Birefringence imaging is one of the powerful methods for non-destructive characterization of defects in the semiconductor crystals. However, due to the complicated and unclear contrasts of dislocations in the birefringence image, it was considered to be difficult to automatically detect the position of the dislocation contrasts by the conventional image processing. In the present study, we designed the automatic detection algorithm for the dislocation contrasts taking into account the characteristic feature of the dislocation contrasts, which were always pair of black and white contrasts. To detect the large change in the contrast level near the dislocation contrast, the automatic detection algorithm was constructed by using a variance filter. Finally, we succeeded in detecting the position of the dislocation contrasts with relatively high precision and sensitivity.

We study a dependently typed extension of a multi-stage programming languageà la MetaOCaml, which supports quasi-quotation and cross-stage persistence for manipulation of code fragments as firstclass values and an evaluation construct for execution of programs dynamically generated by this code manipulation. Dependent types are expected to bring to multi-stage programming enforcement of strong invariant-beyond simple type safety-on the behavior of dynamically generated code. An extension is, however, not trivial because such a type system would have to take stages of types-roughly speaking, the number of surrounding quotations-into account. To rigorously study properties of such an extension, we develop λ MD , which is an extension of Hanada and Igarashi's typed calculus λ ⊲% with dependent types, and prove its properties including preservation, confluence, strong normalization for full reduction, and progress for staged reduction. Motivated by code generators that generate code whose type depends on a value from outside of the quotations, we argue the significance of cross-stage persistence in dependently typed multi-stage programming and certain type equivalences that are not directly derived from reduction rules. A. Kawata, A. Igarashi B ProofsJ is a metavariable for judgments as in Section 4. We say type environment Γ is a subsequence of type environment ∆ if and only if we can get Γ from ∆ by deleting some or no variables without changing the order of the remaining elements.Lemma 4 (Weakening). If Γ ⊢ Σ J @A and Γ is a subsequence of ∆, then ∆ ⊢ Σ J@A.Proof. By straightforward induction on the derivation of typing, kinding, wellformed kinding, term equivalence, type equivalence or kind equivalence. We show only representative cases.

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A smart contract is a program executed on a blockchain, based on which many cryptocurrencies are implemented, and is being used for automating transactions. Due to the large amount of money that smart contracts deal with, there is a surging demand for a method that can statically and formally verify them. This article describes our type-based static verification tool Helmholtz for Michelson, which is a statically typed stack-based language for writing smart contracts that are executed on the blockchain platform Tezos. Helmholtz is designed on top of our extension of Michelson’s type system with refinement types. Helmholtz takes a Michelson program annotated with a user-defined specification written in the form of a refinement type as input; it then typechecks the program against the specification based on the refinement type system, discharging the generated verification conditions with the SMT solver Z3. We briefly introduce our refinement type system for the core calculus Mini-Michelson of Michelson, which incorporates the characteristic features such as compound datatypes (e.g., lists and pairs), higher-order functions, and invocation of another contract. Helmholtz successfully verifies several practical Michelson programs, including one that transfers money to an account and that checks a digital signature.