(* Title: HOL/Matrix_LP/matrixlp.ML
Author: Steven Obua
*)
signature MATRIX_LP =
sig
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
val compute_thms = 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.natnorm"}; (*"ComputeNumeral.number_norm"*)
val spm_mult_le_dual_prts_no_let_real = @{thm "spm_mult_le_dual_prts_no_let" [where ?'a = real]}
fun lp_dual_estimate_prt lptfile prec =
let
val cert = cterm_of @{theory}
fun var s x = (cert (Var ((s, 0), FloatSparseMatrixBuilder.spmatT)), x)
val l = Fspmlp.load lptfile prec false
val (y, (A1, A2), (c1, c2), b, (r1, r2)) =
let
open Fspmlp
in
(y l |> cert, A l |> pairself cert, c l |> pairself cert, b l |> cert, r12 l |> pairself cert)
end
in
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])
spm_mult_le_dual_prts_no_let_real
end
val computer = PCompute.make Compute.SML @{theory} compute_thms []
fun matrix_compute c = hd (PCompute.rewrite computer [c])
fun matrix_simplify th =
let
val simp_th = matrix_compute (cprop_of th)
val th = Thm.strip_shyps (Thm.equal_elim simp_th th)
fun removeTrue th = removeTrue (Thm.implies_elim th TrueI) handle THM _ => th
in
removeTrue th
end
val prove_bound = matrix_simplify oo lp_dual_estimate_prt;
val realFromStr = the o Real.fromString;
fun float2real (x, y) = realFromStr x * Math.pow (2.0, realFromStr y);
end