thm) => Option.map (pair i) (f thm)) |
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net |
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end |
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(* proof combinators *) |
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fun under_assumption f ct = |
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let val ct' = SMT_Util.mk_cprop ct in Thm.implies_intr ct' (f (Thm.assume ct')) end |
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fun discharge p pq = Thm.implies_elim pq p |
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(* a faster COMP *) |
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type compose_data = cterm list * (cterm -> cterm list) * thm |
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fun list2 (x, y) = [x, y] |
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fun precompose f rule = (f (Thm.cprem_of rule 1), f, rule) |
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fun precompose2 f rule = precompose (list2 o f) rule |
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fun compose (cvs, f, rule) thm = |
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discharge thm (Thm.instantiate ([], cvs ~~ f (Thm.cprop_of thm)) rule) |
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(* simpset *) |
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local |
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val antisym_le1 = mk_meta_eq @{thm order_class.antisym_conv} |
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val antisym_le2 = mk_meta_eq @{thm linorder_class.antisym_conv2} |
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val antisym_less1 = mk_meta_eq @{thm linorder_class.antisym_conv1} |
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val antisym_less2 = mk_meta_eq @{thm linorder_class.antisym_conv3} |
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fun eq_prop t thm = HOLogic.mk_Trueprop t aconv Thm.prop_of thm |
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fun dest_binop ((c as Const _) $ t $ u) = (c, t, u) |
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| dest_binop t = raise TERM ("dest_binop", [t]) |
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fun prove_antisym_le ctxt t = |
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let |
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val (le, r, s) = dest_binop t |
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val less = Const (@{const_name less}, Term.fastype_of le) |
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val prems = Simplifier.prems_of ctxt |
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in |
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(case find_first (eq_prop (le $ s $ r)) prems of |
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NONE => |
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find_first (eq_prop (HOLogic.mk_not (less $ r $ s))) prems |
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|> Option.map (fn thm => thm RS antisym_less1) |
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| SOME thm => SOME (thm RS antisym_le1)) |
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end |
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handle THM _ => NONE |
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fun prove_antisym_less ctxt t = |
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let |
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val (less, r, s) = dest_binop (HOLogic.dest_not t) |
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val le = Const (@{const_name less_eq}, Term.fastype_of less) |
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val prems = Simplifier.prems_of ctxt |
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in |
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(case find_first (eq_prop (le $ r $ s)) prems of |
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NONE => |
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find_first (eq_prop (HOLogic.mk_not (less $ s $ r))) prems |
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|> Option.map (fn thm => thm RS antisym_less2) |
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| SOME thm => SOME (thm RS antisym_le2)) |
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end |
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handle THM _ => NONE |
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val basic_simpset = |
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simpset_of (put_simpset HOL_ss @{context} |
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addsimps @{thms field_simps times_divide_eq_right times_divide_eq_left arith_special |
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arith_simps rel_simps array_rules z3div_def z3mod_def} |
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addsimprocs [@{simproc binary_int_div}, @{simproc binary_int_mod}, |
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Simplifier.simproc_global @{theory} "fast_int_arith" [ |
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"(m::int) < n", "(m::int) <= n", "(m::int) = n"] Lin_Arith.simproc, |
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Simplifier.simproc_global @{theory} "antisym_le" ["(x::'a::order) <= y"] prove_antisym_le, |
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Simplifier.simproc_global @{theory} "antisym_less" ["~ (x::'a::linorder) < y"] |
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prove_antisym_less]) |
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|
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structure Simpset = Generic_Data |
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( |
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type T = simpset |
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val empty = basic_simpset |
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val extend = I |
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val merge = Simplifier.merge_ss |
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) |
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in |
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|
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fun add_simproc simproc context = |
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Simpset.map (simpset_map (Context.proof_of context) |
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(fn ctxt => ctxt addsimprocs [simproc])) context |
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|
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fun make_simpset ctxt rules = |
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simpset_of (put_simpset (Simpset.get (Context.Proof ctxt)) ctxt addsimps rules) |
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|
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end |
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|
57229 | 150 |
end; |