1. Sub-system interfaces
Sub-system A
Sub-system B

2. Larch Family of Languages
Family of Specification Languages
Specification components:
Larch Shared Language – common to all languages
Larch Interface Language – particular to specific PL
LSL: an algebraic language
LIL: tailored to a programming language

3. Larch Interface Language (Larch/L) Two-tiered specification in Larch
Programming Language L
Program unit
Implementation
satisfies
Larch Interface Language (Larch/L)
Interface spec
Local Specification
Based on
Root trait
Incorporates (includes, imports, or assumes)
Larch shared language …
Trait
Trait
Two-tiered specification in Larch

4. Some Aspects of Larch Languages
Composability. Incremental construction of specifications from other specifications
Emphasis on Presentation. Readable. Larch composition mechanisms are operations on specification, rather than on theories or models.
Suitability for integrated interactive tools. Good for interactive construction and incremental checking of specs.
Semantic Checking. Checking of specs when they are being constructed. (i.e. theorem prover for semantic checking)

5. Trait: is the basic unit of specification in LSL
Trait: is the basic unit of specification in LSL. It introduces operators and specifies their properties. Sometimes collection of operators correspond to an ADT.
Theory: is a set of theorems that can be proved about the terms defined in a trait.
Theory contains equations and inequation (~(true = false)) that can be proved by substituting equal for equal. BUT, if 2 terms can not be proven to be equal then they are not necessarily unequal. Also if two terms are not provably unequal, it does not mean they are equal.
Signature: domains and ranges of the operators used for sort-check (similar to type-check in PL).
Constraints: limit the operators by means of equations that relate the terms containing them.

6. Larch Interface Language (LIL)
Localized programming language dependencies
Each LIL encapsulates features needed to write specifications in a particular Programming Language and incorporates LSL in a uniform way.

7. Larch Prover (LP)
LP is an interactive theorem proving system for multi-sorted first-order logic
Assist users in finding and correcting flaws in conjectures
Works efficiently on large problems
Is not designed to find difficult proofs automatically
Checks for syntax and type errors in LSL specifications
Two files of input suitable for use with LP:
LP axiomatization for an LSL specification
LP proof obligations associated with logical claims made by specifiers about the logical properties of their specifications

8. The Larch Shared Language (LSL)
LSL specifications define two kinds of symbols, operators and sorts.
operators stand for total functions from tuples of values to values.
Sorts stand for disjoint non-empty sets of values, and are used to indicate the domains and ranges of operators.
The trait is the basic unit of specification in LSL.
A trait introduces some operators and specifies some of their properties.
Sometimes the trait defines an abstract type. However, it is frequently useful to define a set of properties that does not fully characterize a type.

9. Example - Table
Table: trait includes Integer introduces new:  Tab add: Tab, Ind, Val  Tab - - : Ind, Tab  Bool lookup: Tab, Ind  Val size: Tab  Int

10. Example - Table
asserts  i, i1: Ind, v: Val, t: Tab (i  new); i  add(t, i1, v) == i = i1  i  t; lookup(add(t, i, v), i1) == if i = i1 then v else lookup(t, i1); size(new) == 0; size(add(t, i, v)) == if i  t then size(t) else size(t) + 1