Much research has documented the elevated levels of stress experienced by families of autistic children. Yet remarkably little research has examined the types of support that these families perceive to be beneficial to their lives. This study, co-produced by researchers and school-based professionals, sought to establish these families' support needs from their own perspectives. In total, 139 parents of autistic children with additional intellectual disabilities and limited spoken communication, all attending an inner-city London school, participated in an initial survey examining parental wellbeing, self-efficacy and the extent to which they felt supported. Semi-structured interviews were conducted with a subgroup of parents ( n = 17), some of whom reported in the survey that they felt unsupported, in order to gain their in-depth perspectives. The results from both the survey and the interviews suggested that existing support (particularly from formal support services) was not meeting parents' needs, which ultimately made them feel isolated and alienated. Parents who were interviewed called for service provision that adopted a relational, family-centred approach - one that understands the specific needs of the whole family, builds a close working relationship with them and ensures that they are supported at times when the parents and families feel they need it most.

Lucid is a formal system in which programs can be written and proofs of programs carried out. The proofs are particularly easy to follow and straightforward to produce because the statements in a Lucid program are simply axioms from which the proof proceeds by (almost) conventional logical reasoning, with the help of a few axioms and rules of inference for the special Lucid functions. As a programming language, Lucid is unconventional because, among other things, the order of statements is irrelevant and assignment statements are equations. Nevertheless, Lucid programs need not look much different than iterative programs in a conventional structured programming language using assignment and conditional statements and loops.

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Lucid is both a programming language and a formal system for proving properties of Lucid programs. The programming language is unconventional in many ways, although programs are readily understood as using assignment statements and loops in a "structured" fashion. Semantically, an assignment statement is really an equation between "histories", and a whole program is simply an unordered set of such equations. From these equations, properties of the program can be derived by straightforward mathematical reasoning, using the Lucid formal system. The rules of this system are mainly those of first-order logic, together with extra axioms and rules for the special Lucid functions. This paper formally described the syntax and semantics of programs, and justifies the axioms and rules of the formal system.

A class of (monadic) functional schemas which properly includes "Ianov" flowchart schemas is defined It is shown that the terminatmn, divergence, and freedom problems for functional schemas are decidable Although it is posmble to translate a large class of nonfree functional schemas into equivalent free functional schemas, it is shown that m general this cannot be done It is also shown that the equivalence problem for free functional schemas is decidable. Most oi the results are obtained from well-known results m formal languages and automata theory.KEY WORDS AND PHRASES monadic functional schemas, declsmn problems, equivalence, freedom, formal languages, automata theory CR CATEGORIES" 5.22, 5.24 Monadic Functwnal SchemasAn alphabet Xs of a (monadic) functional schema S consists of one individual variable x, a finite set of monadic function variables {F~} (with a designated initial function variable F0), a finite set of monadic function constants {f~l, and a finite set of monadic predicate constants {p~}. Note that individual constants are not allowed.A term over ~s is any term in the normal sense constructed from the monadic function variables IF,}, monadic function constants If, l, and the variable x, e.g. f l ( Fa ( Fo (f : ( x ) ) ) ) . A conditwnal term over Z s is any finite expression of the form if p, (x) then T1 else T2, where p, is any predicate constant of Zs, and vl and r2 are any terms or conditional terms over Zs. A definitwn of F, over Zs is of the form F,(x) ~ r, where r is any