author | boehmes |
Thu, 03 Dec 2009 15:56:06 +0100 | |
changeset 34010 | ac78f5cdc430 |
parent 33895 | 3e7c51bbeb24 |
child 35116 | 133be405a6f1 |
permissions | -rw-r--r-- |
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(* Title: HOL/SMT/Tools/smt_normalize.ML |
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Author: Sascha Boehme, TU Muenchen |
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Normalization steps on theorems required by SMT solvers: |
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* unfold trivial let expressions, |
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* replace negative numerals by negated positive numerals, |
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* embed natural numbers into integers, |
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* add extra rules specifying types and constants which occur frequently, |
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* lift lambda terms, |
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* make applications explicit for functions with varying number of arguments, |
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* fully translate into object logic, add universal closure. |
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*) |
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signature SMT_NORMALIZE = |
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sig |
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val normalize_rule: Proof.context -> thm -> thm |
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val instantiate_free: cterm * cterm -> thm -> thm |
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val discharge_definition: cterm -> thm -> thm |
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val trivial_let: Proof.context -> thm list -> thm list |
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val positive_numerals: Proof.context -> thm list -> thm list |
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val nat_as_int: Proof.context -> thm list -> thm list |
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val unfold_defs: bool Config.T |
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val add_pair_rules: Proof.context -> thm list -> thm list |
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val add_fun_upd_rules: Proof.context -> thm list -> thm list |
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val add_abs_min_max_rules: Proof.context -> thm list -> thm list |
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datatype config = |
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RewriteTrivialLets | |
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RewriteNegativeNumerals | |
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RewriteNaturalNumbers | |
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AddPairRules | |
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AddFunUpdRules | |
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AddAbsMinMaxRules |
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val normalize: config list -> Proof.context -> thm list -> |
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cterm list * thm list |
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val setup: theory -> theory |
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end |
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structure SMT_Normalize: SMT_NORMALIZE = |
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struct |
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local |
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val all1 = @{lemma "All P == ALL x. P x" by (rule reflexive)} |
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val all2 = @{lemma "All == (%P. ALL x. P x)" by (rule reflexive)} |
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val ex1 = @{lemma "Ex P == EX x. P x" by (rule reflexive)} |
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val ex2 = @{lemma "Ex == (%P. EX x. P x)" by (rule reflexive)} |
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val let1 = @{lemma "Let c P == let x = c in P x" by (rule reflexive)} |
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val let2 = @{lemma "Let c == (%P. let x = c in P x)" by (rule reflexive)} |
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val let3 = @{lemma "Let == (%c P. let x = c in P x)" by (rule reflexive)} |
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fun all_abs_conv cv ctxt = |
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Conv.abs_conv (all_abs_conv cv o snd) ctxt else_conv cv ctxt |
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fun keep_conv ctxt = More_Conv.binder_conv norm_conv ctxt |
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and unfold_conv rule ctxt = |
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Conv.rewr_conv rule then_conv all_abs_conv keep_conv ctxt |
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and unfold_let_conv rule ctxt = |
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Conv.rewr_conv rule then_conv |
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all_abs_conv (fn cx => Conv.combination_conv |
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(Conv.arg_conv (norm_conv cx)) (Conv.abs_conv (norm_conv o snd) cx)) ctxt |
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and norm_conv ctxt ct = |
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(case Thm.term_of ct of |
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Const (@{const_name All}, _) $ Abs _ => keep_conv |
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| Const (@{const_name All}, _) $ _ => unfold_conv all1 |
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| Const (@{const_name All}, _) => unfold_conv all2 |
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| Const (@{const_name Ex}, _) $ Abs _ => keep_conv |
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| Const (@{const_name Ex}, _) $ _ => unfold_conv ex1 |
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| Const (@{const_name Ex}, _) => unfold_conv ex2 |
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| Const (@{const_name Let}, _) $ _ $ Abs _ => keep_conv |
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| Const (@{const_name Let}, _) $ _ $ _ => unfold_let_conv let1 |
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| Const (@{const_name Let}, _) $ _ => unfold_let_conv let2 |
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| Const (@{const_name Let}, _) => unfold_let_conv let3 |
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| Abs _ => Conv.abs_conv (norm_conv o snd) |
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| _ $ _ => Conv.comb_conv o norm_conv |
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| _ => K Conv.all_conv) ctxt ct |
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fun is_normed t = |
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(case t of |
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Const (@{const_name All}, _) $ Abs (_, _, u) => is_normed u |
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| Const (@{const_name All}, _) $ _ => false |
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| Const (@{const_name All}, _) => false |
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| Const (@{const_name Ex}, _) $ Abs (_, _, u) => is_normed u |
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| Const (@{const_name Ex}, _) $ _ => false |
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| Const (@{const_name Ex}, _) => false |
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| Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) => |
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is_normed u1 andalso is_normed u2 |
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| Const (@{const_name Let}, _) $ _ $ _ => false |
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| Const (@{const_name Let}, _) $ _ => false |
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| Const (@{const_name Let}, _) => false |
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| Abs (_, _, u) => is_normed u |
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| u1 $ u2 => is_normed u1 andalso is_normed u2 |
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| _ => true) |
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in |
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fun norm_binder_conv ctxt ct = |
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if is_normed (Thm.term_of ct) then Conv.all_conv ct else norm_conv ctxt ct |
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end |
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fun cert ctxt = Thm.cterm_of (ProofContext.theory_of ctxt) |
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fun norm_meta_def cv thm = |
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let val thm' = Thm.combination thm (Thm.reflexive cv) |
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in Thm.transitive thm' (Thm.beta_conversion false (Thm.rhs_of thm')) end |
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fun norm_def ctxt thm = |
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(case Thm.prop_of thm of |
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Const (@{const_name "=="}, _) $ _ $ Abs (_, T, _) => |
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let val v = Var ((Name.uu, #maxidx (Thm.rep_thm thm) + 1), T) |
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in norm_def ctxt (norm_meta_def (cert ctxt v) thm) end |
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| @{term Trueprop} $ (Const (@{const_name "op ="}, _) $ _ $ Abs _) => |
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norm_def ctxt (thm RS @{thm fun_cong}) |
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| _ => thm) |
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fun atomize_conv ctxt ct = |
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(case Thm.term_of ct of |
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@{term "op ==>"} $ _ $ _ => |
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Conv.binop_conv (atomize_conv ctxt) then_conv |
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Conv.rewr_conv @{thm atomize_imp} |
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| Const (@{const_name "=="}, _) $ _ $ _ => |
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Conv.binop_conv (atomize_conv ctxt) then_conv |
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Conv.rewr_conv @{thm atomize_eq} |
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| Const (@{const_name all}, _) $ Abs _ => |
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More_Conv.binder_conv atomize_conv ctxt then_conv |
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Conv.rewr_conv @{thm atomize_all} |
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| _ => Conv.all_conv) ct |
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fun normalize_rule ctxt = |
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Conv.fconv_rule ( |
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Thm.beta_conversion true then_conv |
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Thm.eta_conversion then_conv |
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norm_binder_conv ctxt) #> |
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norm_def ctxt #> |
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Drule.forall_intr_vars #> |
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Conv.fconv_rule (atomize_conv ctxt) |
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136 |
|
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fun instantiate_free (cv, ct) thm = |
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if Term.exists_subterm (equal (Thm.term_of cv)) (Thm.prop_of thm) |
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then Thm.forall_elim ct (Thm.forall_intr cv thm) |
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else thm |
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141 |
|
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fun discharge_definition ct thm = |
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let val (cv, cu) = Thm.dest_equals ct |
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in |
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Thm.implies_intr ct thm |
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|> instantiate_free (cv, cu) |
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|> (fn thm => Thm.implies_elim thm (Thm.reflexive cu)) |
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end |
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149 |
|
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fun if_conv c cv1 cv2 ct = (if c (Thm.term_of ct) then cv1 else cv2) ct |
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fun if_true_conv c cv = if_conv c cv Conv.all_conv |
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152 |
|
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153 |
|
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154 |
(* simplification of trivial let expressions (whose bound variables occur at |
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most once) *) |
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156 |
|
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157 |
local |
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fun count i (Bound j) = if j = i then 1 else 0 |
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| count i (t $ u) = count i t + count i u |
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| count i (Abs (_, _, t)) = count (i + 1) t |
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| count _ _ = 0 |
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162 |
|
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fun is_trivial_let (Const (@{const_name Let}, _) $ _ $ Abs (_, _, t)) = |
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(count 0 t <= 1) |
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| is_trivial_let _ = false |
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166 |
|
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fun let_conv _ = if_true_conv is_trivial_let (Conv.rewr_conv @{thm Let_def}) |
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168 |
|
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fun cond_let_conv ctxt = if_true_conv (Term.exists_subterm is_trivial_let) |
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(More_Conv.top_conv let_conv ctxt) |
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171 |
in |
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fun trivial_let ctxt = map (Conv.fconv_rule (cond_let_conv ctxt)) |
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173 |
end |
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174 |
|
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175 |
|
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176 |
(* rewriting of negative integer numerals into positive numerals *) |
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177 |
|
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178 |
local |
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fun neg_numeral @{term Int.Min} = true |
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| neg_numeral _ = false |
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181 |
fun is_number_sort thy T = Sign.of_sort thy (T, @{sort number_ring}) |
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fun is_neg_number ctxt (Const (@{const_name number_of}, T) $ t) = |
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183 |
Term.exists_subterm neg_numeral t andalso |
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184 |
is_number_sort (ProofContext.theory_of ctxt) (Term.body_type T) |
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185 |
| is_neg_number _ _ = false |
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186 |
fun has_neg_number ctxt = Term.exists_subterm (is_neg_number ctxt) |
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187 |
|
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188 |
val pos_numeral_ss = HOL_ss |
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189 |
addsimps [@{thm Int.number_of_minus}, @{thm Int.number_of_Min}] |
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190 |
addsimps [@{thm Int.numeral_1_eq_1}] |
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191 |
addsimps @{thms Int.pred_bin_simps} |
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192 |
addsimps @{thms Int.normalize_bin_simps} |
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193 |
addsimps @{lemma |
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194 |
"Int.Min = - Int.Bit1 Int.Pls" |
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195 |
"Int.Bit0 (- Int.Pls) = - Int.Pls" |
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196 |
"Int.Bit0 (- k) = - Int.Bit0 k" |
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197 |
"Int.Bit1 (- k) = - Int.Bit1 (Int.pred k)" |
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198 |
by simp_all (simp add: pred_def)} |
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199 |
|
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200 |
fun pos_conv ctxt = if_conv (is_neg_number ctxt) |
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201 |
(Simplifier.rewrite (Simplifier.context ctxt pos_numeral_ss)) |
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202 |
Conv.no_conv |
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203 |
|
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204 |
fun cond_pos_conv ctxt = if_true_conv (has_neg_number ctxt) |
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205 |
(More_Conv.top_sweep_conv pos_conv ctxt) |
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206 |
in |
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207 |
fun positive_numerals ctxt = map (Conv.fconv_rule (cond_pos_conv ctxt)) |
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208 |
end |
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209 |
|
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210 |
|
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211 |
(* embedding of standard natural number operations into integer operations *) |
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212 |
|
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213 |
local |
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214 |
val nat_embedding = @{lemma |
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215 |
"nat (int n) = n" |
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216 |
"i >= 0 --> int (nat i) = i" |
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217 |
"i < 0 --> int (nat i) = 0" |
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218 |
by simp_all} |
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219 |
|
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220 |
val nat_rewriting = @{lemma |
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221 |
"0 = nat 0" |
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222 |
"1 = nat 1" |
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223 |
"number_of i = nat (number_of i)" |
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224 |
"int (nat 0) = 0" |
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225 |
"int (nat 1) = 1" |
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226 |
"a < b = (int a < int b)" |
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227 |
"a <= b = (int a <= int b)" |
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228 |
"Suc a = nat (int a + 1)" |
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229 |
"a + b = nat (int a + int b)" |
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|
230 |
"a - b = nat (int a - int b)" |
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231 |
"a * b = nat (int a * int b)" |
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|
232 |
"a div b = nat (int a div int b)" |
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|
233 |
"a mod b = nat (int a mod int b)" |
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|
234 |
"int (nat (int a + int b)) = int a + int b" |
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235 |
"int (nat (int a * int b)) = int a * int b" |
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236 |
"int (nat (int a div int b)) = int a div int b" |
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237 |
"int (nat (int a mod int b)) = int a mod int b" |
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238 |
by (simp add: nat_mult_distrib nat_div_distrib nat_mod_distrib |
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|
239 |
int_mult[symmetric] zdiv_int[symmetric] zmod_int[symmetric])+} |
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240 |
|
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241 |
fun on_positive num f x = |
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|
242 |
(case try HOLogic.dest_number (Thm.term_of num) of |
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243 |
SOME (_, i) => if i >= 0 then SOME (f x) else NONE |
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244 |
| NONE => NONE) |
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245 |
|
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246 |
val cancel_int_nat_ss = HOL_ss |
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247 |
addsimps [@{thm Nat_Numeral.nat_number_of}] |
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248 |
addsimps [@{thm Nat_Numeral.int_nat_number_of}] |
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249 |
addsimps @{thms neg_simps} |
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250 |
|
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251 |
fun cancel_int_nat_simproc _ ss ct = |
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252 |
let |
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253 |
val num = Thm.dest_arg (Thm.dest_arg ct) |
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254 |
val goal = Thm.mk_binop @{cterm "op == :: int => _"} ct num |
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255 |
val simpset = Simplifier.inherit_context ss cancel_int_nat_ss |
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256 |
fun tac _ = Simplifier.simp_tac simpset 1 |
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257 |
in on_positive num (Goal.prove_internal [] goal) tac end |
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258 |
|
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259 |
val nat_ss = HOL_ss |
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260 |
addsimps nat_rewriting |
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|
261 |
addsimprocs [Simplifier.make_simproc { |
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262 |
name = "cancel_int_nat_num", lhss = [@{cpat "int (nat _)"}], |
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263 |
proc = cancel_int_nat_simproc, identifier = [] }] |
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264 |
|
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265 |
fun conv ctxt = Simplifier.rewrite (Simplifier.context ctxt nat_ss) |
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266 |
|
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|
267 |
val uses_nat_type = Term.exists_type (Term.exists_subtype (equal @{typ nat})) |
33895 | 268 |
val uses_nat_int = |
269 |
Term.exists_subterm (member (op aconv) [@{term int}, @{term nat}]) |
|
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270 |
in |
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271 |
fun nat_as_int ctxt thms = |
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272 |
let |
33895 | 273 |
fun norm thm = thm |
274 |
|> uses_nat_type (Thm.prop_of thm) ? Conv.fconv_rule (conv ctxt) |
|
275 |
val thms' = map norm thms |
|
276 |
in |
|
277 |
if exists (uses_nat_int o Thm.prop_of) thms' then nat_embedding @ thms' |
|
278 |
else thms' |
|
279 |
end |
|
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280 |
end |
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|
281 |
|
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|
282 |
|
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|
283 |
(* include additional rules *) |
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|
284 |
|
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|
285 |
val (unfold_defs, unfold_defs_setup) = |
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|
286 |
Attrib.config_bool "smt_unfold_defs" true |
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|
287 |
|
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|
288 |
local |
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|
289 |
val pair_rules = [@{thm fst_conv}, @{thm snd_conv}, @{thm pair_collapse}] |
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|
290 |
|
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|
291 |
val pair_type = (fn Type (@{type_name "*"}, _) => true | _ => false) |
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|
292 |
val exists_pair_type = Term.exists_type (Term.exists_subtype pair_type) |
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|
293 |
|
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|
294 |
val fun_upd_rules = [@{thm fun_upd_same}, @{thm fun_upd_apply}] |
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|
295 |
val is_fun_upd = (fn Const (@{const_name fun_upd}, _) => true | _ => false) |
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|
296 |
val exists_fun_upd = Term.exists_subterm is_fun_upd |
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changeset
|
297 |
in |
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|
298 |
fun add_pair_rules _ thms = |
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|
299 |
thms |
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|
300 |
|> exists (exists_pair_type o Thm.prop_of) thms ? append pair_rules |
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|
301 |
|
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|
302 |
fun add_fun_upd_rules _ thms = |
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|
303 |
thms |
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|
304 |
|> exists (exists_fun_upd o Thm.prop_of) thms ? append fun_upd_rules |
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changeset
|
305 |
end |
42865636d006
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changeset
|
306 |
|
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changeset
|
307 |
|
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changeset
|
308 |
local |
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changeset
|
309 |
fun mk_entry t thm = (Term.head_of t, (thm, thm RS @{thm eq_reflection})) |
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changeset
|
310 |
fun prepare_def thm = |
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parents:
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changeset
|
311 |
(case HOLogic.dest_Trueprop (Thm.prop_of thm) of |
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changeset
|
312 |
Const (@{const_name "op ="}, _) $ t $ _ => mk_entry t thm |
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changeset
|
313 |
| t => raise TERM ("prepare_def", [t])) |
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changeset
|
314 |
|
42865636d006
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parents:
diff
changeset
|
315 |
val defs = map prepare_def [ |
42865636d006
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parents:
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changeset
|
316 |
@{thm abs_if[where 'a = int]}, @{thm abs_if[where 'a = real]}, |
42865636d006
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parents:
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changeset
|
317 |
@{thm min_def[where 'a = int]}, @{thm min_def[where 'a = real]}, |
42865636d006
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parents:
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changeset
|
318 |
@{thm max_def[where 'a = int]}, @{thm max_def[where 'a = real]}] |
42865636d006
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parents:
diff
changeset
|
319 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
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parents:
diff
changeset
|
320 |
fun add_sym t = if AList.defined (op =) defs t then insert (op =) t else I |
42865636d006
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boehmes
parents:
diff
changeset
|
321 |
fun add_syms thms = fold (Term.fold_aterms add_sym o Thm.prop_of) thms [] |
42865636d006
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boehmes
parents:
diff
changeset
|
322 |
|
34010
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
323 |
fun unfold_def_conv ds ct = |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
324 |
(case AList.lookup (op =) ds (Term.head_of (Thm.term_of ct)) of |
32618
42865636d006
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parents:
diff
changeset
|
325 |
SOME (_, eq) => Conv.rewr_conv eq |
42865636d006
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parents:
diff
changeset
|
326 |
| NONE => Conv.all_conv) ct |
34010
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
327 |
|
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
328 |
fun unfold_conv ctxt thm = |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
329 |
(case filter (member (op =) (add_syms [thm]) o fst) defs of |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
330 |
[] => thm |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
331 |
| ds => thm |> Conv.fconv_rule |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
332 |
(More_Conv.bottom_conv (K (unfold_def_conv ds)) ctxt)) |
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
333 |
in |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
334 |
fun add_abs_min_max_rules ctxt thms = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
335 |
if Config.get ctxt unfold_defs |
34010
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
336 |
then map (unfold_conv ctxt) thms |
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
337 |
else map fst (map_filter (AList.lookup (op =) defs) (add_syms thms)) @ thms |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
338 |
end |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
339 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
340 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
341 |
(* lift lambda terms into additional rules *) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
342 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
343 |
local |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
344 |
val meta_eq = @{cpat "op =="} |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
345 |
val meta_eqT = hd (Thm.dest_ctyp (Thm.ctyp_of_term meta_eq)) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
346 |
fun inst_meta cT = Thm.instantiate_cterm ([(meta_eqT, cT)], []) meta_eq |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
347 |
fun mk_meta_eq ct cu = Thm.mk_binop (inst_meta (Thm.ctyp_of_term ct)) ct cu |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
348 |
|
33010 | 349 |
val fresh_name = yield_singleton Name.variants |
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
350 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
351 |
fun used_vars cvs ct = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
352 |
let |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
353 |
val lookup = AList.lookup (op aconv) (map (` Thm.term_of) cvs) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
354 |
val add = (fn (SOME ct) => insert (op aconvc) ct | _ => I) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
355 |
in Term.fold_aterms (add o lookup) (Thm.term_of ct) [] end |
33010 | 356 |
fun make_def cvs eq = Thm.symmetric (fold norm_meta_def cvs eq) |
357 |
fun add_def ct thm = Termtab.update (Thm.term_of ct, (serial (), thm)) |
|
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
358 |
|
33010 | 359 |
fun replace ctxt cvs ct (cx as (nctxt, defs)) = |
360 |
let |
|
361 |
val cvs' = used_vars cvs ct |
|
33355
ee5b5ef5e970
abstract over variables in reversed order (application uses given order)
boehmes
parents:
33299
diff
changeset
|
362 |
val ct' = fold_rev Thm.cabs cvs' ct |
33010 | 363 |
in |
364 |
(case Termtab.lookup defs (Thm.term_of ct') of |
|
365 |
SOME (_, eq) => (make_def cvs' eq, cx) |
|
366 |
| NONE => |
|
367 |
let |
|
33664 | 368 |
val {T, ...} = Thm.rep_cterm ct' |
33010 | 369 |
val (n, nctxt') = fresh_name "" nctxt |
370 |
val eq = Thm.assume (mk_meta_eq (cert ctxt (Free (n, T))) ct') |
|
371 |
in (make_def cvs' eq, (nctxt', add_def ct' eq defs)) end) |
|
372 |
end |
|
373 |
||
374 |
fun none ct cx = (Thm.reflexive ct, cx) |
|
375 |
fun in_comb f g ct cx = |
|
376 |
let val (cu1, cu2) = Thm.dest_comb ct |
|
377 |
in cx |> f cu1 ||>> g cu2 |>> uncurry Thm.combination end |
|
378 |
fun in_arg f = in_comb none f |
|
379 |
fun in_abs f cvs ct (nctxt, defs) = |
|
380 |
let |
|
381 |
val (n, nctxt') = fresh_name Name.uu nctxt |
|
382 |
val (cv, cu) = Thm.dest_abs (SOME n) ct |
|
383 |
in f (cv :: cvs) cu (nctxt', defs) |>> Thm.abstract_rule n cv end |
|
384 |
||
385 |
fun replace_lambdas ctxt = |
|
386 |
let |
|
387 |
fun repl cvs ct = |
|
388 |
(case Thm.term_of ct of |
|
389 |
Const (@{const_name All}, _) $ Abs _ => in_arg (in_abs repl cvs) |
|
390 |
| Const (@{const_name Ex}, _) $ Abs _ => in_arg (in_abs repl cvs) |
|
391 |
| Const _ $ Abs _ => in_arg (at_lambda cvs) |
|
392 |
| Const (@{const_name Let}, _) $ _ $ Abs _ => |
|
393 |
in_comb (in_arg (repl cvs)) (in_abs repl cvs) |
|
394 |
| Abs _ => at_lambda cvs |
|
395 |
| _ $ _ => in_comb (repl cvs) (repl cvs) |
|
396 |
| _ => none) ct |
|
33299 | 397 |
and at_lambda cvs ct = |
398 |
in_abs repl cvs ct #-> (fn thm => |
|
399 |
replace ctxt cvs (Thm.rhs_of thm) #>> Thm.transitive thm) |
|
33010 | 400 |
in repl [] end |
34010
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
401 |
|
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
402 |
fun has_free_lambdas t = |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
403 |
(case t of |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
404 |
Const (@{const_name All}, _) $ Abs (_, _, u) => has_free_lambdas u |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
405 |
| Const (@{const_name Ex}, _) $ Abs (_, _, u) => has_free_lambdas u |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
406 |
| Const (@{const_name Let}, _) $ u1 $ Abs (_, _, u2) => |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
407 |
has_free_lambdas u1 orelse has_free_lambdas u2 |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
408 |
| Abs _ => true |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
409 |
| u1 $ u2 => has_free_lambdas u1 orelse has_free_lambdas u2 |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
410 |
| _ => false) |
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
411 |
in |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
412 |
fun lift_lambdas ctxt thms = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
413 |
let |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
414 |
val declare_frees = fold (Thm.fold_terms Term.declare_term_frees) |
33010 | 415 |
fun rewrite f thm cx = |
34010
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
416 |
if not (has_free_lambdas (Thm.prop_of thm)) then (thm, cx) |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
417 |
else f (Thm.cprop_of thm) cx |>> (fn thm' => Thm.equal_elim thm' thm) |
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
418 |
|
33010 | 419 |
val rev_int_fst_ord = rev_order o int_ord o pairself fst |
420 |
fun ordered_values tab = |
|
421 |
Termtab.fold (fn (_, x) => OrdList.insert rev_int_fst_ord x) tab [] |
|
422 |
|> map snd |
|
423 |
||
424 |
val (thms', (_, defs)) = |
|
425 |
(declare_frees thms (Name.make_context []), Termtab.empty) |
|
426 |
|> fold_map (rewrite (replace_lambdas ctxt)) thms |
|
427 |
val eqs = ordered_values defs |
|
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
428 |
in |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
429 |
(maps (#hyps o Thm.crep_thm) eqs, map (normalize_rule ctxt) eqs @ thms') |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
430 |
end |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
431 |
end |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
432 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
433 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
434 |
(* make application explicit for functions with varying number of arguments *) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
435 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
436 |
local |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
437 |
val const = prefix "c" and free = prefix "f" |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
438 |
fun min i (e as (_, j)) = if i <> j then (true, Int.min (i, j)) else e |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
439 |
fun add t i = Symtab.map_default (t, (false, i)) (min i) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
440 |
fun traverse t = |
42865636d006
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boehmes
parents:
diff
changeset
|
441 |
(case Term.strip_comb t of |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
442 |
(Const (n, _), ts) => add (const n) (length ts) #> fold traverse ts |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
443 |
| (Free (n, _), ts) => add (free n) (length ts) #> fold traverse ts |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
444 |
| (Abs (_, _, u), ts) => fold traverse (u :: ts) |
42865636d006
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boehmes
parents:
diff
changeset
|
445 |
| (_, ts) => fold traverse ts) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
446 |
val prune = (fn (n, (true, i)) => Symtab.update (n, i) | _ => I) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
447 |
fun prune_tab tab = Symtab.fold prune tab Symtab.empty |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
448 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
449 |
fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2 |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
450 |
fun nary_conv conv1 conv2 ct = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
451 |
(Conv.combination_conv (nary_conv conv1 conv2) conv2 else_conv conv1) ct |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
452 |
fun abs_conv conv tb = Conv.abs_conv (fn (cv, cx) => |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
453 |
let val n = fst (Term.dest_Free (Thm.term_of cv)) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
454 |
in conv (Symtab.update (free n, 0) tb) cx end) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
455 |
val apply_rule = @{lemma "f x == apply f x" by (simp add: apply_def)} |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
456 |
in |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
457 |
fun explicit_application ctxt thms = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
458 |
let |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
459 |
fun sub_conv tb ctxt ct = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
460 |
(case Term.strip_comb (Thm.term_of ct) of |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
461 |
(Const (n, _), ts) => app_conv tb (const n) (length ts) ctxt |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
462 |
| (Free (n, _), ts) => app_conv tb (free n) (length ts) ctxt |
33664 | 463 |
| (Abs _, _) => nary_conv (abs_conv sub_conv tb ctxt) (sub_conv tb ctxt) |
464 |
| (_, _) => nary_conv Conv.all_conv (sub_conv tb ctxt)) ct |
|
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
465 |
and app_conv tb n i ctxt = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
466 |
(case Symtab.lookup tb n of |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
467 |
NONE => nary_conv Conv.all_conv (sub_conv tb ctxt) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
468 |
| SOME j => apply_conv tb ctxt (i - j)) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
469 |
and apply_conv tb ctxt i ct = ( |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
470 |
if i = 0 then nary_conv Conv.all_conv (sub_conv tb ctxt) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
471 |
else |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
472 |
Conv.rewr_conv apply_rule then_conv |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
473 |
binop_conv (apply_conv tb ctxt (i-1)) (sub_conv tb ctxt)) ct |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
474 |
|
34010
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
475 |
fun needs_exp_app tab = Term.exists_subterm (fn |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
476 |
Bound _ $ _ => true |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
477 |
| Const (n, _) => Symtab.defined tab (const n) |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
478 |
| Free (n, _) => Symtab.defined tab (free n) |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
479 |
| _ => false) |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
480 |
|
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
481 |
fun rewrite tab ctxt thm = |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
482 |
if not (needs_exp_app tab (Thm.prop_of thm)) then thm |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
483 |
else Conv.fconv_rule (sub_conv tab ctxt) thm |
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
484 |
|
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
485 |
val tab = prune_tab (fold (traverse o Thm.prop_of) thms Symtab.empty) |
34010
ac78f5cdc430
faster preprocessing: before applying a step, test if it is applicable (normalization of binders, unfolding of abs/min/max definitions, lambda lifting, explicit application, monomorphization),
boehmes
parents:
33895
diff
changeset
|
486 |
in map (rewrite tab ctxt) thms end |
32618
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
487 |
end |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
488 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
489 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
490 |
(* combined normalization *) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
491 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
492 |
datatype config = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
493 |
RewriteTrivialLets | |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
494 |
RewriteNegativeNumerals | |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
495 |
RewriteNaturalNumbers | |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
496 |
AddPairRules | |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
497 |
AddFunUpdRules | |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
498 |
AddAbsMinMaxRules |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
499 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
500 |
fun normalize config ctxt thms = |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
501 |
let fun if_enabled c f = member (op =) config c ? f ctxt |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
502 |
in |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
503 |
thms |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
504 |
|> if_enabled RewriteTrivialLets trivial_let |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
505 |
|> if_enabled RewriteNegativeNumerals positive_numerals |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
506 |
|> if_enabled RewriteNaturalNumbers nat_as_int |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
507 |
|> if_enabled AddPairRules add_pair_rules |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
508 |
|> if_enabled AddFunUpdRules add_fun_upd_rules |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
509 |
|> if_enabled AddAbsMinMaxRules add_abs_min_max_rules |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
510 |
|> map (normalize_rule ctxt) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
511 |
|> lift_lambdas ctxt |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
512 |
|> apsnd (explicit_application ctxt) |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
513 |
end |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
514 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
515 |
val setup = unfold_defs_setup |
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
516 |
|
42865636d006
added new method "smt": an oracle-based connection to external SMT solvers
boehmes
parents:
diff
changeset
|
517 |
end |