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The paper presents a novel approach for type specification manipulations as the basic operations intended to develop various forms of compositions in information systems. Among them are interoperable compositions of pre-existing components formed during the information systems design, heterogeneous multidatabase compositions, database schema and ontology integration, compositions of workflows, compositions of the type of the result of algebraic operations over typed data collections. In the paper the compositional specification calculus is presented in context of one of such application - the compositional information systems development. Principle of decomposition of type specifications into a collection of type reducts serving as units of reuse and composition is formulated. An operation of taking most common reduct for component and specification of requirements types is defined. The refinement property of the common reduct leads to a justifiable identification of reusable component fragments. Type lattice and algebra based on partially ordered set of complete type specifications and the type commonality principle are defined. Type specification composition operations of the algebra are based on identification of common information in the composed specifications. Paper presents a combination of semi-formal and formal modeling facilities to perform provably correct operations of common reduct identification, type specification composition and reuse.