(* Title: HOL/Matrix/cplex/matrixlp.ML Author: Steven Obua *) signature MATRIX_LP = sig val lp_dual_estimate_prt : string -> int -> thm val lp_dual_estimate_prt_primitive : cterm * (cterm * cterm) * (cterm * cterm) * cterm * (cterm * cterm) -> thm val matrix_compute : cterm -> thm val matrix_simplify : thm -> thm val prove_bound : string -> int -> thm val float2real : string * string -> Real.real end structure MatrixLP : MATRIX_LP = struct fun inst_real thm = let val certT = ctyp_of (Thm.theory_of_thm thm) in standard (Thm.instantiate ([(certT (TVar (hd (OldTerm.term_tvars (prop_of thm)))), certT HOLogic.realT)], []) thm) end local val cert = cterm_of @{theory} in fun lp_dual_estimate_prt_primitive (y, (A1, A2), (c1, c2), b, (r1, r2)) = let val th = inst_real @{thm "spm_mult_le_dual_prts_no_let"} fun var s x = (cert (Var ((s,0), FloatSparseMatrixBuilder.spmatT)), x) val th = Thm.instantiate ([], [var "A1" A1, var "A2" A2, var "y" y, var "c1" c1, var "c2" c2, var "r1" r1, var "r2" r2, var "b" b]) th in th end fun lp_dual_estimate_prt lptfile prec = let val certificate = let open Fspmlp val l = load lptfile prec false in (y l |> cert, A l |> pairself cert, c l |> pairself cert, b l |> cert, r12 l |> pairself cert) end in lp_dual_estimate_prt_primitive certificate end end fun prep ths = ComputeHOL.prep_thms ths fun inst_tvar ty thm = let val certT = Thm.ctyp_of (Thm.theory_of_thm thm); val ord = prod_ord (prod_ord string_ord int_ord) (list_ord string_ord) val v = TVar (hd (sort ord (OldTerm.term_tvars (prop_of thm)))) in standard (Thm.instantiate ([(certT v, certT ty)], []) thm) end fun inst_tvars [] thms = thms | inst_tvars (ty::tys) thms = inst_tvars tys (map (inst_tvar ty) thms) local val ths = ComputeHOL.prep_thms @{thms "ComputeHOL.compute_list_case" "ComputeHOL.compute_let" "ComputeHOL.compute_if" "ComputeFloat.arith" "SparseMatrix.sparse_row_matrix_arith_simps" "ComputeHOL.compute_bool" "ComputeHOL.compute_pair" "SparseMatrix.sorted_sp_simps" "ComputeNumeral.number_norm" "ComputeNumeral.natnorm"}; val computer = PCompute.make Compute.SML @{theory} ths [] in fun matrix_compute c = hd (PCompute.rewrite computer [c]) end fun matrix_simplify th = let val simp_th = matrix_compute (cprop_of th) val th = strip_shyps (equal_elim simp_th th) fun removeTrue th = removeTrue (implies_elim th TrueI) handle _ => th (* FIXME avoid handle _ *) in removeTrue th end fun prove_bound lptfile prec = let val th = lp_dual_estimate_prt lptfile prec in matrix_simplify th end val realFromStr = the o Real.fromString; fun float2real (x, y) = realFromStr x * Math.pow (2.0, realFromStr y); end