author | wenzelm |
Tue, 28 Sep 2021 22:50:22 +0200 | |
changeset 74386 | 40804452ab6b |
parent 74113 | 228adc502803 |
child 74518 | de4f151c2a34 |
permissions | -rw-r--r-- |
68630 | 1 |
signature EXP_LOG_EXPRESSION = sig |
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exception DUP |
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datatype expr = |
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ConstExpr of term |
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| X |
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| Uminus of expr |
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| Add of expr * expr |
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| Minus of expr * expr |
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| Inverse of expr |
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| Mult of expr * expr |
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| Div of expr * expr |
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| Ln of expr |
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| Exp of expr |
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| Power of expr * term |
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| LnPowr of expr * expr |
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| ExpLn of expr |
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| Powr of expr * expr |
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| Powr_Nat of expr * expr |
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| Powr' of expr * term |
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| Root of expr * term |
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| Absolute of expr |
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| Sgn of expr |
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| Min of expr * expr |
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| Max of expr * expr |
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| Floor of expr |
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| Ceiling of expr |
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| Frac of expr |
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| NatMod of expr * expr |
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| Sin of expr |
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| Cos of expr |
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| ArcTan of expr |
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| Custom of string * term * expr list |
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||
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val preproc_term_conv : Proof.context -> conv |
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val expr_to_term : expr -> term |
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val reify : Proof.context -> term -> expr * thm |
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val reify_simple : Proof.context -> term -> expr * thm |
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type custom_handler = |
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Lazy_Eval.eval_ctxt -> term -> thm list * Asymptotic_Basis.basis -> thm * Asymptotic_Basis.basis |
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val register_custom : |
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binding -> term -> custom_handler -> local_theory -> local_theory |
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val register_custom_from_thm : |
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binding -> thm -> custom_handler -> local_theory -> local_theory |
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val expand_custom : Proof.context -> string -> custom_handler option |
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val to_mathematica : expr -> string |
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val to_maple : expr -> string |
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val to_maxima : expr -> string |
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val to_sympy : expr -> string |
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val to_sage : expr -> string |
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val reify_mathematica : Proof.context -> term -> string |
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val reify_maple : Proof.context -> term -> string |
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val reify_maxima : Proof.context -> term -> string |
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val reify_sympy : Proof.context -> term -> string |
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val reify_sage : Proof.context -> term -> string |
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val limit_mathematica : string -> string |
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val limit_maple : string -> string |
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val limit_maxima : string -> string |
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val limit_sympy : string -> string |
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val limit_sage : string -> string |
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end |
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structure Exp_Log_Expression : EXP_LOG_EXPRESSION = struct |
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datatype expr = |
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ConstExpr of term |
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| X |
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| Uminus of expr |
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| Add of expr * expr |
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| Minus of expr * expr |
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| Inverse of expr |
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| Mult of expr * expr |
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| Div of expr * expr |
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| Ln of expr |
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| Exp of expr |
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| Power of expr * term |
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| LnPowr of expr * expr |
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| ExpLn of expr |
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| Powr of expr * expr |
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| Powr_Nat of expr * expr |
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| Powr' of expr * term |
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| Root of expr * term |
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| Absolute of expr |
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| Sgn of expr |
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| Min of expr * expr |
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| Max of expr * expr |
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| Floor of expr |
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| Ceiling of expr |
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| Frac of expr |
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| NatMod of expr * expr |
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| Sin of expr |
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| Cos of expr |
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| ArcTan of expr |
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| Custom of string * term * expr list |
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type custom_handler = |
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Lazy_Eval.eval_ctxt -> term -> thm list * Asymptotic_Basis.basis -> thm * Asymptotic_Basis.basis |
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type entry = { |
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name : string, |
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pat : term, |
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net_pat : term, |
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expand : custom_handler |
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} |
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type entry' = { |
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pat : term, |
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net_pat : term, |
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expand : custom_handler |
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} |
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exception DUP |
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structure Custom_Funs = Generic_Data |
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( |
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type T = { |
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name_table : entry' Name_Space.table, |
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net : entry Item_Net.T |
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} |
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fun eq_entry ({name = name1, ...}, {name = name2, ...}) = (name1 = name2) |
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val empty = |
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{ |
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74113
228adc502803
proper name space "kind": this is a formal name, not comment;
wenzelm
parents:
69597
diff
changeset
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name_table = Name_Space.empty_table "exp_log_custom_function", |
68630 | 132 |
net = Item_Net.init eq_entry (fn {net_pat, ...} => [net_pat]) |
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} |
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fun merge ({name_table = tbl1, net = net1}, {name_table = tbl2, net = net2}) = |
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{name_table = Name_Space.join_tables (fn _ => raise DUP) (tbl1, tbl2), |
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net = Item_Net.merge (net1, net2)} |
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val extend = I |
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) |
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fun rewrite' ctxt old_prems bounds thms ct = |
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let |
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val thy = Proof_Context.theory_of ctxt |
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fun apply_rule t thm = |
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let |
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val lhs = thm |> Thm.concl_of |> Logic.dest_equals |> fst |
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val _ = Pattern.first_order_match thy (lhs, t) (Vartab.empty, Vartab.empty) |
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val insts = (lhs, t) |> apply2 (Thm.cterm_of ctxt) |> Thm.first_order_match |
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val thm = Thm.instantiate insts thm |
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val prems = Thm.prems_of thm |
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val frees = fold Term.add_frees prems [] |
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in |
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if exists (member op = bounds o fst) frees then |
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NONE |
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else |
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let |
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val thm' = thm OF (map (Thm.assume o Thm.cterm_of ctxt) prems) |
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val prems' = fold (insert op aconv) prems old_prems |
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val crhs = thm |> Thm.concl_of |> Logic.dest_equals |> snd |> Thm.cterm_of ctxt |
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in |
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SOME (thm', crhs, prems') |
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end |
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end |
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handle Pattern.MATCH => NONE |
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fun rewrite_subterm prems ct (Abs (x, _, _)) = |
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let |
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val (u, ctxt') = yield_singleton Variable.variant_fixes x ctxt; |
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val (v, ct') = Thm.dest_abs (SOME u) ct; |
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val (thm, prems) = rewrite' ctxt' prems (x :: bounds) thms ct' |
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in |
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if Thm.is_reflexive thm then |
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(Thm.reflexive ct, prems) |
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else |
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(Thm.abstract_rule x v thm, prems) |
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end |
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| rewrite_subterm prems ct (_ $ _) = |
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let |
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val (cs, ct) = Thm.dest_comb ct |
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val (thm, prems') = rewrite' ctxt prems bounds thms cs |
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val (thm', prems'') = rewrite' ctxt prems' bounds thms ct |
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in |
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(Thm.combination thm thm', prems'') |
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end |
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| rewrite_subterm prems ct _ = (Thm.reflexive ct, prems) |
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val t = Thm.term_of ct |
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in |
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case get_first (apply_rule t) thms of |
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NONE => rewrite_subterm old_prems ct t |
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| SOME (thm, rhs, prems) => |
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case rewrite' ctxt prems bounds thms rhs of |
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(thm', prems) => (Thm.transitive thm thm', prems) |
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end |
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fun rewrite ctxt thms ct = |
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let |
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val thm1 = Thm.eta_long_conversion ct |
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val rhs = thm1 |> Thm.cprop_of |> Thm.dest_comb |> snd |
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val (thm2, prems) = rewrite' ctxt [] [] thms rhs |
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val rhs = thm2 |> Thm.cprop_of |> Thm.dest_comb |> snd |
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val thm3 = Thm.eta_conversion rhs |
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val thm = Thm.transitive thm1 (Thm.transitive thm2 thm3) |
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in |
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fold (fn prem => fn thm => Thm.implies_intr (Thm.cterm_of ctxt prem) thm) prems thm |
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end |
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fun preproc_term_conv ctxt = |
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let |
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69597 | 208 |
val thms = Named_Theorems.get ctxt \<^named_theorems>\<open>real_asymp_reify_simps\<close> |
68630 | 209 |
val thms = map (fn thm => thm RS @{thm HOL.eq_reflection}) thms |
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in |
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rewrite ctxt thms |
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end |
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fun register_custom' binding pat expand context = |
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let |
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val n = pat |> fastype_of |> strip_type |> fst |> length |
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val maxidx = Term.maxidx_of_term pat |
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69597 | 218 |
val vars = map (fn i => Var ((Name.uu_, maxidx + i), \<^typ>\<open>real\<close>)) (1 upto n) |
68630 | 219 |
val net_pat = Library.foldl betapply (pat, vars) |
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val {name_table = tbl, net = net} = Custom_Funs.get context |
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val entry' = {pat = pat, net_pat = net_pat, expand = expand} |
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val (name, tbl) = Name_Space.define context true (binding, entry') tbl |
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val entry = {name = name, pat = pat, net_pat = net_pat, expand = expand} |
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val net = Item_Net.update entry net |
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in |
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Custom_Funs.put {name_table = tbl, net = net} context |
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end |
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fun register_custom binding pat expand = |
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let |
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fun decl phi = |
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register_custom' binding (Morphism.term phi pat) expand |
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in |
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Local_Theory.declaration {syntax = false, pervasive = false} decl |
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end |
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fun register_custom_from_thm binding thm expand = |
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let |
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val pat = thm |> Thm.concl_of |> HOLogic.dest_Trueprop |> dest_comb |> snd |
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in |
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register_custom binding pat expand |
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end |
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fun expand_custom ctxt name = |
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let |
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val {name_table, ...} = Custom_Funs.get (Context.Proof ctxt) |
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in |
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case Name_Space.lookup name_table name of |
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NONE => NONE |
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| SOME {expand, ...} => SOME expand |
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end |
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fun expr_to_term e = |
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let |
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fun expr_to_term' (ConstExpr c) = c |
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| expr_to_term' X = Bound 0 |
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| expr_to_term' (Add (a, b)) = |
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69597 | 258 |
\<^term>\<open>(+) :: real => _\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 259 |
| expr_to_term' (Mult (a, b)) = |
69597 | 260 |
\<^term>\<open>(*) :: real => _\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 261 |
| expr_to_term' (Minus (a, b)) = |
69597 | 262 |
\<^term>\<open>(-) :: real => _\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 263 |
| expr_to_term' (Div (a, b)) = |
69597 | 264 |
\<^term>\<open>(/) :: real => _\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 265 |
| expr_to_term' (Uminus a) = |
69597 | 266 |
\<^term>\<open>uminus :: real => _\<close> $ expr_to_term' a |
68630 | 267 |
| expr_to_term' (Inverse a) = |
69597 | 268 |
\<^term>\<open>inverse :: real => _\<close> $ expr_to_term' a |
68630 | 269 |
| expr_to_term' (Ln a) = |
69597 | 270 |
\<^term>\<open>ln :: real => _\<close> $ expr_to_term' a |
68630 | 271 |
| expr_to_term' (Exp a) = |
69597 | 272 |
\<^term>\<open>exp :: real => _\<close> $ expr_to_term' a |
68630 | 273 |
| expr_to_term' (Powr (a,b)) = |
69597 | 274 |
\<^term>\<open>(powr) :: real => _\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 275 |
| expr_to_term' (Powr_Nat (a,b)) = |
69597 | 276 |
\<^term>\<open>powr_nat :: real => _\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 277 |
| expr_to_term' (LnPowr (a,b)) = |
69597 | 278 |
\<^term>\<open>ln :: real => _\<close> $ |
279 |
(\<^term>\<open>(powr) :: real => _\<close> $ expr_to_term' a $ expr_to_term' b) |
|
68630 | 280 |
| expr_to_term' (ExpLn a) = |
69597 | 281 |
\<^term>\<open>exp :: real => _\<close> $ (\<^term>\<open>ln :: real => _\<close> $ expr_to_term' a) |
68630 | 282 |
| expr_to_term' (Powr' (a,b)) = |
69597 | 283 |
\<^term>\<open>(powr) :: real => _\<close> $ expr_to_term' a $ b |
68630 | 284 |
| expr_to_term' (Power (a,b)) = |
69597 | 285 |
\<^term>\<open>(^) :: real => _\<close> $ expr_to_term' a $ b |
68630 | 286 |
| expr_to_term' (Floor a) = |
69597 | 287 |
\<^term>\<open>Multiseries_Expansion.rfloor\<close> $ expr_to_term' a |
68630 | 288 |
| expr_to_term' (Ceiling a) = |
69597 | 289 |
\<^term>\<open>Multiseries_Expansion.rceil\<close> $ expr_to_term' a |
68630 | 290 |
| expr_to_term' (Frac a) = |
69597 | 291 |
\<^term>\<open>Archimedean_Field.frac :: real \<Rightarrow> real\<close> $ expr_to_term' a |
68630 | 292 |
| expr_to_term' (NatMod (a,b)) = |
69597 | 293 |
\<^term>\<open>Multiseries_Expansion.rnatmod\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 294 |
| expr_to_term' (Root (a,b)) = |
69597 | 295 |
\<^term>\<open>root :: nat \<Rightarrow> real \<Rightarrow> _\<close> $ b $ expr_to_term' a |
68630 | 296 |
| expr_to_term' (Sin a) = |
69597 | 297 |
\<^term>\<open>sin :: real => _\<close> $ expr_to_term' a |
68630 | 298 |
| expr_to_term' (ArcTan a) = |
69597 | 299 |
\<^term>\<open>arctan :: real => _\<close> $ expr_to_term' a |
68630 | 300 |
| expr_to_term' (Cos a) = |
69597 | 301 |
\<^term>\<open>cos :: real => _\<close> $ expr_to_term' a |
68630 | 302 |
| expr_to_term' (Absolute a) = |
69597 | 303 |
\<^term>\<open>abs :: real => _\<close> $ expr_to_term' a |
68630 | 304 |
| expr_to_term' (Sgn a) = |
69597 | 305 |
\<^term>\<open>sgn :: real => _\<close> $ expr_to_term' a |
68630 | 306 |
| expr_to_term' (Min (a,b)) = |
69597 | 307 |
\<^term>\<open>min :: real => _\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 308 |
| expr_to_term' (Max (a,b)) = |
69597 | 309 |
\<^term>\<open>max :: real => _\<close> $ expr_to_term' a $ expr_to_term' b |
68630 | 310 |
| expr_to_term' (Custom (_, t, args)) = Envir.beta_eta_contract ( |
311 |
fold (fn e => fn t => betapply (t, expr_to_term' e )) args t) |
|
312 |
in |
|
69597 | 313 |
Abs ("x", \<^typ>\<open>real\<close>, expr_to_term' e) |
68630 | 314 |
end |
315 |
||
316 |
fun reify_custom ctxt t = |
|
317 |
let |
|
318 |
val thy = Proof_Context.theory_of ctxt |
|
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val t = Envir.beta_eta_contract t |
|
69597 | 320 |
val t' = Envir.beta_eta_contract (Term.abs ("x", \<^typ>\<open>real\<close>) t) |
68630 | 321 |
val {net, ...} = Custom_Funs.get (Context.Proof ctxt) |
69597 | 322 |
val entries = Item_Net.retrieve_matching net (Term.subst_bound (Free ("x", \<^typ>\<open>real\<close>), t)) |
68630 | 323 |
fun go {pat, name, ...} = |
324 |
let |
|
325 |
val n = pat |> fastype_of |> strip_type |> fst |> length |
|
326 |
val maxidx = Term.maxidx_of_term t' |
|
327 |
val vs = map (fn i => (Name.uu_, maxidx + i)) (1 upto n) |
|
69597 | 328 |
val args = map (fn v => Var (v, \<^typ>\<open>real => real\<close>) $ Bound 0) vs |
68630 | 329 |
val pat' = |
69597 | 330 |
Envir.beta_eta_contract (Term.abs ("x", \<^typ>\<open>real\<close>) |
68630 | 331 |
(Library.foldl betapply (pat, args))) |
332 |
val (T_insts, insts) = Pattern.match thy (pat', t') (Vartab.empty, Vartab.empty) |
|
333 |
fun map_option _ [] acc = SOME (rev acc) |
|
334 |
| map_option f (x :: xs) acc = |
|
335 |
case f x of |
|
336 |
NONE => NONE |
|
337 |
| SOME y => map_option f xs (y :: acc) |
|
338 |
val t = Envir.subst_term (T_insts, insts) pat |
|
339 |
in |
|
340 |
Option.map (pair (name, t)) (map_option (Option.map snd o Vartab.lookup insts) vs []) |
|
341 |
end |
|
342 |
handle Pattern.MATCH => NONE |
|
343 |
in |
|
344 |
get_first go entries |
|
345 |
end |
|
346 |
||
347 |
fun reify_aux ctxt t' t = |
|
348 |
let |
|
349 |
fun is_const t = |
|
69597 | 350 |
fastype_of (Abs ("x", \<^typ>\<open>real\<close>, t)) = \<^typ>\<open>real \<Rightarrow> real\<close> |
68630 | 351 |
andalso not (exists_subterm (fn t => t = Bound 0) t) |
352 |
fun is_const' t = not (exists_subterm (fn t => t = Bound 0) t) |
|
69597 | 353 |
fun reify'' (\<^term>\<open>(+) :: real => _\<close> $ s $ t) = |
68630 | 354 |
Add (reify' s, reify' t) |
69597 | 355 |
| reify'' (\<^term>\<open>(-) :: real => _\<close> $ s $ t) = |
68630 | 356 |
Minus (reify' s, reify' t) |
69597 | 357 |
| reify'' (\<^term>\<open>(*) :: real => _\<close> $ s $ t) = |
68630 | 358 |
Mult (reify' s, reify' t) |
69597 | 359 |
| reify'' (\<^term>\<open>(/) :: real => _\<close> $ s $ t) = |
68630 | 360 |
Div (reify' s, reify' t) |
69597 | 361 |
| reify'' (\<^term>\<open>uminus :: real => _\<close> $ s) = |
68630 | 362 |
Uminus (reify' s) |
69597 | 363 |
| reify'' (\<^term>\<open>inverse :: real => _\<close> $ s) = |
68630 | 364 |
Inverse (reify' s) |
69597 | 365 |
| reify'' (\<^term>\<open>ln :: real => _\<close> $ (\<^term>\<open>(powr) :: real => _\<close> $ s $ t)) = |
68630 | 366 |
LnPowr (reify' s, reify' t) |
69597 | 367 |
| reify'' (\<^term>\<open>exp :: real => _\<close> $ (\<^term>\<open>ln :: real => _\<close> $ s)) = |
68630 | 368 |
ExpLn (reify' s) |
69597 | 369 |
| reify'' (\<^term>\<open>ln :: real => _\<close> $ s) = |
68630 | 370 |
Ln (reify' s) |
69597 | 371 |
| reify'' (\<^term>\<open>exp :: real => _\<close> $ s) = |
68630 | 372 |
Exp (reify' s) |
69597 | 373 |
| reify'' (\<^term>\<open>(powr) :: real => _\<close> $ s $ t) = |
68630 | 374 |
(if is_const t then Powr' (reify' s, t) else Powr (reify' s, reify' t)) |
69597 | 375 |
| reify'' (\<^term>\<open>powr_nat :: real => _\<close> $ s $ t) = |
68630 | 376 |
Powr_Nat (reify' s, reify' t) |
69597 | 377 |
| reify'' (\<^term>\<open>(^) :: real => _\<close> $ s $ t) = |
68630 | 378 |
(if is_const' t then Power (reify' s, t) else raise TERM ("reify", [t'])) |
69597 | 379 |
| reify'' (\<^term>\<open>root\<close> $ s $ t) = |
68630 | 380 |
(if is_const' s then Root (reify' t, s) else raise TERM ("reify", [t'])) |
69597 | 381 |
| reify'' (\<^term>\<open>abs :: real => _\<close> $ s) = |
68630 | 382 |
Absolute (reify' s) |
69597 | 383 |
| reify'' (\<^term>\<open>sgn :: real => _\<close> $ s) = |
68630 | 384 |
Sgn (reify' s) |
69597 | 385 |
| reify'' (\<^term>\<open>min :: real => _\<close> $ s $ t) = |
68630 | 386 |
Min (reify' s, reify' t) |
69597 | 387 |
| reify'' (\<^term>\<open>max :: real => _\<close> $ s $ t) = |
68630 | 388 |
Max (reify' s, reify' t) |
69597 | 389 |
| reify'' (\<^term>\<open>Multiseries_Expansion.rfloor\<close> $ s) = |
68630 | 390 |
Floor (reify' s) |
69597 | 391 |
| reify'' (\<^term>\<open>Multiseries_Expansion.rceil\<close> $ s) = |
68630 | 392 |
Ceiling (reify' s) |
69597 | 393 |
| reify'' (\<^term>\<open>Archimedean_Field.frac :: real \<Rightarrow> real\<close> $ s) = |
68630 | 394 |
Frac (reify' s) |
69597 | 395 |
| reify'' (\<^term>\<open>Multiseries_Expansion.rnatmod\<close> $ s $ t) = |
68630 | 396 |
NatMod (reify' s, reify' t) |
69597 | 397 |
| reify'' (\<^term>\<open>sin :: real => _\<close> $ s) = |
68630 | 398 |
Sin (reify' s) |
69597 | 399 |
| reify'' (\<^term>\<open>arctan :: real => _\<close> $ s) = |
68630 | 400 |
ArcTan (reify' s) |
69597 | 401 |
| reify'' (\<^term>\<open>cos :: real => _\<close> $ s) = |
68630 | 402 |
Cos (reify' s) |
403 |
| reify'' (Bound 0) = X |
|
404 |
| reify'' t = |
|
405 |
case reify_custom ctxt t of |
|
406 |
SOME ((name, t), ts) => |
|
407 |
let |
|
408 |
val args = map (reify_aux ctxt t') ts |
|
409 |
in |
|
410 |
Custom (name, t, args) |
|
411 |
end |
|
412 |
| NONE => raise TERM ("reify", [t']) |
|
413 |
and reify' t = if is_const t then ConstExpr t else reify'' t |
|
414 |
in |
|
415 |
case Envir.eta_long [] t of |
|
69597 | 416 |
Abs (_, \<^typ>\<open>real\<close>, t'') => reify' t'' |
68630 | 417 |
| _ => raise TERM ("reify", [t]) |
418 |
end |
|
419 |
||
420 |
fun reify ctxt t = |
|
421 |
let |
|
422 |
val thm = preproc_term_conv ctxt (Thm.cterm_of ctxt t) |
|
423 |
val rhs = thm |> Thm.concl_of |> Logic.dest_equals |> snd |
|
424 |
in |
|
425 |
(reify_aux ctxt t rhs, thm) |
|
426 |
end |
|
427 |
||
428 |
fun reify_simple_aux ctxt t' t = |
|
429 |
let |
|
430 |
fun is_const t = |
|
69597 | 431 |
fastype_of (Abs ("x", \<^typ>\<open>real\<close>, t)) = \<^typ>\<open>real \<Rightarrow> real\<close> |
68630 | 432 |
andalso not (exists_subterm (fn t => t = Bound 0) t) |
433 |
fun is_const' t = not (exists_subterm (fn t => t = Bound 0) t) |
|
69597 | 434 |
fun reify'' (\<^term>\<open>(+) :: real => _\<close> $ s $ t) = |
68630 | 435 |
Add (reify'' s, reify'' t) |
69597 | 436 |
| reify'' (\<^term>\<open>(-) :: real => _\<close> $ s $ t) = |
68630 | 437 |
Minus (reify'' s, reify'' t) |
69597 | 438 |
| reify'' (\<^term>\<open>(*) :: real => _\<close> $ s $ t) = |
68630 | 439 |
Mult (reify'' s, reify'' t) |
69597 | 440 |
| reify'' (\<^term>\<open>(/) :: real => _\<close> $ s $ t) = |
68630 | 441 |
Div (reify'' s, reify'' t) |
69597 | 442 |
| reify'' (\<^term>\<open>uminus :: real => _\<close> $ s) = |
68630 | 443 |
Uminus (reify'' s) |
69597 | 444 |
| reify'' (\<^term>\<open>inverse :: real => _\<close> $ s) = |
68630 | 445 |
Inverse (reify'' s) |
69597 | 446 |
| reify'' (\<^term>\<open>ln :: real => _\<close> $ s) = |
68630 | 447 |
Ln (reify'' s) |
69597 | 448 |
| reify'' (\<^term>\<open>exp :: real => _\<close> $ s) = |
68630 | 449 |
Exp (reify'' s) |
69597 | 450 |
| reify'' (\<^term>\<open>(powr) :: real => _\<close> $ s $ t) = |
68630 | 451 |
Powr (reify'' s, reify'' t) |
69597 | 452 |
| reify'' (\<^term>\<open>powr_nat :: real => _\<close> $ s $ t) = |
68630 | 453 |
Powr_Nat (reify'' s, reify'' t) |
69597 | 454 |
| reify'' (\<^term>\<open>(^) :: real => _\<close> $ s $ t) = |
68630 | 455 |
(if is_const' t then Power (reify'' s, t) else raise TERM ("reify", [t'])) |
69597 | 456 |
| reify'' (\<^term>\<open>root\<close> $ s $ t) = |
68630 | 457 |
(if is_const' s then Root (reify'' t, s) else raise TERM ("reify", [t'])) |
69597 | 458 |
| reify'' (\<^term>\<open>abs :: real => _\<close> $ s) = |
68630 | 459 |
Absolute (reify'' s) |
69597 | 460 |
| reify'' (\<^term>\<open>sgn :: real => _\<close> $ s) = |
68630 | 461 |
Sgn (reify'' s) |
69597 | 462 |
| reify'' (\<^term>\<open>min :: real => _\<close> $ s $ t) = |
68630 | 463 |
Min (reify'' s, reify'' t) |
69597 | 464 |
| reify'' (\<^term>\<open>max :: real => _\<close> $ s $ t) = |
68630 | 465 |
Max (reify'' s, reify'' t) |
69597 | 466 |
| reify'' (\<^term>\<open>Multiseries_Expansion.rfloor\<close> $ s) = |
68630 | 467 |
Floor (reify'' s) |
69597 | 468 |
| reify'' (\<^term>\<open>Multiseries_Expansion.rceil\<close> $ s) = |
68630 | 469 |
Ceiling (reify'' s) |
69597 | 470 |
| reify'' (\<^term>\<open>Archimedean_Field.frac :: real \<Rightarrow> real\<close> $ s) = |
68630 | 471 |
Frac (reify'' s) |
69597 | 472 |
| reify'' (\<^term>\<open>Multiseries_Expansion.rnatmod\<close> $ s $ t) = |
68630 | 473 |
NatMod (reify'' s, reify'' t) |
69597 | 474 |
| reify'' (\<^term>\<open>sin :: real => _\<close> $ s) = |
68630 | 475 |
Sin (reify'' s) |
69597 | 476 |
| reify'' (\<^term>\<open>cos :: real => _\<close> $ s) = |
68630 | 477 |
Cos (reify'' s) |
478 |
| reify'' (Bound 0) = X |
|
479 |
| reify'' t = |
|
480 |
if is_const t then |
|
481 |
ConstExpr t |
|
482 |
else |
|
483 |
case reify_custom ctxt t of |
|
484 |
SOME ((name, t), ts) => |
|
485 |
let |
|
486 |
val args = map (reify_aux ctxt t') ts |
|
487 |
in |
|
488 |
Custom (name, t, args) |
|
489 |
end |
|
490 |
| NONE => raise TERM ("reify", [t']) |
|
491 |
in |
|
492 |
case Envir.eta_long [] t of |
|
69597 | 493 |
Abs (_, \<^typ>\<open>real\<close>, t'') => reify'' t'' |
68630 | 494 |
| _ => raise TERM ("reify", [t]) |
495 |
end |
|
496 |
||
497 |
fun reify_simple ctxt t = |
|
498 |
let |
|
499 |
val thm = preproc_term_conv ctxt (Thm.cterm_of ctxt t) |
|
500 |
val rhs = thm |> Thm.concl_of |> Logic.dest_equals |> snd |
|
501 |
in |
|
502 |
(reify_simple_aux ctxt t rhs, thm) |
|
503 |
end |
|
504 |
||
505 |
fun simple_print_const (Free (x, _)) = x |
|
69597 | 506 |
| simple_print_const (\<^term>\<open>uminus :: real => real\<close> $ a) = |
68630 | 507 |
"(-" ^ simple_print_const a ^ ")" |
69597 | 508 |
| simple_print_const (\<^term>\<open>(+) :: real => _\<close> $ a $ b) = |
68630 | 509 |
"(" ^ simple_print_const a ^ "+" ^ simple_print_const b ^ ")" |
69597 | 510 |
| simple_print_const (\<^term>\<open>(-) :: real => _\<close> $ a $ b) = |
68630 | 511 |
"(" ^ simple_print_const a ^ "-" ^ simple_print_const b ^ ")" |
69597 | 512 |
| simple_print_const (\<^term>\<open>(*) :: real => _\<close> $ a $ b) = |
68630 | 513 |
"(" ^ simple_print_const a ^ "*" ^ simple_print_const b ^ ")" |
69597 | 514 |
| simple_print_const (\<^term>\<open>inverse :: real => _\<close> $ a) = |
68630 | 515 |
"(1 / " ^ simple_print_const a ^ ")" |
69597 | 516 |
| simple_print_const (\<^term>\<open>(/) :: real => _\<close> $ a $ b) = |
68630 | 517 |
"(" ^ simple_print_const a ^ "/" ^ simple_print_const b ^ ")" |
518 |
| simple_print_const t = Int.toString (snd (HOLogic.dest_number t)) |
|
519 |
||
520 |
fun to_mathematica (Add (a, b)) = "(" ^ to_mathematica a ^ " + " ^ to_mathematica b ^ ")" |
|
521 |
| to_mathematica (Minus (a, b)) = "(" ^ to_mathematica a ^ " - " ^ to_mathematica b ^ ")" |
|
522 |
| to_mathematica (Mult (a, b)) = "(" ^ to_mathematica a ^ " * " ^ to_mathematica b ^ ")" |
|
523 |
| to_mathematica (Div (a, b)) = "(" ^ to_mathematica a ^ " / " ^ to_mathematica b ^ ")" |
|
524 |
| to_mathematica (Powr (a, b)) = "(" ^ to_mathematica a ^ " ^ " ^ to_mathematica b ^ ")" |
|
525 |
| to_mathematica (Powr_Nat (a, b)) = "(" ^ to_mathematica a ^ " ^ " ^ to_mathematica b ^ ")" |
|
526 |
| to_mathematica (Powr' (a, b)) = "(" ^ to_mathematica a ^ " ^ " ^ |
|
527 |
to_mathematica (ConstExpr b) ^ ")" |
|
528 |
| to_mathematica (LnPowr (a, b)) = "Log[" ^ to_mathematica a ^ " ^ " ^ to_mathematica b ^ "]" |
|
529 |
| to_mathematica (ExpLn a) = "Exp[Ln[" ^ to_mathematica a ^ "]]" |
|
530 |
| to_mathematica (Power (a, b)) = "(" ^ to_mathematica a ^ " ^ " ^ |
|
531 |
to_mathematica (ConstExpr b) ^ ")" |
|
69597 | 532 |
| to_mathematica (Root (a, \<^term>\<open>2::real\<close>)) = "Sqrt[" ^ to_mathematica a ^ "]" |
68630 | 533 |
| to_mathematica (Root (a, b)) = "Surd[" ^ to_mathematica a ^ ", " ^ |
534 |
to_mathematica (ConstExpr b) ^ "]" |
|
535 |
| to_mathematica (Uminus a) = "(-" ^ to_mathematica a ^ ")" |
|
536 |
| to_mathematica (Inverse a) = "(1/(" ^ to_mathematica a ^ "))" |
|
537 |
| to_mathematica (Exp a) = "Exp[" ^ to_mathematica a ^ "]" |
|
538 |
| to_mathematica (Ln a) = "Log[" ^ to_mathematica a ^ "]" |
|
539 |
| to_mathematica (Sin a) = "Sin[" ^ to_mathematica a ^ "]" |
|
540 |
| to_mathematica (Cos a) = "Cos[" ^ to_mathematica a ^ "]" |
|
541 |
| to_mathematica (ArcTan a) = "ArcTan[" ^ to_mathematica a ^ "]" |
|
542 |
| to_mathematica (Absolute a) = "Abs[" ^ to_mathematica a ^ "]" |
|
543 |
| to_mathematica (Sgn a) = "Sign[" ^ to_mathematica a ^ "]" |
|
544 |
| to_mathematica (Min (a, b)) = "Min[" ^ to_mathematica a ^ ", " ^ to_mathematica b ^ "]" |
|
545 |
| to_mathematica (Max (a, b)) = "Max[" ^ to_mathematica a ^ ", " ^ to_mathematica b ^ "]" |
|
546 |
| to_mathematica (Floor a) = "Floor[" ^ to_mathematica a ^ "]" |
|
547 |
| to_mathematica (Ceiling a) = "Ceiling[" ^ to_mathematica a ^ "]" |
|
548 |
| to_mathematica (Frac a) = "Mod[" ^ to_mathematica a ^ ", 1]" |
|
549 |
| to_mathematica (ConstExpr t) = simple_print_const t |
|
550 |
| to_mathematica X = "X" |
|
551 |
||
552 |
(* TODO: correct translation of frac() for Maple and Sage *) |
|
553 |
fun to_maple (Add (a, b)) = "(" ^ to_maple a ^ " + " ^ to_maple b ^ ")" |
|
554 |
| to_maple (Minus (a, b)) = "(" ^ to_maple a ^ " - " ^ to_maple b ^ ")" |
|
555 |
| to_maple (Mult (a, b)) = "(" ^ to_maple a ^ " * " ^ to_maple b ^ ")" |
|
556 |
| to_maple (Div (a, b)) = "(" ^ to_maple a ^ " / " ^ to_maple b ^ ")" |
|
557 |
| to_maple (Powr (a, b)) = "(" ^ to_maple a ^ " ^ " ^ to_maple b ^ ")" |
|
558 |
| to_maple (Powr_Nat (a, b)) = "(" ^ to_maple a ^ " ^ " ^ to_maple b ^ ")" |
|
559 |
| to_maple (Powr' (a, b)) = "(" ^ to_maple a ^ " ^ " ^ |
|
560 |
to_maple (ConstExpr b) ^ ")" |
|
561 |
| to_maple (LnPowr (a, b)) = "ln(" ^ to_maple a ^ " ^ " ^ to_maple b ^ ")" |
|
562 |
| to_maple (ExpLn a) = "ln(exp(" ^ to_maple a ^ "))" |
|
563 |
| to_maple (Power (a, b)) = "(" ^ to_maple a ^ " ^ " ^ |
|
564 |
to_maple (ConstExpr b) ^ ")" |
|
69597 | 565 |
| to_maple (Root (a, \<^term>\<open>2::real\<close>)) = "sqrt(" ^ to_maple a ^ ")" |
68630 | 566 |
| to_maple (Root (a, b)) = "root(" ^ to_maple a ^ ", " ^ |
567 |
to_maple (ConstExpr b) ^ ")" |
|
568 |
| to_maple (Uminus a) = "(-" ^ to_maple a ^ ")" |
|
569 |
| to_maple (Inverse a) = "(1/(" ^ to_maple a ^ "))" |
|
570 |
| to_maple (Exp a) = "exp(" ^ to_maple a ^ ")" |
|
571 |
| to_maple (Ln a) = "ln(" ^ to_maple a ^ ")" |
|
572 |
| to_maple (Sin a) = "sin(" ^ to_maple a ^ ")" |
|
573 |
| to_maple (Cos a) = "cos(" ^ to_maple a ^ ")" |
|
574 |
| to_maple (ArcTan a) = "arctan(" ^ to_maple a ^ ")" |
|
575 |
| to_maple (Absolute a) = "abs(" ^ to_maple a ^ ")" |
|
576 |
| to_maple (Sgn a) = "signum(" ^ to_maple a ^ ")" |
|
577 |
| to_maple (Min (a, b)) = "min(" ^ to_maple a ^ ", " ^ to_maple b ^ ")" |
|
578 |
| to_maple (Max (a, b)) = "max(" ^ to_maple a ^ ", " ^ to_maple b ^ ")" |
|
579 |
| to_maple (Floor a) = "floor(" ^ to_maple a ^ ")" |
|
580 |
| to_maple (Ceiling a) = "ceil(" ^ to_maple a ^ ")" |
|
581 |
| to_maple (Frac a) = "frac(" ^ to_maple a ^ ")" |
|
582 |
| to_maple (ConstExpr t) = simple_print_const t |
|
583 |
| to_maple X = "x" |
|
584 |
||
585 |
fun to_maxima (Add (a, b)) = "(" ^ to_maxima a ^ " + " ^ to_maxima b ^ ")" |
|
586 |
| to_maxima (Minus (a, b)) = "(" ^ to_maxima a ^ " - " ^ to_maxima b ^ ")" |
|
587 |
| to_maxima (Mult (a, b)) = "(" ^ to_maxima a ^ " * " ^ to_maxima b ^ ")" |
|
588 |
| to_maxima (Div (a, b)) = "(" ^ to_maxima a ^ " / " ^ to_maxima b ^ ")" |
|
589 |
| to_maxima (Powr (a, b)) = "(" ^ to_maxima a ^ " ^ " ^ to_maxima b ^ ")" |
|
590 |
| to_maxima (Powr_Nat (a, b)) = "(" ^ to_maxima a ^ " ^ " ^ to_maxima b ^ ")" |
|
591 |
| to_maxima (Powr' (a, b)) = "(" ^ to_maxima a ^ " ^ " ^ |
|
592 |
to_maxima (ConstExpr b) ^ ")" |
|
593 |
| to_maxima (ExpLn a) = "exp (log (" ^ to_maxima a ^ "))" |
|
594 |
| to_maxima (LnPowr (a, b)) = "log(" ^ to_maxima a ^ " ^ " ^ to_maxima b ^ ")" |
|
595 |
| to_maxima (Power (a, b)) = "(" ^ to_maxima a ^ " ^ " ^ |
|
596 |
to_maxima (ConstExpr b) ^ ")" |
|
69597 | 597 |
| to_maxima (Root (a, \<^term>\<open>2::real\<close>)) = "sqrt(" ^ to_maxima a ^ ")" |
68630 | 598 |
| to_maxima (Root (a, b)) = to_maxima a ^ "^(1/" ^ |
599 |
to_maxima (ConstExpr b) ^ ")" |
|
600 |
| to_maxima (Uminus a) = "(-" ^ to_maxima a ^ ")" |
|
601 |
| to_maxima (Inverse a) = "(1/(" ^ to_maxima a ^ "))" |
|
602 |
| to_maxima (Exp a) = "exp(" ^ to_maxima a ^ ")" |
|
603 |
| to_maxima (Ln a) = "log(" ^ to_maxima a ^ ")" |
|
604 |
| to_maxima (Sin a) = "sin(" ^ to_maxima a ^ ")" |
|
605 |
| to_maxima (Cos a) = "cos(" ^ to_maxima a ^ ")" |
|
606 |
| to_maxima (ArcTan a) = "atan(" ^ to_maxima a ^ ")" |
|
607 |
| to_maxima (Absolute a) = "abs(" ^ to_maxima a ^ ")" |
|
608 |
| to_maxima (Sgn a) = "signum(" ^ to_maxima a ^ ")" |
|
609 |
| to_maxima (Min (a, b)) = "min(" ^ to_maxima a ^ ", " ^ to_maxima b ^ ")" |
|
610 |
| to_maxima (Max (a, b)) = "max(" ^ to_maxima a ^ ", " ^ to_maxima b ^ ")" |
|
611 |
| to_maxima (Floor a) = "floor(" ^ to_maxima a ^ ")" |
|
612 |
| to_maxima (Ceiling a) = "ceil(" ^ to_maxima a ^ ")" |
|
613 |
| to_maxima (Frac a) = let val x = to_maxima a in "(" ^ x ^ " - floor(" ^ x ^ "))" end |
|
614 |
| to_maxima (ConstExpr t) = simple_print_const t |
|
615 |
| to_maxima X = "x" |
|
616 |
||
617 |
fun to_sympy (Add (a, b)) = "(" ^ to_sympy a ^ " + " ^ to_sympy b ^ ")" |
|
618 |
| to_sympy (Minus (a, b)) = "(" ^ to_sympy a ^ " - " ^ to_sympy b ^ ")" |
|
619 |
| to_sympy (Mult (a, b)) = "(" ^ to_sympy a ^ " * " ^ to_sympy b ^ ")" |
|
620 |
| to_sympy (Div (a, b)) = "(" ^ to_sympy a ^ " / " ^ to_sympy b ^ ")" |
|
621 |
| to_sympy (Powr (a, b)) = "(" ^ to_sympy a ^ " ** " ^ to_sympy b ^ ")" |
|
622 |
| to_sympy (Powr_Nat (a, b)) = "(" ^ to_sympy a ^ " ** " ^ to_sympy b ^ ")" |
|
623 |
| to_sympy (Powr' (a, b)) = "(" ^ to_sympy a ^ " ** " ^ |
|
624 |
to_sympy (ConstExpr b) ^ ")" |
|
625 |
| to_sympy (ExpLn a) = "exp (log (" ^ to_sympy a ^ "))" |
|
626 |
| to_sympy (LnPowr (a, b)) = "log(" ^ to_sympy a ^ " ** " ^ to_sympy b ^ ")" |
|
627 |
| to_sympy (Power (a, b)) = "(" ^ to_sympy a ^ " ** " ^ |
|
628 |
to_sympy (ConstExpr b) ^ ")" |
|
69597 | 629 |
| to_sympy (Root (a, \<^term>\<open>2::real\<close>)) = "sqrt(" ^ to_sympy a ^ ")" |
68630 | 630 |
| to_sympy (Root (a, b)) = "root(" ^ to_sympy a ^ ", " ^ to_sympy (ConstExpr b) ^ ")" |
631 |
| to_sympy (Uminus a) = "(-" ^ to_sympy a ^ ")" |
|
632 |
| to_sympy (Inverse a) = "(1/(" ^ to_sympy a ^ "))" |
|
633 |
| to_sympy (Exp a) = "exp(" ^ to_sympy a ^ ")" |
|
634 |
| to_sympy (Ln a) = "log(" ^ to_sympy a ^ ")" |
|
635 |
| to_sympy (Sin a) = "sin(" ^ to_sympy a ^ ")" |
|
636 |
| to_sympy (Cos a) = "cos(" ^ to_sympy a ^ ")" |
|
637 |
| to_sympy (ArcTan a) = "atan(" ^ to_sympy a ^ ")" |
|
638 |
| to_sympy (Absolute a) = "abs(" ^ to_sympy a ^ ")" |
|
639 |
| to_sympy (Sgn a) = "sign(" ^ to_sympy a ^ ")" |
|
640 |
| to_sympy (Min (a, b)) = "min(" ^ to_sympy a ^ ", " ^ to_sympy b ^ ")" |
|
641 |
| to_sympy (Max (a, b)) = "max(" ^ to_sympy a ^ ", " ^ to_sympy b ^ ")" |
|
642 |
| to_sympy (Floor a) = "floor(" ^ to_sympy a ^ ")" |
|
643 |
| to_sympy (Ceiling a) = "ceiling(" ^ to_sympy a ^ ")" |
|
644 |
| to_sympy (Frac a) = "frac(" ^ to_sympy a ^ ")" |
|
645 |
| to_sympy (ConstExpr t) = simple_print_const t |
|
646 |
| to_sympy X = "x" |
|
647 |
||
648 |
fun to_sage (Add (a, b)) = "(" ^ to_sage a ^ " + " ^ to_sage b ^ ")" |
|
649 |
| to_sage (Minus (a, b)) = "(" ^ to_sage a ^ " - " ^ to_sage b ^ ")" |
|
650 |
| to_sage (Mult (a, b)) = "(" ^ to_sage a ^ " * " ^ to_sage b ^ ")" |
|
651 |
| to_sage (Div (a, b)) = "(" ^ to_sage a ^ " / " ^ to_sage b ^ ")" |
|
652 |
| to_sage (Powr (a, b)) = "(" ^ to_sage a ^ " ^ " ^ to_sage b ^ ")" |
|
653 |
| to_sage (Powr_Nat (a, b)) = "(" ^ to_sage a ^ " ^ " ^ to_sage b ^ ")" |
|
654 |
| to_sage (Powr' (a, b)) = "(" ^ to_sage a ^ " ^ " ^ |
|
655 |
to_sage (ConstExpr b) ^ ")" |
|
656 |
| to_sage (ExpLn a) = "exp (log (" ^ to_sage a ^ "))" |
|
657 |
| to_sage (LnPowr (a, b)) = "log(" ^ to_sage a ^ " ^ " ^ to_sage b ^ ")" |
|
658 |
| to_sage (Power (a, b)) = "(" ^ to_sage a ^ " ^ " ^ |
|
659 |
to_sage (ConstExpr b) ^ ")" |
|
69597 | 660 |
| to_sage (Root (a, \<^term>\<open>2::real\<close>)) = "sqrt(" ^ to_sage a ^ ")" |
68630 | 661 |
| to_sage (Root (a, b)) = to_sage a ^ "^(1/" ^ to_sage (ConstExpr b) ^ ")" |
662 |
| to_sage (Uminus a) = "(-" ^ to_sage a ^ ")" |
|
663 |
| to_sage (Inverse a) = "(1/(" ^ to_sage a ^ "))" |
|
664 |
| to_sage (Exp a) = "exp(" ^ to_sage a ^ ")" |
|
665 |
| to_sage (Ln a) = "log(" ^ to_sage a ^ ")" |
|
666 |
| to_sage (Sin a) = "sin(" ^ to_sage a ^ ")" |
|
667 |
| to_sage (Cos a) = "cos(" ^ to_sage a ^ ")" |
|
668 |
| to_sage (ArcTan a) = "atan(" ^ to_sage a ^ ")" |
|
669 |
| to_sage (Absolute a) = "abs(" ^ to_sage a ^ ")" |
|
670 |
| to_sage (Sgn a) = "sign(" ^ to_sage a ^ ")" |
|
671 |
| to_sage (Min (a, b)) = "min(" ^ to_sage a ^ ", " ^ to_sage b ^ ")" |
|
672 |
| to_sage (Max (a, b)) = "max(" ^ to_sage a ^ ", " ^ to_sage b ^ ")" |
|
673 |
| to_sage (Floor a) = "floor(" ^ to_sage a ^ ")" |
|
674 |
| to_sage (Ceiling a) = "ceil(" ^ to_sage a ^ ")" |
|
675 |
| to_sage (Frac a) = "frac(" ^ to_sage a ^ ")" |
|
676 |
| to_sage (ConstExpr t) = simple_print_const t |
|
677 |
| to_sage X = "x" |
|
678 |
||
679 |
fun reify_mathematica ctxt = to_mathematica o fst o reify_simple ctxt |
|
680 |
fun reify_maple ctxt = to_maple o fst o reify_simple ctxt |
|
681 |
fun reify_maxima ctxt = to_maxima o fst o reify_simple ctxt |
|
682 |
fun reify_sympy ctxt = to_sympy o fst o reify_simple ctxt |
|
683 |
fun reify_sage ctxt = to_sage o fst o reify_simple ctxt |
|
684 |
||
685 |
fun limit_mathematica s = "Limit[" ^ s ^ ", X -> Infinity]" |
|
686 |
fun limit_maple s = "limit(" ^ s ^ ", x = infinity);" |
|
687 |
fun limit_maxima s = "limit(" ^ s ^ ", x, inf);" |
|
688 |
fun limit_sympy s = "limit(" ^ s ^ ", x, oo)" |
|
689 |
fun limit_sage s = "limit(" ^ s ^ ", x = Infinity)" |
|
690 |
||
691 |
end |