Type-Based Structural Analysis for Modular Systems of Equations
نویسنده
چکیده
ion over Structural Types (1) Now consider encapsulating the equations: bar = sigrel (u, y) where foo ⋄ (u, v ,w) foo ⋄ (w , u + x , v + y) The equations of the body of bar needs to be partitioned into • Local Equations: equations used to solve for the local variables • Interface Equations: equations contributed to the outside Type-Based Structural Analysis for Modular Systems of Equations – p.19/23 Abstraction over Structural Types (2) How to partition?ion over Structural Types (2) How to partition? Type-Based Structural Analysis for Modular Systems of Equations – p.20/23 Abstraction over Structural Types (2) How to partition? • A priori local equations: equations over local variables only.ion over Structural Types (2) How to partition? • A priori local equations: equations over local variables only. Type-Based Structural Analysis for Modular Systems of Equations – p.20/23 Abstraction over Structural Types (2) How to partition? • A priori local equations: equations over local variables only. • A priori interface equations: equations over interface variables only.ion over Structural Types (2) How to partition? • A priori local equations: equations over local variables only. • A priori interface equations: equations over interface variables only. Type-Based Structural Analysis for Modular Systems of Equations – p.20/23 Abstraction over Structural Types (2) How to partition? • A priori local equations: equations over local variables only. • A priori interface equations: equations over interface variables only. • Mixed equations: equations over local and interface variables.ion over Structural Types (2) How to partition? • A priori local equations: equations over local variables only. • A priori interface equations: equations over interface variables only. • Mixed equations: equations over local and interface variables. Type-Based Structural Analysis for Modular Systems of Equations – p.20/23 Abstraction over Structural Types (2) How to partition? • A priori local equations: equations over local variables only. • A priori interface equations: equations over interface variables only. • Mixed equations: equations over local and interface variables. Note: too few or too many local equations gives an opportunity to catch locally underdetermined or overdeteremined systems of equations. Type-Based Structural Analysis for Modular Systems of Equations – p.20/23ion over Structural Types (2) How to partition? • A priori local equations: equations over local variables only. • A priori interface equations: equations over interface variables only. • Mixed equations: equations over local and interface variables. Note: too few or too many local equations gives an opportunity to catch locally underdetermined or overdeteremined systems of equations. Type-Based Structural Analysis for Modular Systems of Equations – p.20/23 Abstraction over Structural Types (3) In our case:ion over Structural Types (3) In our case: Type-Based Structural Analysis for Modular Systems of Equations – p.21/23 Abstraction over Structural Types (3) In our case: • We have 1 a priori local equation, 3 mixed equationsion over Structural Types (3) In our case: • We have 1 a priori local equation, 3 mixed equations Type-Based Structural Analysis for Modular Systems of Equations – p.21/23 Abstraction over Structural Types (3) In our case: • We have 1 a priori local equation, 3 mixed equations • We need to choose 3 local equations and 1 interface equationion over Structural Types (3) In our case: • We have 1 a priori local equation, 3 mixed equations • We need to choose 3 local equations and 1 interface equation Type-Based Structural Analysis for Modular Systems of Equations – p.21/23 Abstraction over Structural Types (3) In our case: • We have 1 a priori local equation, 3 mixed equations • We need to choose 3 local equations and 1 interface equation • Consequently, 3 possibilities, yielding the following possible structural types for bar : u y (ion over Structural Types (3) In our case: • We have 1 a priori local equation, 3 mixed equations • We need to choose 3 local equations and 1 interface equation • Consequently, 3 possibilities, yielding the following possible structural types for bar : u y (
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