src/HOL/Matrix/cplex/matrixlp.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Matrix/cplex/matrixlp.ML	Fri Sep 29 22:47:51 2006 +0200
@@ -0,0 +1,123 @@
+(*  Title:      HOL/Matrix/cplex/MatrixLP.ML
+    ID:         $Id$
+    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 (term_tvars (prop_of thm)))), certT HOLogic.realT)], []) thm)
+  end
+
+val spm_mult_le_dual_prts_no_let = thm "SparseMatrix.spm_mult_le_dual_prts_no_let"
+
+fun lp_dual_estimate_prt_primitive (y, (A1, A2), (c1, c2), b, (r1, r2)) =
+  let
+    val cert = cterm_of (Thm.theory_of_thm spm_mult_le_dual_prts_no_let)
+    val th = inst_real spm_mult_le_dual_prts_no_let
+    fun var s x = (cert (Var ((s,0), FloatSparseMatrixBuilder.real_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, A l, c l, b l, r12 l)
+            end
+    in
+        lp_dual_estimate_prt_primitive certificate
+    end
+
+fun is_meta_eq th =
+    let
+        fun check ((Const ("==", _)) $ _ $ _) = true
+          | check _ = false
+    in
+        check (concl_of th)
+    end
+
+fun prep ths = (Library.filter is_meta_eq ths) @ (map (standard o mk_meta_eq) (Library.filter (not o is_meta_eq) 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 (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)
+
+val matrix_compute =
+    let
+        val spvecT = FloatSparseMatrixBuilder.real_spvecT
+        val spmatT = FloatSparseMatrixBuilder.real_spmatT
+        val spvecT_elem = HOLogic.mk_prodT (HOLogic.natT, HOLogic.realT)
+        val spmatT_elem = HOLogic.mk_prodT (HOLogic.natT, spvecT)
+        val case_compute = map thm ["list_case_compute", "list_case_compute_empty", "list_case_compute_cons"]
+        val ths =
+            prep (
+            (inst_tvars [HOLogic.intT, HOLogic.natT] (thms "Let_compute"))
+            @ (inst_tvars [HOLogic.intT, HOLogic.intT] (thms "Let_compute"))
+            @ (map (fn t => inst_tvar t (thm "If_True")) [HOLogic.intT, HOLogic.natT, HOLogic.realT, spvecT, spmatT, HOLogic.boolT])
+            @ (map (fn t => inst_tvar t (thm "If_False")) [HOLogic.intT, HOLogic.natT, HOLogic.realT, spvecT, spmatT, HOLogic.boolT])
+            @ (thms "MatrixLP.float_arith")
+            @ (map (inst_tvar HOLogic.realT) (thms "MatrixLP.sparse_row_matrix_arith_simps"))
+            @ (thms "MatrixLP.boolarith")
+            @ (inst_tvars [HOLogic.natT, HOLogic.realT] [thm "fst_compute", thm "snd_compute"])
+            @ (inst_tvars [HOLogic.natT, FloatSparseMatrixBuilder.real_spvecT] [thm "fst_compute", thm "snd_compute"])
+            @ (inst_tvars [HOLogic.boolT, spmatT_elem] case_compute)
+            @ (inst_tvars [HOLogic.boolT, spvecT_elem] case_compute)
+            @ (inst_tvars [HOLogic.boolT, HOLogic.realT] case_compute)
+            @ (inst_tvars [spvecT] (thms "MatrixLP.sorted_sp_simps"))
+            @ (inst_tvars [HOLogic.realT] (thms "MatrixLP.sorted_sp_simps"))
+            @ [thm "zero_eq_Numeral0_nat", thm "one_eq_Numeral1_nat"]
+            @ (inst_tvars [HOLogic.intT] [thm "zero_eq_Numeral0_nring", thm "one_eq_Numeral1_nring"])
+            @ (inst_tvars [HOLogic.realT] [thm "zero_eq_Numeral0_nring", thm "one_eq_Numeral1_nring"]))
+
+        val c = Compute.basic_make (the_context ()) ths
+    in
+        Compute.rewrite 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
+    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