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In logic and computer science, specifically automated reasoning, unification is an algorithmic process of solving equations between symbolic expressions, each of the form Left-hand side = Right-hand side. For example, using x, y, z as variables, and taking f to be an uninterpreted function, the singleton equation set { f (1, y) = f ( x ,2) } is ...
- Type Inference
- Matrix Example
- Unification
- Unification Algorithm
- Type Inference and Unification
Type inference refers to the process of determining the appropriate types forexpressions based on how they are used. For example, in theexpression f 3, OCaml knows that f must be a function, because it isapplied to something (not because its name is f!) and that it takesan int as input. It knows nothing about the output type. Therefore the type inf...
Let's illustrate the inference process with a simple example. Supposewe have matrices of different sizes and shapes. Let's write the type of anm x n matrix as m -> n. I can multiply two matrices if and only if thecolumn dimension of the first is equal to the row dimension of the second. This can be represented by a typing rule which says that if ma...
Both polymorphic type inference and pattern matching in OCaml are instances of avery general mechanism called unification. Briefly, unification isthe process of finding a substitution that makes two given terms equal. Pattern matching in OCaml is done by applying unification to OCaml expressions (e.g. Somex), whereas type inference is done by apply...
We need unification for not just for pairs of terms, but more generally, for setsof pairs of terms. We say that a substitution S is a unifier for[(s1,t1),...,(sn,tn)]if si S = ti S for all 1 <= i <= n. The unification algorithm consists of two mutually recursive procedures unifyand unify_one, which try to unify a list of pairs and a single pair,res...
Now we show how type inference in OCaml can be done with unification on typeexpressions. Keep the matrix example above in mind; we will be doingroughly the same thing, but with different typing rules. For simplicity, let's take a very small subset of OCaml consisting of This subset has a name: the λ-calculus (lambda calculus). Let's also introduce ...
Jun 30, 2023 · Unification is a concept that is linked to logic programming. Unification, as the name suggests, is a binding logic between two or more variables. The goal is to make two expressions look identical by using substitution. For simple logic, we use first-order unification, and to unify typed lambda terms, we use higher-order unification.
Jan 1, 1989 · Unification has become important in computer science because of its connections to mechanical theorem proving and so-called logic programming and in linguistics because of its connections to so-called unification grammar. Other examples include Scott domain equations, linear programming, type inference, and differential equations.
- Joseph A. Goguen, Joseph A. Goguen
- 1989
Research on unification arising in several areas of computer science is surveyed, these areas include theorem proving, logic programming, and natural language processing.
Research on unification arising in several areas of computer science is surveyed; these areas include theorem proving, logic programming, and natural language processing. Sections of the paper include examples that highlight particular uses of unification and the special problems encountered.
In logic and computer science, unification is an algorithmic process of solving equations between symbolic expressions. Depending on which expressions (also called terms) are allowed to occur in an equation set (also called unification problem), and which expressions are considered equal, several frameworks of unification are distinguished.
